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Figure S2: The derivative ௗெ ௗ் as a function of T for Laଵି௫Sr௫Mnଵି୬Fe୬O<sup>ଷ</sup> ( = 0.15, 0.15 and 0.7, = 0.1 and 0.15) at Ts = 1170°C and Ts = 1250°C.
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# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 9: Magnetization as a function of temperature for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO⁽ଷ⁾ and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 4: Phase fractions as a function of nominal strontium doping level in the Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ(0.025 ≤ ≤ 0.7) samples sintered at 1170˚C.
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 5: Crystallites size from the Debye-Sherrer equation as a function of Sr content in Laଵି୫Sr୫Mnଵି୷Fe୬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15).
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure S3: Example of isothermal magnetization curves for La।ହSr।ୱହMn।ଽଽFe।୵O<sup>ଷ</sup> sintered at Ts = 1170˚C from 5 to 350 K in intervals of 5K used to evaluate the isothermal entropy change.
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 2: Magnified view of the XRD peak with the highest intensity (2θ ≈ 32°) for Laଵି௫Sr௫Mnଵି୷Fe୬O⁽ଷ⁾ (0.025 ≤ x ≤ 0.7) prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b).
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) Laଵି୫Sr௫Mnଵି୷Fe୬O₍ଷ₎, (b) Laଵି୫Sr௫Mnଵି୷Fe୬O₍ଷ₎, (c) LaହSrହMnଽଽFe୬O₍ଷ₎, (d) LaହSrହMn଼ହFe୬O₍ଷ₎, (e) LaଷSr.MnଽଽFe୬O⁽ଷ⁾ and (f) LaଷSr.Mn଼ହFe୬O₍ଷ₎.
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) Laଵି୫Sr୫Mnଵି୷Fe୬Oଷ, (b) Laଵି୫Sr୫Mnଵି୷Fe୬Oଷ, (c) LaହSr୭ହMnଽଽFe୬Oଷ and (d) LaହSr୭ହMnଽଽFe୬Oଷ and for () Laଵି୫Sr୫Mnଵି୷Fe୬Oଷ, (f) Laଵି୫Sr୫MnଽଽFe୬Oଷ. (a) – (d): samples sintered at Ts = 1170˚C, (e) and (f): samples sintered at Ts = 1250˚C.
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 12: Specific heat as a function of temperature in zero magnetic field for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ .
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 7: SEM images for La.଼ହSr.ଵହMnଵି୷Fe୬O<sup>ଷ</sup> (y = 0.01 and 0.15) ceramics subjected to a sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively.
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe୬O⁽ଷ⁾ (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn₃O₄ , ♠ for SrCO₃ and ∇ for La₂O₃.
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.଼ହSr.ଶହMnଵି୷Fe୬O⁽ଷ⁾ compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହO⁽ଷ⁾ in Fig. 3(b) is fitted by considering a single rhombohedral phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵO⁽ଷ⁾ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the Mn₃O₄ ( 41/) impurity phase.
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
Figure S2: The derivative ∂M/∂T as a function of T for Laଵି୫Sr௫Mnଵି୬Fe୬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at Ts = 1170˚C and Ts = 1250˚C.
|
# Influence of chemical substitution and sintering temperature on the structural, magnetic and magnetocaloric properties of ିି
# ABSTRACT
The effects of sintering temperature (Ts) and chemical substitution on the structural and magnetic properties of manganite compounds Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) are explored in a search to optimize their magnetocaloric properties around room temperature. A ferromagnetic (FM) to paramagnetic (PM) phase transition is observed at a Curie temperature T<sup>c</sup> that can be controlled to approach room temperature by Sr and Fe substitution, but also by adjusting the sintering temperature Ts. Accordingly, the magnetic entropy change (−∆S) quantifying the magnetocaloric effect (MCE) presents a peak at or close to Tc that shifts and broadens with both Sr and Fe doping and is further tuned with sintering temperature. Altogether, we show that it is possible to adjust the strength and dominance of the ferromagnetic coupling in these ceramics, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change.
Keywords: Magnetocaloric effect, manganite perovskite oxides, chemical substitution.
# INTRODUCTION
The magnetocaloric effect (MCE) has been used for many years to reach very low temperatures [1-5]. Nearly a century ago, changes in nickel temperature when varying the external magnetic field were originally discovered by Pierre Weiss and Auguste Piccard in 1917 during their study of magnetization as a function of temperature and magnetic field near the magnetic phase transition [1, 6]. The observed temperature increase was then called by Weiss and Piccard "le phénomène magnétocalorique" (the magnetocaloric phenomenon) [1, 6]. In the late 1920s, Debye in 1926 [7] and Giauque in 1927 [8] independently proposed an additional thermodynamic explanation of the magnetocaloric effect and suggested a refrigeration process to reach low temperatures using adiabatic demagnetization of paramagnetic salts. The concept was experimentally implemented in 1933 by Giauque and MacDougall [9] allowing them to reach 0.25 K using Gdଶ(SOସ)଼ • HଶO salts from the temperatures of liquid helium.
The MCE is an intrinsic property of magnetic materials. It relies on a coupling between the spin system and the lattice as a mean to transfer magnetic entropy to or from the lattice, inducing warming or cooling while magnetizing or demagnetizing it. When a magnetic field is applied adiabatically to a ferromagnetic material, the magnetic entropy decreases due to ordering of the spins. This reduction in magnetic entropy is compensated by an increase in the lattice entropy to preserve total entropy [1-5]. As a result, the magnetic material warms up. Reversely, under an adiabatic decrease of the magnetic field, the moments tend to randomize again leading to an increase of magnetic entropy decreasing accordingly the material temperature.
In recent years, cooling applications based on magnetocaloric materials as refrigerants have attracted more attention because of its potential high energy efficiency in contrast to the fluid compression – expansion conventional systems [1-5]. Magnetic refrigeration near room temperature was implemented for the first time in 1976 by Brown who unveiled an innovative and energy-efficient magnetocaloric device working with gadolinium metal as a magnetic refrigerant [10]. It took advantage of a large variation of the magnetic entropy close to the magnetic transition temperature of Gd under an external applied magnetic field change. The MCE in terms of magnetic isothermal entropy change (∆S) can be evaluated from magnetic measurements using the Maxwell relation [1, 11]:
$$-\Delta \mathbf{S}\_{\mathbf{M}}(\mathbf{T}, \mathbf{0} \to \mathbf{H}) = \mu\_0 \int\_0^\mathbf{H} \left(\frac{\partial \mathbf{M}}{\partial \mathbf{T}}\right)\_\mathbf{H'} \mathbf{d} \mathbf{H'} \tag{1}$$
Using magnetic isotherms, magnetization as a function of applied magnetic field for successive temperatures, ∆S is found to be maximum for temperatures where ப ப is maximum. This occurs generally in the vicinity of the magnetic phase transition: broadening this transition (with disorder) while preserving a large value of ∆S is the target of the present work.
A giant MCE was observed in GdହSiଶGeଶ based compounds near room temperature by Pecharsky and Gschneidner [12]. Since then, a large variety of advanced magnetocaloric materials was proposed and explored for room temperature tasks [1, 11-19]. Since the 1990s, the perovskite manganese oxides also called manganites of general formula Rଵି௫A௫MnO<sup>ଷ</sup> (R= trivalent rare earth, A= divalent ion) have been a subject of intensive investigations due to their various functional properties such as colossal and giant magnetoresistance, giant piezoelectric properties, and MCE near room temperature [2024]. With growing A for R substitution, x, the same amount x of Mnଷା with the electronic configuration ൫3d, tଶ↑ <sup>ଷ</sup> e↑ ଵ , = 2൯ is replaced by Mnସା with the electronic configuration ቀ3d, tଶ↑ <sup>ଷ</sup> e↑ , = ଷ ଶ ቁ [25]. Large carrier mobility and ferromagnetism are promoted from a strong electron transfer between the filled and empty e states of nearby Mn3+ and Mn4+ ions mediated by oxygen 2p states via the double exchange (DE) mechanism [26]. Moreover, the perovskites structure usually show lattice distortions from the ideal cubic structure to orthorhombic and rhombohedral structures that are mainly caused by Jahn-Teller (JT) distortions and the mismatch of the Mn-O and R-O bond lengths [27]. These lattice distortions play a significant role in determining the physical properties of manganites and have been widely studied in this family (see for example Refs. [27, 28] and references therein). Chemical substitution of the rare earth (R) and metal (Mn) sites offers an obvious path to tune the magnetic, transport and magnetocaloric properties of these manganites in an effort to optimize their cooling capacity. For example, a large MCE from polycrystalline Laଵି௫A௫MnOଷ(A = Ca, Sr, Ba) for x = 0.2 and 0.25 was reported by Guo et al. [29, 30]. Maximum magnetic entropy changes of about 5.5 J/kg K at 230 K and 4.7 J/kg K at 260 K were obtained under an applied magnetic field change of 1.5 T, respectively.
The magnetic and magnetocaloric properties of nano-sized La.଼Ca.ଶMnଵି௫Fe௫O<sup>ଷ</sup> (x = 0, 0.01, 0.15 and 0.2) manganites prepared by sol-gel method was studied by Fatnassi et al. [31]. They reported that the ferromagnetic-paramagnetic transition occurring in these materials is sensitive to iron doping. In addition, a large MCE near Tc is observed. −∆S under a magnetic field change of 5 T reaches 4.42, 4.32 and 0.54 J/kg K , for x = 0, 0.01 and 0.15, respectively. In a similar context, Barik et al. [32] investigated the effect of
Fe substitution on the magnetocaloric effect in La.Sr.ଷMnଵି௫Fe௫O<sup>ଷ</sup> (0.05 ≤ ≤ 0.2). It was shown that the Fe substitution gradually decreases both the Curie temperature and the saturation magnetization. They also showed that a La.Sr.ଷMn.ଽଷFe.Oଷ sample exhibits a large magnetic entropy change ∆ெ that reaches 4 J/kg K under ∆H = 5 T. This sample exhibits a refrigerant capacity of 225 J/kg and an operating temperature range over 60 K wide around room temperature. In fact, Leung et al. [33] were among the first to study the effect of iron substitution in manganites in the mid-70's. They studied the magnetic properties of Laଵି௫Pb௫Mnଵି୷Fe୷Oଷ compounds, where a ferromagnetic Mnଷା − O − Mnସା double-exchange (DE) interaction competes with antiferromagnetic Feଷା − O − Mnଷା and Feଷା − O − Feଷା interactions. More recently, Ait Bouzid et al. [34], investigated the magnetocaloric effect in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ compounds. It was shown that the addition of 10% of iron in Laଵି௫Na௫Mnଵି୷Fe୷Oଷ decreases the Curie temperature and the magnetic entropy change, while the relative cooling efficiency increases. Altogether, these selected studies demonstrate that Fe for Mn substitution can be used to finely control the Curie temperature and the magnitude of the entropy change.
For the present study, we synthesize co-doped manganites Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics with extended doping levels up to x = 0.7 and study the influence of strontium and iron substitution at the La and the Mn sites simultaneously. We correlate the impacts of these parallel substitutions on the crystal structure, the magnetic properties and the magnetocaloric effect. As we aim to optimize their magnetocaloric properties for eventual applications in proximity to room temperature, the impact of their growth conditions with a focus on the sintering temperature is also explored for each composition.
# EXPERIMENTAL
Polycrystalline samples of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) were prepared by the conventional solid-state reaction. High-purity oxides or carbonates LaଶOଷ, FeଶOଷ, MnOଶ and SrCOଷ were used as starting materials. Prior to weighing in the appropriate proportions, LaଶOଷ was preheated overnight at 900˚C. These starting materials were then weighted and thoroughly mixed in an agate mortar until homogeneous powders were obtained. All the powders were heated to 1070˚C and then to 1120˚C in air for 24h with intermediate grinding steps. The powders were pressed into pellets and subjected to heating cycles at 1170˚C, 1220˚C and 1250˚C. The ceramic samples heated in air were slowly cooled to room temperature at the rate of 5°C/min. Structural properties were analyzed from powder X-ray diffraction (XRD) measurements on both the powders and the pellets at every heating steps using a Bruker-AXS D8- Discover diffractometer in the θ − 2θ configuration with a CuKα1 source ( = 1.5406Å) over the 2θ range of 10˚ to 80˚. The structural parameters were obtained by fitting the experimental XRD data using the Rietveld structural refinement FULLPROF software applying the Thompson-Cox-Hastings pseudo-Voigt function with axial divergence asymmetry peak shape function and a linear interpolation for background description. The refinements were performed until reaching the convergence as shown by the goodness of fit ( 2 ). The surface morphology of the samples was checked by scanning electron microscopy (SEM).
The DC magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer from Quantum Design. The temperature dependence of the magnetization was measured from 5 to 380 K with a
magnetic field of 0.2 T. The MCE evaluated using the magnetic entropy change was estimated from magnetic isotherms measured as a function of temperature (50-380 K) in 0 to 7 T magnetic fields. The specific heat measurements of x = 0.15, y = 0.01 and x = 0.35, y = 0.01 samples were carried out from 3 to 375 K at 0 and 7 T and were performed using a Physical Properties Measurement System (PPMS) from Quantum Design.
## RESULTS AND DISCUSSION
## Structural properties
X-ray diffraction (XRD) patterns at room temperature of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> ceramics pelletized at 1170˚C are presented in Figure 1 for various values of , for y = 0.01 in (a) and for y = 0.15 in (b). It reveals the presence of the manganite phases together with impurity phases that are virtually absent in the samples with a large Fe doping (y = 0.15) except for x = 0.7. The spectra reveal the presence of the rhombohedral crystal structure with 3ത space group for all the samples which is in accordance with the JCPDS card (no. 53-0058) [35]. However, as shown in the XRD pattern of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ ( < 0.35) with a small amount of iron in Fig. 1(a), a splitting of the diffraction peaks at angles at ~ 40 , ~ 52 , ~ 58 and ~ 68 is an indication that the structure is not purely rhombohedral and includes the orthorhombic () phase [36-38]. Moreover, when ≥ 0.5 , a mixture of the rhombohedral and tetragonal (4/) phases can be observed. These observations confirm the trend to phase segregation in manganites for large Sr doping [39-41]. It is interesting to observe that all the XRD patterns of Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ ( < 0.7) with a large iron content show a single rhombohedral phase with no trace of other symmetry (no doublets) and no impurity phase, suggesting that iron may favor a better Sr homogeneity.
At low Sr and Fe doping, additional peaks with small intensities can be attributed to impurity phases, in particular to MnଷOସ . This impurity phase is known to be widely present in manganites compounds with cation vacancies [42]. MnଷOସ crystallizes in the tetragonal ( 41/) phase [42,43] and is expected to contribute as the dominant impurity phase to the magnetic properties at low temperatures as its paramagnetic to ferrimagnetic transition occurs in the range of 40 to 50 K [43,44].
A magnified view of the peak with the highest intensity (2 ≈ 32°) of the same samples is shown in Figure 2 (a) and (b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ, respectively. The diffraction peak first shifts down in angle when increases from 0.025 to 0.15 before shifting to higher angle when the Sr concentration is further increased ( > 0.15) for both iron contents. This indicates that the lattice parameters increase first with x, but then decrease for > 0.15. Substituting La3+ (ୟయశ = 1.36 Å) with a larger Sr2+ ion (ୗ୰మశ = 1.44 Å) [45] should increase the lattice parameters overall and lead to a decrease of peak angle [46, 47]. However, the density of Mn4+ is also increasing with x. Since the ionic radius of Mn4+ (୬రశ = 0.53 Å) is smaller than that of Mn3+ (୬యశ = 0.645 Å) [45], the reverse trend of the lattice parameters is also expected as observed previously [48]. In order to fully capture and understand the structural evolution observed in Fig. 2, we turn to a full analysis of our diffraction spectra using Rietveld refinement.
Figure 3 shows an example of Rietveld refinement fits performed for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> . The fits for the other samples are presented in Figure S1 of the supplementary materials. The spectrum for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ in Fig. 3(b) is fitted by considering a single rhombohedral
phase (3ത). However, for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ in Fig. 3(a), the best fit to the spectra is achieved when a mixture of the rhombohedral (3ത) and the orthorhombic () phases is assumed together with the MnଷO<sup>ସ</sup> ( 41/) impurity phase. This approach is used to determine the fraction of each phase in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. A similar procedure is used to analyze all the spectra presented in the supplementary materials which allows us to estimate the fraction of the phases as a function of doping.
Figure 4 presents the phase fractions as a function of the nominal Sr doping level for low iron content (y = 0.01) estimated from the Rietveld refinements. We clearly observe a dominant rhombohedral phase for all the samples with a tendency for an increase in the fraction of the high symmetry phases with increasing Sr2+ doping level. The reduction in the density of Jahn-Teller Mn3+ ions with increasing Sr doping is at the origin of this gradual evolution towards higher symmetry and the disappearance of the orthorhombic phase. Furthermore, the single rhombohedral symmetry observed for the samples with high Fe content (y = 0.15) is another signature of the decreasing influence of lattice distortions when Jahn-Teller Mn3+ is substituted by non-Jahn-Teller Fe3+. This effect dominates even for the lowest Sr doping (x = 0.025) where even a small amount of Fe3+ (y = 0.15) is enough to overcome the impact of the Jahn-Teller distortions driven by the Mn3+ cations.
The results of the calculated lattice parameters and unit cell volume () of the dominant rhombohedral phase by Rietveld refinement for these Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7, = 0.01, 0.15) compounds are presented in Table 1 revealing their trends as a function of the Sr and Fe substitution levels. With the definition of B, B' as Mn or Fe, and A as La or Sr with the general formula ABO3, Table 1 includes also the average La(Sr) − O distance (dA-O), the average Mn(Fe) − O bond
length (dB-O), the average Mn(Fe) − O − Mn(Fe) bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs) calculated using dA-O and dB-O. Additional information extracted from the Rietveld refinement is also presented in Table S1 of the supplementary materials. According to Table 1, the highest unit cell volume () is observed for the compositions with x = 0.15. This is in accordance with the shift of the diffraction peaks to lower angles in this composition as it was observed in Fig.2. However, the unit cell volume decreases progressively with further increasing Sr2+ concentration ( > 0.15), driven by a decrease in the average B-O bond length while the B-O-B' bond angle is slowly increasing.
In manganites, lattice distortions and the changes in structural parameters are driven by two factors: 1) the mismatch of the La (Sr)-O and Mn-O bond lengths; and 2) the presence of Jahn-Teller distortions. The impact of the sub-lattices mismatch can be better quantified using the Goldschmidt tolerance factor defined as = ಲାೀ √ଶ(ಳାೀ) [49], where is the average ionic radius of A-site Laଷା and Srଶା, is the average ionic radius of Bsite Mnଷା, Mnସା and Feଷା, and ை is the ionic radius of O ଶି. When increases while decreases with x as seen in our case, we expect an increase in . This tolerance factor has been well-documented for the manganites and is usually limited to the 0.75 ≤ ≤ 1 range [50, 51]. An orthorhombic structure is favored for < 0.96, while a rhombohedral structure is realized for 0.96 < < 1 [51]. The observed tolerance factor determined from our Rietveld refinements can be computed using ,௦ = ௗಲషೀ √ଶ ௗಳషೀ [50], where ିை and ିை are determined using the refinement results. As can be seen from Table 1, the computed Goldschmidt parameter factor is close to unity and increases slightly with increasing Sr content ( ≤ 0.35). Indeed, contrary to Mn3+, Mn4+ does not induce Jahn–
Teller distortions and, due to its lower size and higher charge than Mn3+ , Mnସା − Oଶି distances are shorter than the average Mnଷା − Oଶି ones. As a result, the contraction of the less distorted octahedral skeletons is leading to higher ,௦ values and explains the trend observed in Fig. 2 for large values of x.
Our observation that the rhombohedral structure is preserved over the entire composition range is different from that observed most often for bulk Laଵି௫Sr௫MnOଷ. Manganite perovskites are usually reported to crystallize in an orthorhombic symmetry for x lower than 0.17 [52]. However, according to Mitchell et al., higher symmetries (rhombohedral) can be favoured for the lowest x values in Laଵି௫Sr௫MnOଷ ceramics if prepared in very oxidizing conditions [53]. The influence of high Mn4+ content on symmetry was also reported for bulk Laଵି௫Sr௫MnOଷାஔ elaborated via a soft chemistry route followed by a calcination in air at 1350˚C during 6h [54]. In addition, it was observed that when prepared in air at high temperatures, LaMnOଷ forms the metal-vacant phase with ଵିఌଵିఌ<sup>ଷ</sup> ( = ఋ (ଷାఋ) ) of rhombohedral symmetry, usually described as LaMnOଷାஔ [53,55,56]. These metal vacancies result in the oxidation of Mnଷାinto Mnସା in the presence of oxygen at moderate to high temperatures [53]. Thus, the persistence of the rhombohedral symmetry at our lowest x values is likely a signature of metal-vacant samples leading to higher Mn4+ content than expected from the nominal composition.
Finally, we observe in Table 1 very little changes in the unit cell lattice parameters and volume with increasing iron concentration for a fixed value of Sr content (x). This is consistent with the fact that Feଷା and Mnଷା carry virtually identical ionic radii. Analogous weak tendencies that we have noted in our refinements have also been reported previously [50, 57-59]. A similar trend was also observed in previous works in La-Ca manganites [6066]. To explain the slight increase in volume with the Fe content, the authors of Refs. [62,66,67] suggested the presence of a certain amount of Feସା ions with an ionic radius (r<sup>i</sup> = 0.58 Å) larger than the Mnସା ones (ri = 0.53 Å) [45]. Our data cannot rule out this scenario although a XPS study could provide a definitive answer to the presence of these Fe4+ ions.
where K = 0.9 is a constant, λ is the X-ray wavelength, θ is the angular position of a selected diffraction peak and β is its experimental full width at half-maximum (FWHM). In our case, the grain size is evaluated using the average of values computed from several diffraction peaks in the same spectra. The evolution of grain size, DD,Sh, as a function of Sr doping is shown in Figure 5. The substitution of a larger Sr2+ cation for Laଷା for fixed growth conditions leads to an increase of the crystallite size when x increases from 0.025 to 0.15. However, DD,Sh decreases for Sr-rich compositions ( > 0.15). This trend matches that of the lattice parameters presented in Fig. 2 and in Table 1 from the Rietveld refinement fits (Table 1). A high Sr content, beyond x = 0.15, suppresses grain growth [46]. Such a correlation between lattice parameters, unit cell volume and nanoparticle size has already been observed [68]. It was suggested that compressive lattice strain occurs in manganite nanoparticles (due to crystallite surface tension) and becomes more important with decreasing crystallites size, because of the growing influence of their surface. We expect this grain (domain) size trend to influence the magnetic properties of our samples.
To improve the crystalline quality of our materials and to see the influence on their magnetic properties, all the samples initially pelletized at 1170˚C were further annealed at various high temperatures, heated in successive steps up to 1250˚C in air. To identify the most appropriate growth temperature for each composition, XRD patterns were recorded at every sintering step and their magnetic properties were also measured. XRD patterns for a succession of sintering temperatures Ts for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ are shown in Figure 6 (a) and (b), respectively. The patterns show a decrease in the amount of the secondary phases when increasing Ts. However, some extra peaks corresponding to MnଷOସ secondary phase remain in the structure even at high sintering temperature of 1250˚C in La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. As shown in Table 1 (see boldface values for x = 0.15, y =0.01 and 0.15), the unit cell volume slightly increases when increasing the sintering temperature Ts. It is accompanied by a slight increase in the Mn-O bond length and a decrease in the Mn-O-Mn bond angle. This is likely the consequence of a growing density of oxygen deficiencies with sintering temperature in agreement with previous reports [69,70]. Nevertheless, the lattice parameters are evolving slowly with varying sintering conditions. Since the sintering temperature has a significant impact on the magnetic properties on many of these samples while the structural changes are minimal, other avenues like the presence of oxygen off-stoichiometry [53] or the influence of grain size and morphology must be considered to explain these changes. In what follows, we focus on grain morphology.
## Scanning electron microscopy SEM
sintering at 1070˚C [Figs. 6 (a) and (b)], 1170˚C [Figs. 6 (c) and (d)] and 1250 ˚C [Figs. 6 (e) and (f)], respectively. The images show a close-packed microstructure with grains that are clustering to form large boulders of a few microns in size. The grains have apparent sizes of approximately 500 nm for the lowest sintering temperature (1070 ˚C) but are growing beyond 1 micron in size when increasing Ts. Table 2 presents the average crystallite size values estimated from the SEM images (Dୗ) in Fig. 7 and that calculated from the diffraction spectra using the Debye-Sherrer formula (see Eq. 2 above). Obviously, the apparent particle sizes Dୗ estimated from SEM are several times larger than those calculated by XRD. This indicates that each grain observed by SEM contains several smaller crystallized grains (domains) as DD,Sh can be envisioned as the typical domain size for coherent x-ray diffraction. These values found for DD,Sh agree with those observed in Ref. [71]. Although XRD and Rietveld refinement show gradual structural changes with doping and sintering temperature, we will need to consider in what follows that SEM images reveal an evolution in the microstructure that may also affect the magnetic properties of these ceramics.
# Magnetic properties
The magnetic properties of manganites and their physical origin have been extensively studied over the last three decades [54,72-74]. Jonker and van Santen [75] and Wold and Arrott [76] independently showed that the synthesis temperature and partial oxygen pressure P(O2) can be used to control the Mn3+/Mn4+ ratio of undoped parent compound LaMnOଷ: reducing atmosphere and/or high synthesis temperatures around 1350˚C produce samples with smaller concentrations of Mn4+, while lower temperatures ~1100˚C and/or oxidizing atmospheres result in significant concentration of Mn4+
affecting the magnetic properties. Of course, this Mn3+/Mn4+ ratio is also influenced by the Sr substitution for La allowing this family to exhibit for example ferromagnetism due to double exchange and related colossal magnetoresistance. Fe substitution for Mn disrupts this Mn3+/Mn4+ ratio by adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds affecting the magnetic properties of these materials. In the following, we first explore the impact of these substitutions. We follow with a quick survey of the influence of the sintering temperature on the magnetic properties.
# Effect of Sr and Fe substitutions
Figure 8 shows the field-cooled magnetization as a function of temperature in an applied magnetic field of 0.2 T for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ in (a) and for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ in (c), all sintered at Ts = 1170˚C. As shown in Fig. 8 and summarized in Table 3, the magnetization at the lowest temperature (T = 5 K) first increases with Sr substitution in the range 0.025 ≤ < 0.35, then gradually decreases for ≥ 0.35. The lattice undergoes less Jahn-Teller distortions with increasing x due to the reduction of the density of Mnଷା ions, contributing to the gradual increase of the bond angle toward 180˚ and the increase of the tolerance factor as shown in Table 1. The evolution of the average Mn(Fe) − O bond length and Mn(Fe) − O − Mn bond angle upon the growing content of Srଶା contributes to a strengthening of the magnetic interactions while the density of ferromagnetic Mnସା − O − Mnଷା bonds is also increasing in favor of Mnଷା − O − Mnଷା ones leading to ferromagnetic coupling via the double-exchange mechanism and long-range ferromagnetic order. For higher Sr contents ( > 0.35), the magnetization decreases. This behavior is even more pronounced for the compositions with
The derivative ௗெ ௗ் as a function of T can be used to define the ferromagnetic-toparamagnetic transition temperature Tc in our samples as the inflexion point of the M (T) data as shown in Fig. 8(b) for Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ and in Fig. 8(d) for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ. The values of Tc as a function of Sr content x are presented in Table 3. As can be seen from Table 3, Tc continuously increases with Sr content for 0.025 ≤ ≤ 0.35; y = 0.01, 0.15. For samples with higher Sr contents ( > 0.35), the presence of an inflexion point is less obvious from Figs. 8 (a) and (c) although the derivative curves clearly show minima. We can also note anomalies at low temperature in the derivative from the inset of Fig. 8 (b): the derivative curve for La.ହSr.ହMn.ଽଽFe.ଵOଷ exhibits a minimum at T<sup>c</sup> ≈ 370 K but also a shoulder at around 250 K, while no minimum is observed within the temperature range of our measurements for La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> . We also note a similar shoulder at ~ 250 K for this latter sample indicating probably phase segregation as signaled from the analysis of the XRD patterns. In general, iron substitution for manganese leads to a strong suppression of Tc but also a broadening of the transition. This is most evident for samples with x = 0.35 and different Fe contents as the derivative plot gives a large peak for y = 0.15 with FWHM ~ 150 K compared to ~ 50 K for y = 0.01.
Our results for our samples with low level of iron content match well with those presented for example by Epherre and co-workers [77]. These authors showed that, for x smaller than 0.25, the structural parameters and the saturation magnetization evolve slowly
with x while Tc is continuously increasing. This low x behavior is attributed to the presence of cationic vacancies in the perovskite structure resulting in a constant Mn4+ density. From x = 0.25 to 0.50, the density of vacancies at the B-site becomes small as the Mn4+ density increases with x from ≈35% up to ≈50% tracking closely its expected x dependence [77]. Beyond x = 0.35, this leads to a decrease in magnetization and Tc as the increasing density of Mn4+ induces a growing competition between ferromagnetic (double exchange Mnଷା − O − Mnସା) and antiferromagnetic (superexchange Mnସା − O − Mnସା) interactions. This was also shown by Hemberger et al. who observed a decreasing magnetization when the amount of Mnସା exceeded 40 % [78]. Fe substitution for Mn is adding Fe3+-O-Mn3+ and Fe3+-O-Mn4+ bonds competing with pure manganese-based bonds and thus affecting the magnetic properties of these materials. Fe doping disrupts the possibility to establish longrange magnetic order in the material, affecting in the end the magnitude of Tc and leading to broad transitions.
# Effect of sintering temperature
To tune further the magnetic and the magnetocaloric properties of our samples, we explore the impact of sintering temperature on magnetization and Curie temperature for each composition. Figure 9 shows the temperature dependence of the magnetization for Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (x = 0.15, 0.5 and 0.7, y = 0.01 and 0.15) at a constant magnetic field of 0.2 T with the sintering temperature Ts varying from 1070˚C to 1250˚C. In general, higher sintering temperature results in narrower transitions while reducing anomalies arising from secondary phases. In fact, all samples sintered at 1070˚C show an anomaly around 50 K which is constantly observed for samples prepared at low temperature, independent of x and y, and is consistent with the presence of Mn3O4 that exhibits a
magnetic phase transition around 50 K [43,44]. This feature is weakening with increasing Ts. A comparison between Curie temperatures of Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ( = 0.15, 0.5 and 0.7, = 0.01 and 0.15), sintered at 1170˚C and 1250˚C, extracted from the temperature dependence of ௗெ ௗ் curves at 0.2 T (Figure S2) and enlisted in Table 3, shows that contrary to Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ( = 0.5, 0.7), where Tc is reduced to lower temperatures when the samples were heated at 1250˚C, no significant change in the minimum of the ௗெ ௗ் curves is noticed for Laଵି௫Sr௫Mn.଼ହFe.ଵହOଷ( = 0.5, 0.7) compounds. In addition, as can be seen from Fig. S2, Tc is clearly reduced to lower temperatures with increasing Ts for La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , while it increases with T<sup>s</sup> for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ. Moreover, the M(T) and ௗெ ௗ் curves for La.ଷSr.Mn.ଽଽFe.ଵOଷ sintered at 1250˚C [Fig. 9(e)] clearly show two distinctive magnetic transitions at 102 K and around ~ 370 K. This low temperature transition may be related to the extra tetragonal (I4/mcm) phase observed by XRD for large Sr doping (see Fig. 2).
To better characterize the low temperature magnetization behavior of these ceramics, M (H) curves are performed at 5 K for some selected Ts and are compared in Figure 10. The saturation magnetization values taken at 7 T (M7T) for some selected samples and sintered at different temperatures are summarized in Table 3. The saturation magnetization of Laଵି௫Sr௫Mn.ଽଽFe.ଵOଷ with low Fe content is growing with Ts, reaching its maximum value with the maximum Ts explored. This is fully consistent with previous reports showing that the magnetic, resistive and magnetoresistive properties of ceramics or polycrystalline manganites prepared by the solid-state reaction technique
depend on the preparation conditions, especially on sintering and annealing temperature [79]. However, this trend is not exactly followed for samples with high Fe content as shown in Fig. 10 where the high-field magnetization is reaching a maximum at intermediate Ts ~ 1170˚C, matching the observations made in Fig. 9 with the temperature dependence of the magnetization. Since we do not observe a major difference in the behavior of grain size with Ts for low and high Fe contents as shown in Table 2, the decrease of Tc and the magnetization beyond Ts = 1170˚C is likely affected by local compositional variations. For example, this may come from a growing density of oxygen vacancies that may have more impact when the materials are already heavily disordered by the large level of Fe content. In fact, as can also be seen from Fig. 10 (b), the decrease in the saturation magnetization of samples with large Fe content after a sintering at 1250˚C is more pronounced for low x (x = 0.15) than for large x (x = 0.5 and 0.7). Since Tc evolves quickly with hole doping at low x, its strong variation with Ts is consistent with an increasing density of oxygen vacancies that counters the Sr for La substitution.
Another feature of importance in Fig. 10 is that the addition of iron modifies the high field behavior of the magnetization as samples do not reach saturation even for our highest applied magnetic field and our highest explored Ts. This phenomenon was frequently observed in bulk manganites and was attributed to local disorder (clustering) [54, 80, 81]. This gradual increase without saturation at high fields, most noticeable with large iron content, indicates that the magnetic ground state dramatically changes from longrange to short-range ferromagnetic ordering as iron content is increased. Yusuf et al. [82] indicated the preservation of ferromagnetic domains up to 10% Fe doping in their Fe-doped La.Ca.ଷଷMnOଷ. In the same context, Barandiaràn et al. [83] studied
La.Pb.ଷMnଵି୶Fe୶Oଷ 0 ≤ ≤ 0.3 and concluded that short-range ferromagnetic (FM) and antiferromagnetic (AFM) clusters of different sizes coexist in their = 0.2 sample. Similarly, Barik et al. [32] showed the coexistence of FM and AFM clusters in La.Sr.ଷMn.଼Fe.ଶOଷ with M(H) traces very similar to our data in Fig. 10 [especially Fig. 10 (f)]. Thus, Fe substitution for Mn is driving magnetic phase inhomogeneity which leads to broadened transitions, FM behavior with samples having a hard time reaching the expected saturation magnetization without sacrificing too much on the amplitude of the magnetization.
In summary, it is possible to control the magnetic properties of manganites through the usual Sr for La substitution that controls mostly the proportion of Mn3+ and Mn4+ ions and the dominance of the double exchange interaction in establishing the large magnetization and magnetic transition close to room temperature. Fe for Mn substitution disrupts the long-range order and drives magnetic phase inhomogeneity resulting in transition broadening and critical temperature shifts. The sintering temperature can magnify the effect of iron as it is likely leading to oxygen vacancies that adds more disorder to the system and can even affect hole doping. These three control parameters of these codoped manganites offer an interesting avenue to tune their magnetic properties and, as will be shown below, their magnetocaloric properties in proximity to room temperature.
## Magnetocaloric properties
The magnetocaloric effect (MCE) is an intrinsic property of magnetic materials. It is defined as the warming or the cooling of magnetic materials under the application or suppression of an external magnetic field, respectively. A goal of the present work is to explore how substitution (Sr for La, Fe for Mn) and the growth conditions (Ts) of a manganite-based material can be adjusted to optimize the magnitude of the isothermal magnetic entropy change (∆S) and the temperature range (Tspan) that would allow its potential usage in cooling systems near room temperature. These parameters characterizing the MCE can be evaluated from isothermal magnetization measurements by numerically integrating the Maxwell relation found in Eq. 1 above. ∆S can also be determined from specific heat measurements by using the second law of thermodynamics:
Another important parameter to determine the suitability of magnetocaloric materials for applications in cooling devices is the adiabatic temperature change ∆Tୟୢ. The latter can be determined from specific heat data and magnetization measurements. It is given by [1]:
\Delta \mathbf{T}\_{\rm ad} \{ \mathbf{T}, \mathbf{0} \to \mathbf{H} \} = -\mu\_0 \int\_0^\mathbf{H} \frac{\mathbf{T}}{\mathbf{c}\_\mathbf{p}} \left( \frac{\partial \mathbf{M}}{\partial \mathbf{T}} \right)\_\mathbf{H} \mathbf{d} \mathbf{H}^\prime \quad (4)
In the following, we explore the effect of Sr/La and Fe/Mn substitutions and of the sintering temperature on the magnetocaloric effect of selected samples. For this purpose, the magnetic entropy variation −∆S under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T is deduced using Eq. (1) from isothermal magnetization curves as those in Figure S3 of the Supplementary materials. The isothermal entropy change as a function of temperature for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ (x = 0.15 and 0.35, y = 0.01
and 0.15) sintered at 1170˚C is presented in Figure 11. We first notice that the magnitude of −∆S increases with the external magnetic field and that the maximum peak position remains nearly unaffected by the applied field for all the samples as is generally observed for other materials [1,32]. In addition, all the curves show a maximum of −∆S at a temperature approaching their respective Tc determined previously using the derivative of M (T) from Fig. 8.
Figs. 11 (a, c) and 11 (b, d) show that increasing the Sr content shifts the maximum peak position to higher temperatures as it tracks the evolution of Tc with doping. For a fixed Sr content [comparing (a) with (b) or (c) with (d)], the peak shifts to lower temperature with increasing Fe doping. Moreover, as the magnetic inhomogeneity increases with Fe content, the maximum value of −∆S decreases but the peak widens over a larger temperature range around Tc. This behavior is in accordance with those obtained by Barik et al. [32] and can be mainly attributed, as mentioned previously, to the suppression of the long-range ferromagnetic order as many of the Mn4+-O- Mn3+ DE bonds are replaced by a large number of antiferromagnetic SE bonds between Mn3+ and Fe3+ competing with ferromagnetic ones between Mn4+ and Fe3+ as was observed in La2MnFeO<sup>6</sup> and LaSrMnFeO6 [84]. Thus, it is possible to shift the maximum in −∆S() close to room temperature with a wise choice of Sr and Fe concentrations and control the width of the −∆S() peak (defined here as Tspan) over which it remains important. In some cases, Tspan extends way over 150 K [see Figs. 11 (a) and (d) for x = 0.15, y = 0.01 and x = 0.35, y = 0.15, respectively].
La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ ceramics sintered at 1250˚C under several magnetic field variations of 0 to 1 T, 0 to 3 T, 0 to 5 T and 0 to 7 T shows that the maximum peak position of −∆S for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ remains nearly field independent even after sintering [Fig. 11 (e)]. In addition, the magnitude of −∆S reaches 4.7 J/kg K for a magnetic field variation of 0 to 7 T compared to 3.0 J/kg K for the sample sintered at 1170˚C [see Fig. 11(a)]. This increase of −∆S with Ts is consistent with the increase of the saturation magnetization as a function of Ts observed in Fig. 10 (a). Comparing further the samples in Figs.11 (a) and (e) differing only by the sintering temperature, the −∆S peaks of the sample prepared at 1250˚C become narrower compared to that sintered at 1170˚C. This indicates that sintering temperature can also be used as a tool to control the amount of magnetic inhomogeneities in the samples as in the case of Fe doping.
Furthermore, the impact of sintering at higher temperature has the opposite effect for samples with large Fe substitution levels. This is shown for example with La.଼ହSr.ଵହMn.଼ହFe.ଵହO<sup>ଷ</sup> for which the temperature of maximum entropy change at 7T shifts from 175 down to 102 K for Ts varying from 1170 to 1250˚C. This reduction in the maximum −∆S temperature is also accompanied by a broadening of the temperature range. Again, this trend correlates well with the Tc shift observed in Fig. 9 (b) and the decrease in magnetization reported in Figs. 10 (b).
Altogether, the magnetocaloric effect is sensitive to the actual proportions of Sr for La and Fe for Mn substitutions that play into the doping to adjust the strength and dominance of ferromagnetic coupling, but also using disorder as a tool to broaden and adjust the temperature range with significant magnetic entropy change. Our data show that
an appropriate choice for both can be used to optimize the isothermal entropy change for a given (target) temperature range that requires controlling the temperature of the maximum −∆S but also the temperature range (Tspan) over which it is significant. Finally, the sintering temperature can also be used to tune the magnetocaloric properties.
Using specific heat data measured at 0 T (Figure 12) and the isothermal magnetic entropy changes [Figs. 11 (a) and (c)], the adiabatic temperature change as a function of temperature for La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ and La.ହSr.ଷହMn.ଽଽFe.ଵOଷ is calculated using Eq.(5) and is shown in Figures 13 (a) and (b), respectively. As expected for both samples, ∆Tୟୢ shows a maximum at Tc. It reaches 3 K for La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and 2.9 K for La.ହSr.ଷହMn.ଽଽFe.ଵOଷ for a magnetic field change of 7T. Additional Fe substitution suppresses ∆Tୟୢ roughly by a factor of 2 as a result of the decreasing magnitude of −∆S (see Fig. 11) and assuming the same magnitude for the specific heat. For both La.଼ହSr.ଵହMn.ଽଽFe.ଵO<sup>ଷ</sup> and La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> , adiabatic temperature changes remain moderate when compared to reference magnetocaloric materials [1]. This can be explained essentially by their low entropy changes compared to other materials but also by their large specific heat dominated by the phonon contribution.
To achieve MCE performances suitable to applications, close to room temperature, a large (−ΔS,୫ୟ୶) over a wide temperature span is strongly recommended [1,84]. To explore the magnetocaloric performance of our magnetic refrigerants, we have calculated the relative cooling power (RCP) as it allows one to compare the cooling performances of different materials. It considers the magnitude of −∆S, but also the temperature range Tspan for which it remains significant. It is defined as the product of the maximum value
Figure 14 (a) presents the RCP at 7 T as a function of Sr content for Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> ( ≤ 0.35 ) sintered at 1170ºC. For comparison, the maximum entropy change (−∆S,୫ୟ୶) as a function of Sr content is also presented. The relative cooling power (RCP) values at 7 T are found to vary between 460 and 390 J/kg, comparing well with other oxides [85-87]. Despite the increase of −∆S,୫ୟ୶ with increasing Sr content, the RCP decreases. In fact, as shown in Figure 14 (b), it is directly related to a decrease of the full width at half-maximum (δTୌ) as x increases. These results emphasize the fact that the best doping for the highest RCP is not that corresponding to the maximum Tc (x = 0.35), but rather a compromise at x ~ 0.2 that leads to a large enough entropy change at room temperature and a −∆S peak broadened by magnetic phase inhomogeneity. This highlights the importance of extending the working temperature range on the performance of magnetic refrigerants and justifies also using Fe for Mn substitution to tune further these performances.
Our results demonstrate that compounds with relatively high −∆ெ , but not necessarily the largest ones, and large RCP values due to a large temperature range of significant −∆ெ, can be synthesized. Their exact properties can be controlled mostly by Sr for La, Fe for Mn substitutions and by the growth conditions, leading to imperfect samples with broad transitions that could be nevertheless of interest for applications in room-temperature magnetocaloric devices. Altogether, we see that the ferromagnetic
properties of these co-doped manganites can be adjusted. We can use Sr and Fe substitution to control the actual Tc of the samples and the magnitude of the magnetization. These substitutions affect their magnetization field dependence and the broadness of the transition, controlled by the presence of magnetic phase segregation. The choice of sintering temperature is another lever one can use to finely tune the properties with the goal of maximizing the magnetocaloric effect in a given temperature window.
We should underline that the MCE of these ceramics remains moderate despite all our manipulations. As was shown previously, larger −∆ெ can be achieved in manganites by substituting Ca for Sr in La2/3(Ca1-xSrx)1/3MnO3 [88]. As the crystal symmetry changes to Pnma for Ca-rich compositions (for x < 0.15), −∆ெ is also magnified while the transition temperature is decreasing [88]. This Ca for La substitution path was explored previously by our group in Ref. [84] as we substituted Ca for La into La2MnFeO6 (LMFO). Contrary to Ca-substituted (La,Sr)MnO3, Ca-doped LMFO shows poor ferromagnetism (weak magnetization) and weak MCE despite observing the same transition in crystal symmetry. We concluded in Ref. [84] that a very small B-O-B' bond angle was at the origin of the weak magnetic interaction, together with cation disorder. The same decrease in bond angle is also observed in (La,Ca)MnO3, explaining the suppression of the optimal Tc. We note however that there may be some interest to look for the same gradual Fe substitution for Mn we have been exploring in this paper into La2/3(Ca1-xSrx)1/3MnO3 as a source of disordering that could broaden the transition while taking advantage of the increase in MCE.
# Conclusion
In summary, we have investigated the structural, magnetic and magnetocaloric properties of Laଵି௫Sr௫Mnଵି୷Fe୷O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7; y = 0.01, 0.15) perovskite manganite compounds. We show how one can tune the magnetic and the magnetocaloric properties of these manganite perovskite oxides by chemical substitution and/or growth conditions. We show also that Sr substitution for La favors mainly double-exchange interaction leading to higher magnetization and Tc values, while Fe substitution for Mn drives magnetic disorder. Sintering temperature is another tool to control the magnetic disorder.
All the ceramic samples crystallize in a rhombohedral structure (R3തc) in a large proportion with a decrease of the unit cell volume as Sr content increases. The temperature dependence of the magnetization shows a macroscopic ferromagnetic-like behavior for all compounds. The magnetic and magnetocaloric properties are strongly affected by the chemical substitution and the sintering temperature. Our data reveals that the maximum magnetic entropy change ൫−ΔS,୫ୟ୶൯ at Tc continuously increases with Sr content up to x ~ 0.35 and decreases for larger substitution levels. Fe for Mn substitution suppresses the magnitude of −ΔS,୫ୟ୶ , shifts down the transition temperature, but leads also to a broaden temperature range Tspan with large magnetic entropy change. This operating temperature range is thus affected by the Sr and Fe contents and the sintering temperature. In this way, a significant entropy change over a broad temperature range can be obtained around room temperature. Due to their relatively high magnetic entropy changes, large operating temperature range and high RCP values, the Sr doped manganite perovskite
samples with properties fine-tuned by Fe substitution for Mn could be of interest for applications in magnetocaloric devices at room temperature. With the appropriate control of their stoichiometry through chemical substitution and their exact growth conditions, one can tune their magnetocaloric in a targeted range of temperature for specific cooling applications.
# ACKNOWLEDGMENTS
The authors thank M. Castonguay, S. Pelletier, B. Rivard and M. Dion for technical support. M. Balli acknowledges funding by the International University of Rabat, Morocco. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN-2018-06656, the Canada First Research Excellence Fund (CFREF), the Fonds de Recherche du Québec - Nature et Technologies (FRQNT) and the Université de Sherbrooke.
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## Tables
Table 1: Crystal structure parameters extracted from the Rietveld refinements. It includes the lattice parameters (a and c) and unit cell volume (V), the average La (Sr)-O distance (dA-O), the average Mn (Fe)-O bond length (dB-O), the average Mn (Fe)-O-Mn bond angle (ƟB-O-B') and the observed tolerance factor (tf,obs). All the data are for samples grown at 1170<sup>o</sup>C, except for the boldface ones (x = 0.15, y = 0.01 and 0.15) that are additionally sintered at 1250<sup>o</sup>C.
Table 2: Comparison between average grain sizes extracted from XRD patterns and SEM images.
| | y = 0.01 | | | | | | y = 0.15 | | | | | |
|--------------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|-----------|--------------------------------------|------------------|
| Ts (°C) | 1170 | | 1250 | | | 1170 | | | 1250 | | | |
| Compounds | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) | Tc<br>(K) | M<br>at 5<br>K<br>(μB/f.u.)<br>0.2 T | M7T<br>(μB/f.u.) |
| La.ଽଽSr.ଶହMnଵି୷Fe௬Oଷ | 142 | 2.4 | 3.6 | - | - | - | 102 | 1.58 | - | - | - | - |
| La.଼ହSr.ଵହMnଵି୷Fe௬Oଷ | 255 | 3 | 3.55 | 261 | 2.83 | 3.88 | 161 | 2.08 | 2.7 | 91 | 0.44 | 0.9 |
| La.ହSr.ଷହMnଵି୷Fe௬Oଷ | 374.4 | 2.8 | 3.5 | - | - | - | 212.5 | 2.0 | 2.8 | - | - | - |
| La.ହSr.ହMnଵି୷Fe௬Oଷ | 371 | 2.03 | 2.60 | 351 | 2.08 | 2.70 | 252 | 1.53 | 2.16 | 252 | 1.43 | 2.0 |
| La.ଷSr.Mnଵି୷Fe௬Oଷ | - | 1.34 | 1.85 | 371 | 1.38 | 2.05 | 251 | 0.48 | 0.9 | 251 | 0.4 | 0.8 |
Table 3: Transition temperatures, low temperature magnetization (5K), saturation magnetization taken at 7T for Laଵି௫Sr௫Mnଵି୷Fe௬Oଷ samples sintered at 1170 ºC and at 1250 ºC.
## FIGURE CAPTIONS
Figure 1: Powder XRD patterns of Laଵି௫Sr௫Mnଵି୷Fe௬O<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). Secondary phases are identified as follows: ♦ for Mn3O4 , ♠ for SrCO3 and ∇ for La2O3.
Figure 3: Powder XRD patterns and Rietveld refinement fits of La.ଽହSr.ଶହMnଵି୷Fe௬O<sup>ଷ</sup> compounds prepared at Ts = 1170˚C for y = 0.01 in (a) and y = 0.15 in (b). The refinement fits include the possible presence of various manganite symmetries and of Mn3O4.
Figure 8: Magnetization as a function of temperature for (a) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (c) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples sintered at Ts = 1170˚C under an applied magnetic field of 0.2 T. The derivative ௗெ ௗ் as a function of T for (b) Laଵି௫Sr௫Mn.ଽଽFe.ଵO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) and (d) Laଵି௫Sr௫Mn.଼ହFe.ଵହO<sup>ଷ</sup> (0.025 ≤ ≤ 0.7) samples. Inset in (b) is for x = 0.5 and 0.7 while inset in (d) is for x = 0.7.
Figure 9: Magnetization as a function of temperature for various sintering temperature T<sup>s</sup> for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 10: Magnetization as a function of magnetic field at 5 K for various sintering temperature Ts for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ , (c) La.ହSr.ହMn.ଽଽFe.ଵOଷ, (d) La.ହSr.ହMn.଼ହFe.ଵହOଷ, (e) La.ଷSr.Mn.ଽଽFe.ଵO<sup>ଷ</sup> and (f) La.ଷSr.Mn.଼ହFe.ଵହOଷ.
Figure 11: Temperature dependence of the magnetic entropy change under different magnetic field variations for (a) La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (b) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ, (c) La.ହSr.ଷହMn.ଽଽFe.ଵO<sup>ଷ</sup> and (d) La.ହSr.ଷହMn.଼ହFe.ଵହOଷ and for () La.଼ହSr.ଵହMn.ଽଽFe.ଵOଷ, (f) La.଼ହSr.ଵହMn.଼ହFe.ଵହOଷ . (a) – (d): samples sintered at 1170˚C , (e) and (f) : samples sintered at 1250˚C.
Figure 14: Relative cooling power (RCP) and maximum magnetic entropy change as a function of the strontium content in (a) Tc and full width at half maximum as a function of the Sr content in (b).
](path)
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| Fe content (y) | y = 0.01 | | | | | y = 0.15 | | | | | | |
|--------------------------------------|----------------------------------|----------------------------------|--------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|----------------------------------|------------------------------|--|--|
| Sr content (x) | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | 0.025 | 0.15 | 0.35 | 0.5 | 0.7 | | |
| Space group | R-3c | | | | | | R-3c | | | | | |
| 2<br>Biso (Å)<br>La/Sr<br>Mn/Fe<br>O | 1.107<br>0.183<br>0.857 | 1.037<br>0.862<br>0.712 | 1.744<br>0.081<br>1.464 | 0.052<br>1.544<br>0.5 | 0.439<br>0.473<br>0.8 | 0.206<br>0.043<br>1.026 | 0.694<br>0.396<br>0.691 | 0.295<br>0.386<br>0.400 | 0.406<br>0.319<br>0.412 | 0.331<br>0.565<br>0.854 | | |
| Occupancy<br>La<br>Sr<br>Mn/Fe<br>O | 0.975<br>0.025<br>0.978<br>1.088 | 0.847<br>0.153<br>1.006<br>1.071 | 0.65<br>0.35<br>0.986<br>1.031 | 0.524<br>0.476<br>0.940<br>1.015 | 0.271<br>0.729<br>1.048<br>1.032 | 0.975<br>0.025<br>1.004<br>1.102 | 0.849<br>0.151<br>1.005<br>1.008 | 0.643<br>0.357<br>1.003<br>1.080 | 0.493<br>0.507<br>1.018<br>1.006 | 0.3<br>0.7<br>1.001<br>0.998 | | |
| Atoms | | Coordinates of oxygen ions | | | | | | | | | | |
| X (oxygen<br>position) | 0.550 | 0.548 | 0.523 | 0.558 | 0.556 | 0.545 | 0.550 | 0.536 | 0.533 | 0.546 | | |
| | | | | | Discrepancy factors | | | | | | | |
| 2<br>χ | 1.81 | 1.65 | 1.40 | 1.99 | 2.4 | 1.94 | 2.53 | 1.56 | 1.53 | 1.71 | | |
| 𝑹𝒑 | 3.83 | 3.62 | 3.74 | 4.15 | 4.57 | 4.72 | 4.26 | 3.70 | 3.46 | 3.52 | | |
| 𝑹𝒘𝒑 | 5.05 | 5.03 | 4.84 | 5.43 | 6.04 | 6.04 | 5.93 | 4.78 | 4.51 | 4.57 | | |
| 𝑹𝒆𝒙𝒑 | 3.75 | 3.91 | 4.09 | 3.85 | 3.90 | 4.34 | 3.73 | 3.82 | 3.64 | 3.49 | | |
Table S1: Additional parameters extracted from the Rietveld refinements (not presented in Table 1). It includes the isotropic thermal parameters (Biso), the relative oxygen position (X) and the discrepancy factors. All the data are for samples grown at 1170<sup>o</sup>C.
| |
FIG. 5. Side view of the considered magnetic cells: (a) antiferromagnetic with {001} planes with the same Mn spins shown in the a × a × a cell (AFM001), (b) antiferromagnetic with double {001} planes of the same spins on Mn ions in the a × a × 2a cell (AFM002), (c) antiferromagnetic with ferromagnetic {111} planes realized in the a √2 × a √2 × a √2 cell (AFM111), and (d) ferromagnetic in primitive rhombohedral cell a/<sup>√</sup>2×a/<sup>√</sup>2×a/<sup>√</sup>2 (FM). Mn atoms with different spin directions are indicated as Mn↑ and Mn↓.
|
# Coexistence of Antiferromagnetic Cubic and Ferromagnetic Tetragonal Polymorphs in Epitaxial CuMnSb
High-resolution transmission electron microscopy and superconducting quantum interference device magnetometry shows that epitaxial CuMnSb films exhibit a coexistence of two magnetic phases, coherently intertwined in nanometric scales. The dominant α phase is half-Heusler cubic antiferromagnet with the N´eel temperature of 62 K, the equilibrium structure of bulk CuMnSb. The secondary phase is its ferromagnetic tetragonal β polymorph with the Curie temperature of about 100 K. First principles calculations provide a consistent interpretation of experiment, since (i) total energy of β–CuMnSb is higher than that of α–CuMnSb only by 0.12 eV per formula unit, which allows for epitaxial stabilization of this phase, (ii) the metallic character of β–CuMnSb favors the Ruderman-Kittel-Kasuya-Yoshida ferromagnetic coupling, and (iii) the calculated effective Curie-Weiss magnetic moment of Mn ions in both phases is about 5.5 µB, favorably close to the measured value. Calculated properties of all point native defects indicate that the most likely to occur are MnCu antisites. They affect magnetic properties of epilayers, but they cannot induce the ferromagnetic order in CuMnSb. Combined, the findings highlight a practical route towards fabrication of functional materials in which coexisting polymorphs provide complementing functionalities in one host.
#### I. INTRODUCTION
One of the most challenging and long-standing problems in fundamental magnetism is a competition between ferromagnetic and antiferromagnetic phases. Their interplay at the interface results in a well known effect of the exchange bias,[1](#page-11-1)[,2](#page-11-2) which fuels now a rapid development of spintronics[3](#page-11-3) and unconventional computing.[4](#page-11-4) The material class of Heusler alloys was previously used to study the origin of the transition between magnetic phases because it offers a wide spectrum of functionalities.[5](#page-11-5) Indeed, Heusler alloys exhibit ferromagnetic (FM), antiferromagnetic (AFM), and canted ferromagnetic order. This indicates that different types of magnetic coupling are competing in this family. Moreover, some of its members display structural polymorphism, which allows studying relationships between the crystalline phase, the magnetic phase, and the corresponding electronic structure.
Heusler alloys incorporate full-Heusler (X2YZ) and half-Heusler (XYZ) variants, where X and Y stand for transition metals, whereas Z denotes anions from the main group. In this class, qualitative changes in material characteristics can be achieved by chemical substitution on either the transition metal cation or on the anion sublattice. Typically, the change of the cation does not change the crystal structure, but it can induce a crossover between the AFM and the FM magnetic phases. A rarely met complete solubility with only marginally affected crystallinity of the otherwise chemically homogenous systems allowed to study the FM-AFM phase competition in detail. The prominent examples are quaternary solid solutions such as Ru2Mn1−xFexSn[6–](#page-11-6)[8](#page-11-7)
Heuslers, and Co1−xNixMnSb,[9](#page-11-8)[,10](#page-11-9) Cu1−xNixMnSb,[11–](#page-11-10)[13](#page-11-11) Co1−xCuxMnSb,[14](#page-11-12) and Cu1−xPdxMnSb[15](#page-11-13) half-Heuslers. In the latter case, the crossover between AFM to FM phases is related to a change in the electronic structure from semimetallic to half-metallic.[16](#page-11-14)[,17](#page-12-0)
Cu–based CuMnZ compounds are antiferromagnets. This feature attracts attention given the recent progress achieved in the AFM spintronics.[18](#page-12-1) Of particular interest is CuMnAs, with a high N´eel temperature T<sup>N</sup> = 480 K.[19](#page-12-2) In this case, features essential for applications, such as anisotropic magnetoresistance,[20,](#page-12-3)[21](#page-12-4) current-induced electrical switching of the N´eel vector[22](#page-12-5) and of the magnetic domains,[23](#page-12-6) have been demonstrated.
The AFM order of CuMnZ is independent of the actual crystalline structure. The equilibrium structure of bulk CuMnP and CuMnAs is orthorhombic, while that of CuMnSb is half-Heusler cubic, referred to below as the α phase. On the other hand, epitaxial growth can stabilizes metastable phases. This is the case of epitaxial layers of CuMnAs, grown on both GaP[19](#page-12-2)[–21](#page-12-4)[,24](#page-12-7)[,25](#page-12-8) and GaAs[23](#page-12-6) substrates, which crystalize in the tetragonal structure, referred to below as the β phase. Theoretical investigations of the crystalline properties of CuMnZ series show that the total energy difference between the cubic and orthorhombic phase is about 1 eV per f.u. (formula unit) for CuMnP, and about 0.5 eV per f.u. for CuMnAs.[26](#page-12-9) This suggests that the orthorhombic phase of CuMnSb, the last member of the CuMnZ series, may not be stable, and indeed the stable structure is the α phase. However, as we show here, epitaxial stabilization of CuMnSb in the β phase is in principle possible, because the calculated energy difference between
Concerning the magnetic properties, the N´eel temperature of both orthorhombic CuMnAs and β–CuMnAs is well above the room temperature,[19](#page-12-2) whereas that of α– CuMnSb is lower, about 60 K.[28,](#page-12-11)[29](#page-12-12) Theory agrees with experiment, since according to Ref. [30,](#page-12-13) in the orthorhombic CuMnP and CuMnAs, the AFM order is more stable than the FM by about 250 meV/Mn. This energy difference is smaller in the cubic phase of CuMnZ compounds, for which the AFM order is lower in energy than FM one by about 50 meV per f.u.[30](#page-12-13)[,31](#page-12-14) Finally, the AFM order of α–CuMnSb is stable under applied magnetic field, as T<sup>N</sup> does not change up to 50 Tesla.[32](#page-12-15)
Turning to the electronic structure of the CuMnP-CuMnAs-CuMnSb series we observe that the character of the energy band gap depends on the anion. Similar to the case of e.g. zinc blende semiconductors, the band gap decreases with the increasing atomic number of the anion.[30](#page-12-13) Indeed, CuMnP is a semiconductor, CuMnAs has a practically vanishing band gap, and CuMnSb is a semimetal.[33](#page-12-16)
Here we experimentally confirm a puzzling coexistence of AFM and FM phases in epitaxial stoichiometric CuMnSb films, observed by us previously,[34](#page-12-17) and explain the underlying mechanism responsible for this effect. A fine analysis of transmission electron microscopy (TEM) images, Sec. [II B,](#page-2-0) points to the formation of tetragonal β–CuMnSb inclusions embedded coherently within the cubic α–CuMnSb host. The tetragonal structure of these inclusions is the same as that of the tetragonal β– CuMnAs. Magnetic properties of our films, Sec. [II C,](#page-4-0) demonstrate coexistence of two magnetic phases: apart from the dominant AFM one, expected for CuMnSb, the measurements reveal the presence of a FM contribution. This is an unexpected feature within the CuMnZ series, exhibiting the AFM order.
In Sec. [III,](#page-5-0) we employ calculations based on the density functional theory to assess properties of CuMnSb films. In agreement with the experiment, β–CuMnSb is weakly metastable, but its magnetic ground state is FM. Band structures of α and β polymorphs are close, but changes in the density of states at the Fermi level account for the change of the dominant mechanism of the magnetic coupling from AFM superexchange to FM Ruderman-Kittel- Kasuya-Yoshida (RKKY). Finally, in Sec. [III E](#page-8-0) native point defects in CuMnSb are examined to assess their possible influence on the magnetic properties.[35](#page-12-18) Our results indicate that the dominant native defects in α–CuMnSb are Mn antisites, and their presence in the films can possibly account for small differences between the measured and the calculated magnetic characteristics, but they do not stabilize the FM order of α–CuMnSb.
# II. EXPERIMENTAL RESULTS
## A. Experimental Methods
# Growth conditions.
CuMnSb layers about 200 nm thick are grown by molecular beam epitaxy. Separate growth chambers connected by an ultra-high vacuum transfer system are used for the growth of the individual layers. Low telluriumdoped epi-ready GaSb (001) wafers are used as substrates. Prior to the growth, the natural oxide layer is desorbed in an Sb atmosphere. Then, 150 nm thick GaSb buffer layers are grown on the substrates to ensure a high-quality interface for the growth of CuMnSb. The GaSb buffer layers are grown at a substrate temperature of 530◦C and a beam equivalent pressure of 4.0 × 10−<sup>6</sup> mbar and 5.3 × 10−<sup>7</sup> mbar for Sb and Ga, respectively. Sb supply is facilitated by a single-filament effusion cell, while Ga is provided by a double-filament effusion cell.
A substrate temperature of 250◦C is used for the growth of CuMnSb films. The corresponding beam equivalent pressures are as follows: BEPCu = 5.80 × 10<sup>−</sup><sup>9</sup> mbar, BEPMn = 9.03 × 10<sup>−</sup><sup>9</sup> mbar, and BEPSb = 4.23 × 10<sup>−</sup><sup>8</sup> mbar. Cu is supplied by a double filament effusion cell, while Mn and Sb are supplied by single filament effusion cells. Following the growth of CuMnSb, a 2.5 nm thick layer of Al2O<sup>3</sup> is deposited on the samples through a sequential process of aluminum DC magnetron sputtering and oxidation. Please, refer to Ref. [29](#page-12-12) for a comprehensive analysis of the growth process and physical properties of the CuMnSb layers produced using the methodology outlined above.
Transmission Electron Microscopy. Specimens for the transmission electron microscopy (TEM) investigations are prepared by the focused ion beam method in the form of lamellas cut along the [100] and [110] directions, i.e., perpendicularly to the surface (001) plane. Titan Cubed 80-300 electron transmission microscope operating with accelerating voltage 300 kV and equipped with energy-dispersive X-ray spectrometer (EDXS) is used for the study. Most of the investigations are done on Cu grids, but for EDXS elemental analysis a Mo grid is used to avoid interference of Cu fluorescence signal from the grid. This analysis yields percentage atomic concentration at 37(3) : 32(5) : 31(7) for Cu, Mn, and Sb, respectively, which, within the experimental errors (given in the parentheses), correspond to the expected stoichiometric ratio of 33 : 33 : 33.
SQUID Magnetometry. Magnetic characterization is performed in a commercial superconducting quantum interference device (SQUID) magnetometer MPMS XL7. The magnetic moment of antiferromagnetic layers is generally very weak and by far dominated by the magnetic response of the bulky semiconductor substrates. Therefore, to counter act the typical shortcomings of commercial magnetometers built around superconducting magnets[36](#page-12-19) and to minimize subtraction errors during
![<span id="page-2-1"></span>FIG. 1. (a) High-angle annular dark-field scanning transmission electron microscopy image of a CuMnSb layer in the [100] zone axis. The inset in the top-right corner brings up a part of the image in atomic resolution, where bright dots represent columns of Mn and Sb atoms. (b) Electron diffraction pattern of the layer. (c) Schematics of the positions of Bragg's spots from (b). Big bullets represent the main reflections from the cubic CuMnSb structure, whereas the open triangles mark the positions of the weak extra reflections. The orientation of the triangles follows from the analysis of the data in panels (d-g). (d-e) Blown up two regions from (a), in which either vertical or horizontal strips dominate. The corresponding Fourier transforms are showed in the top right corners of both panels. (f) Selected area electron diffraction pattern taken at the regions dominated by the vertically oriented strips. (g) Diffraction intensity profiles taken along the horizontal [010]\* and the vertical [001]\* lines passing through the center the diffraction pattern. The solid line corresponds to the horizontal [010]\* direction and the dashed one to the vertical [001]\* one in panel (f). Stars denote directions in the reciprocal space. The arrows α and β indicate the length of α–2g(002) and β–2g(002) diffraction vectors, respectively.](path)
data reduction we actively employ the in situ compensation.[37](#page-12-20) It allows us to reduce the coupling of the signal of the substrates to about 10% of their original strength. The actual effectiveness of the compensation depends on the mass of the sample and its orientation with respect to the SQUID pick-up coils.[36,](#page-12-19)[38](#page-12-21) We also strongly underline the importance of a thorough mechanical removal of the metallic MBE glue from the backside of the samples for any magnetic studies. Its strongly nonlinear magnetic contribution can be of the same magnitude as that of the layer of interest.[39](#page-12-22) To accurately establish the magnitude of magnetic moment specific to CuMnSb we measure a reference sample grown without the CuMnSb layer[29](#page-12-12) using the same sample holder and following exactly the
#### <span id="page-2-0"></span>B. Structural characterization
An exemplary atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF/STEM) image obtained for the [100] zone axis (the direction of the projection) is in Fig. [1](#page-2-1) (a). It confirms a high quality cubic constitution of the material, as it is underlined in the inset. However, at the contrast chosen here, the image in this field of view reveals the presence of stripe-like features, which are the main subject of this analysis. In this image, the apparent lengths and widths of the strips are about 40 nm and about 4 nm, respectively, running predominantly either vertically or horizontally in this particular projection. On other images, the strips exhibit a relatively wide distribution of lengths in the 10-100 nm window. Since similarly distributed shadowy stripes are observed also in the [110] zone axis, we conclude that they form along all three principal crystallographic directions without any particular preferences. The expected F43m cubic structure of α–CuMnSb is clearly confirmed by the fourfold symmetry of the dominant (bright) spots seen on electron diffraction pattern presented in Fig. [1](#page-2-1) (b).
Importantly, the diffraction pattern in Fig. [1](#page-2-1) (b) contains also a second set of much fainter reflections, situated halfway between two adjacent reflections of the main pattern. This indicates the presence of a second crystallographic β phase, which periodicity in the corresponding direction is doubled relative to that of α–CuMnSb, but otherwise coherent with this host structure. We bring all the Bragg's spots up in Fig. [1](#page-2-1) (c), in which the bullets represent the main reflections from α–CuMnSb, whereas the open triangles mark the positions of the weak ones, which are forbidden for this structure.
The presence of β–CuMnSb is further substantiated by the inspection of the two close-ups from Fig. [1](#page-2-1) (a), shown in Fig. [1](#page-2-1) (d) and (e). At this magnification they reveal that, on top of the otherwise cubic arrangement of atomic columns, the strips' brightness alternates every second {002} plane along the direction perpendicular to strip's long axis. The modulation is vertical in Fig. [1](#page-2-1) (d), whereas it goes horizontally in Fig. [1](#page-2-1) (e). The top right corners of these figures contain the corresponding Fourier transform of the parent image, and, similarly to Fig. [1](#page-2-1) (b), both patterns are dominated by the main reflections of α–CuMnSb. The additional spots are embedded either along vertical [Fig. [1](#page-2-1) (d)] or horizontal [Fig. [1](#page-2-1) (e)] lines, i.e., the presence of vertical and horizontal orientations is mutually exclusive. This feature is reflected in Fig. [1](#page-2-1) (c), where the additional spots are marked by differently oriented triangles. The triangles with apexes directed vertically correspond to the vertical orientation of the brightness modulation in Fig. [1](#page-2-1) (d), whereas the horizontal direction of apexes corresponds to the horizontal modulation.
Based on the data shown above we propose that the second phase of CuMnSb, present in our films in the form of strips, is a tetragonal structure, which also is the structure of epitaxial CuMnAs,[19–](#page-12-2)[21](#page-12-4)[,23](#page-12-6)[–25](#page-12-8) and of CuMnSb at high pressures.[27](#page-12-10) This β–CuMnSb polymorph is shown in the panel (b) of Fig. [2.](#page-3-0) The difference between α and β phases consists in the location of Cu ions: in the α phase every (001) plane between two consecutive MnSb planes is half-occupied by Cu, whereas in the β phase Cu ions completely fill up every second (001) plane, and the overall stoichiometry of the material is preserved.
![<span id="page-3-0"></span>FIG. 2. Crystal structures of (a) α–CuMnSb with the cubic lattice constant a, (b) tetragonal β–CuMnSb with the lattice constants a in the (x, y) plane and c in the [001] direction, and (c) Cu3Mn2Sb2.](path)
regions with different orientations of the strips. Diffraction pattern of an area dominated by the vertically oriented strips is shown in more detail in Fig. [1](#page-2-1) (f). In agreement with the Fourier transforms, SAED shows the occurrence of specific reflections corresponding to this particular orientation. The reflections common to both the cubic α and the tetragonal β polymorphs are split along the [010]\* direction, i.e., orthogonal to the strip's axis, whereas the weak spots of the β phase are not split and are commensurate with the cubic phase. (A star denotes a direction in the reciprocal space.)
We quantify the effect analyzing intensity profiles taken along lines passing through the center of diffraction. The profiles are superimposed, and presented in Fig. [1](#page-2-1) (g). The profile along the [001]\* direction reflects the periodicity of α–CuMnSb, while that along [010]\* is additionally split. From the Figure it follows that in our specimens the c lattice parameter of the β–CuMnSb strips is equal to that of the host α–CuMnSb, 6.2(1) ˚A, whereas the a and b parameters of the β phase, 5.8(1) ˚A, are smaller by about 7%. Analogous features are observed for the [010]-oriented strips.
The existence of such a significant strain is confirmed by the calculation of strain maps. We apply the geometrical phase analysis method[40](#page-12-23) for the main image presented in Fig. [1](#page-2-1) (a), and the results are presented in Fig. [3](#page-4-1) (a) and (b) for the horizontal, ϵxx, and the vertical, ϵzz, components of strain, respectively. It is seen that stripes' strain is negative (dark shade) perpendicular to strips and almost zero along the strips. For example, on the horizontal strain map [Fig. [3](#page-4-1) (a)] only vertical strips are visible because they are compressed horizontally, whereas the horizontal strips are invisible because they are not deformed in the horizontal direction.
 (a). (a) The horizontal component of strain ϵxx, and (b) the vertical one, ϵzz. Geometrical phase analysis method has been applied.[40](#page-12-23)](path)
The calculated properties of β–CuMnSb, such as its lattice parameters, stability, and magnetic properties, are discussed in detail in Sec. [III C.](#page-7-0) Anticipating, we mention that they are consistent with experiment. We have also considered a second possible structure which is (almost) compatible with the TEM data, Cu3Mn2Sb2, depicted in Fig. [2](#page-3-0) (c). However, this compound is higher in energy than the β phase, and was dropped from further considerations.
#### <span id="page-4-0"></span>C. Magnetic properties
The temperature T dependence of magnetization, M(T), of the 200 nm thick layer of CuMnSb, is depicted in Fig. [4](#page-4-2) (a). The clear kink on M(T) at T<sup>N</sup> = 62 K marks the position of the paramagnetic to antiferromagnetic N´eel transition in the layer. This value corresponds precisely to the values of T<sup>N</sup> established previously for CuMnSb/GaSb layers of the thickness t ≥ 200 nm, what, indirectly, indicates stoichiometric material composition of this layer.[29](#page-12-12)
More specific information about the magnetic state of that sample is obtained from the examination of the temperature dependence of the inverse magnetic susceptibility, χ −1 (T), shown in Fig. [4](#page-4-2) (b). We take here χ(T) = M(T)/H, where H = 10 kOe is the external magnetic field applied during the measurements. χ −1 (T) can be approximated by two straight lines. The abscissa of the first one, which approximates χ −1 (T) above 200 K (the solid orange line in Fig. [4\)](#page-4-2), yields exactly the same magnitude of the Curie-Weiss temperature TCW = −100(5) K as that established previously for a thicker 510 nm layer, for which χ −1 (T) formed a single straight line above T<sup>N</sup> at the same experimental conditions.[29](#page-12-12) Also the slope of this line yields the value of the effective magnetic moment meff = 5.4(1)µ<sup>B</sup> per f.u., which is very close to that found previously, meff = 5.6µ<sup>B</sup> per f.u.[29](#page-12-12) This correspondence indicates that the high temperature part of χ −1 (T) is determined predominantly by AFM excitations in the paramagnetic matrix of CuMnSb.
The abscissa of the second straight line, which approximates the experimental data between T<sup>N</sup> and about 200 K (marked as the dashed orange line in Fig. [4\)](#page-4-2), yields a more positive value of the Curie-Weiss temperature, T ′ CW = −10(10) K. This clear positive shift of TCW indicates the existence of a ferromagnetic contribution to the overall antiferromagnetic phase of the material, and that these FM excitations gain in importance below about 200 K. Interestingly, a somewhat stronger effect, characterized by a change of sign of TCW to T ′ CW = +60(10) K, was noted in 40 nm CuMnSb layer grown on InAs.[34](#page-12-17) In accordance with the findings of structural characterization we propose that the by far stronger AFM component originates from the dominant α phase, whereas the FM one is brought about by β–CuMnSb polymorph.
<span id="page-5-1"></span>TABLE I. Experimental N´eel temperature TN, effective Curie-Weiss magnetic moment of Mn ions meff (Mn), and Curie-Weiss temperature TCW of α–CuMnSb. Measured orientation of the AFM axis is also given (n.e. = not established). Refs. [42](#page-12-24) and [41](#page-12-25) report the saturation Mn moment.
Turning now to the magnetic characteristics established here for α–CuMnSb we note that they are close to those reported previously, as shown in Tab. [I.](#page-5-1) The published data exhibit a certain distribution, which may indicate that other factors, such as a weak crystalline disorder, may be at work. In particular, either additional Mn interstitial ions or CuMn-MnCu antisite pairs are likely to form.[35](#page-12-18) The presence of such defects was suggested to stabilize the experimentally observed AFM {111}-oriented phase of α–CuMnSb.[35](#page-12-18) Finally, we do not observe a canted AFM order at low temperatures[41](#page-12-25) in any of our samples.
#### <span id="page-5-0"></span>III. THEORY
## A. Theoretical Methods
Calculations are performed within the density functional theory[46,](#page-13-2)[47](#page-13-3) in the generalized gradient approximation of the exchange-correlation potential proposed by Perdew, Burke and Ernzerhof.[48](#page-13-4) To improve description of 3d electrons, the Hubbard-type +U correction on Mn is added.[49–](#page-13-5)[51](#page-13-6) The parameter U(Mn) = 1 eV reproduces the known formation energy of the intermetallic CuMn alloy and gives a reasonable value of the Mn cohesive energy. We use the pseudopotential method implemented in the Quantum ESPRESSO code,[52](#page-13-7) with the valence atomic configuration 4s <sup>1</sup>.<sup>5</sup>p <sup>0</sup>3d 9.5 for Cu,
3s 2p <sup>6</sup>4s 2p <sup>0</sup>3d 5 for Mn and 5s 2p 3 for Sb ions. The planewaves kinetic energy cutoffs of 50 Ry for wave functions and 250 Ry for charge density are employed. Finally, geometry relaxations are performed with a 0.05 GPa convergence criterion for pressure. In defected crystals ionic positions are optimized until the forces acting on ions become smaller than 0.02 eV/˚A.
The properties of defected α–CuMnSb are examined using cubic 2a×2a×2a supercells with 96 atoms (i.e., 32 f.u.), while magnetic order of ideal crystals are checked using the smallest possible supercells. Here a is the equilibrium lattice parameter. The k-space summations are performed with a 6 × 6 × 6 k-point grid for the largest supercell, and correspondingly denser grids are used for smaller cells.
Magnetic interactions and magnetic order depend on several factors, such as the exchange spin splitting of the d(TM) shells, charge states of TM ions, concentration of free carriers and their spin polarization, and the density of states (DOS) at the Fermi energy EF. These factors are interrelated, and are calculated self-consistently within ab initio approach.
Considering first the localized magnetic moments we note that spin polarization of Co, Ni, and Cu ions in XMnZ compounds practically vanishes, while that of the d(Mn) shell is substantial.[16,](#page-11-14)[17](#page-12-0)[,31](#page-12-14) The robustness of the Mn magnetic moment results from the large, 3 – 5 eV, spin splitting of the 3d(Mn) states. In fact, in XMnZ the d(Mn) spin up channel is occupied, while most of the spin down d(Mn) states lay above the Fermi level. Here, one can observe that spin polarization of the d(TM) electrons in free atoms depends on the difference in the number of spin up and spin down electrons, which is the highest in the case of Mn. Consequently, the Mn spin polarization persists in XMnZ. On the other hand, spin splitting of d electrons of Co and Ni atoms is smaller, and thus it vanishes in XMnSb hosts, see the analysis for TM dopants in ZnO.[53](#page-13-8)
In CuMnSb, the magnetic sublattice consists of Mn ions, which are second neighbors distant by 4.3 ˚A. Therefore, the direct exchange coupling between two Mn ions, given by overlaps of their d(Mn) orbitals, is negligibly small. The remaining indirect exchange coupling is the sum of two contributions, and the exchange constant Jindirect = Jsr + JRKKY . [16](#page-11-14)[,17](#page-12-0)[,54](#page-13-9) The first term Jsr has a short-range AFM character, and it is inversely proportional to the energy distance between the unoccupied d(Mn) states and EF. The second coupling channel is of RKKY type mediated by free carriers. This channel depends on the detailed electronic structure in the vicinity of EF, and JRKKY is proportional to DOS(EF). In particular, CoMnSb and NiMnSb half-metals are FM, while CuMnP and CuMnAs insulators are AFM. As we show here, CuMnSb is the border case.
#### <span id="page-5-2"></span>B. Crystal and magnetic properties of α–CuMnSb
A rhombohedral primitive cell of α–CuMnSb contains one formula unit. This structure consist in four interpenetrating fcc sublattices, one of them being empty. The consecutive (001) MnSb planes are followed by the "halfempty" Cu planes, in which the planar atomic density is twice lower. The cubic unit cell is presented in Fig. [2](#page-3-0) (a). Local coordination of Mn ions can be relevant from the point of view of magnetic interactions. With this respect we notice that the magnetic coordination of an Mn ion consists in 12 equidistant Mn atoms at a/<sup>√</sup> 2. More-
We consider four magnetic phases of α–CuMnSb. The corresponding supercells are shown in Fig. [5.](#page-6-0) Antiferromagnetic order with parallel Mn spins in the (001) planes, AFM001, is calculated using the cubic a×a×a cell with 4 f.u. (12 atoms), and shown in Fig. [5](#page-6-0) (a). The AFM order with a period doubled in the [001] direction with parallel Mn spins in each (001) plane, denoted as AFM002, is shown in Fig. [5](#page-6-0) (b). The corresponding a×a×2a cell contains 8 f.u., and is one of the possible supercells in which this phase can be realized. In the AFM111 phase, the Mn spins are parallel in each (111) plane, but the consecutive (111) planes are AFM, as shown in Fig. [5](#page-6-0) (c), and the corresponding rhombohedral unit cell a √ 2 × a √ 2 × a √ 2 contains 8 primitive cells with 24 atoms. Finally, the FM phase requires a primitive cell a/<sup>√</sup> 2×a/<sup>√</sup> 2×a/<sup>√</sup> 2 with 1 f.u., presented in Fig. [5](#page-6-0) (d).
<span id="page-6-1"></span>TABLE II. The calculated lattice parameter a, the saturation Mn magnetic moment, msat, and the energy of the given magnetic order relative to α–CuMnSb in the AFM001 ground state, ∆Etot. All energies are per one formula unit. Our measured TEM values are also given.
higher in energy. The least stable is the FM order, higher in energy than AFM001 by about 20 meV per f.u. The equilibrium lattice parameters a ≈ 6.1 ˚A are practically independent of the magnetic order, and close to the experimental value 6.088 ˚A.[42](#page-12-24) Some phases are characterized by a small distortion of the cubic symmetry caused by different bond lengths between ferromagnetically and antiferromagnetically oriented Mn ions. Differences in the lattice parameters between various magnetic phases are below 0.01 ˚A, and are not reported in the Table. Similar results for the AFM001 order were obtained in Ref. [35,](#page-12-18) while in Refs [16](#page-11-14) and [31](#page-12-14) the AFM order is more stable than FM by 50 and 90 meV per Mn, respectively.
The last property reported in Tab. [II](#page-6-1) is the saturation magnetic moment of Mn, which also is similar in all phases, and equal to about 4.6µB. This value corresponds to the Curie-Weiss moment of 5.5(1)µB, and compares favorably with the experimental values given in Tab. [I.](#page-5-1)
The obtained results allow estimating the relative roles of the short- and long-range contributions to the magnetic coupling. To this end, we assume the hamiltonian in the form Hex = −J/2 P i,j ⃗si⃗s<sup>j</sup> , where the short range interaction is limited to the Mn NNs neighbors, and the long-range term is neglected. The spin value, s<sup>i</sup> ≈ 2.3, is one half of the calculated magnetic moment of Mn.
The exchange constant J is positive (negative) for the FM (AFM) coupling, and is obtained by comparing energies of various magnetic orders. In the AFM001 phase, each Mn ion has 4 ferromagnetically oriented Mn NNs in the (001) plane and 8 antiferromagnetically oriented Mn NNs in the two adjacent planes. For the remaining magnetic phases, the energies calculated relative to the ground state E<sup>0</sup> ≡ EAFM001 depend on the magnetic order as shown in Tab. [II.](#page-6-1) These results give the coupling constant in the range −0.6 ≥ Jsr ≥ −0.2 meV. This spread is quite large and cannot be explained by (negligible) changes in atomic distances in cells with different magnetic ordering. Therefore, we conclude that the Heisenberg nearest neighbor model does not describe magnetic properties of bulk phases. Indeed, such a model is not appropriate for metallic or semimetallic systems such as α–CuMnSb, where the long-range RKKY coupling is present.
An opposite conclusion comes from the analysis of single spin excitations from the AFM001 ground state. We use a 2a×2a×2a supercell to calculate the energy differences ∆E for the following cases, in which we change (i) spin of one Mn ion, 1Mn ↑→ 1Mn ↓, called a single spin-flip, (ii) 2Mn↑→ 2Mn↓ for spins of two nearest Mn ions belonging to one layer and (iii) 2Mn ↑→ 2Mn ↓ for two distant Mn ions. In these processes the long-range coupling is not important, and indeed the calculated exchange constant consistently is Jsr ≈ −0.4 meV.
#### <span id="page-7-0"></span>C. Crystal and magnetic properties of β–CuMnSb
We now consider two possible structures of the secondary phase proposed based on the experimental results. They are characterized by doubling the periodicity in the [001] direction. The unit cell of β–CuMnSb, shown in Fig. [2,](#page-3-0) is tetragonally deformed relative to that of α–CuMnSb, with the corresponding lattice parameters a = 5.88 ˚A and c = 6.275 ˚A. They differ by about 3 per cent from our calculated cubic a(α– CuMnSb) = 6.105 ˚A. The two interlayer spacings between the consecutive MnSb planes in the [001] direction in the unit cell, shown in Fig. [2](#page-3-0) (b), are quite different, namely dinter<sup>1</sup> = 2.80 ˚A (no Cu), and dinter<sup>2</sup> = 3.48 ˚A (with Cu). Turing to the magnetic order of β–CuMnSb, we find that the FM phase constitutes the ground state with msat = 4.6µ<sup>B</sup> and is lower than the AFM phase by 11 meV per f.u., as indicated in Tab. [II.](#page-6-1) Thus, the
The experimental[27](#page-12-10) lattice parameters of β–CuMnSb reasonably agree with our values, i.e., the calculated a = 6.28 ˚A and c/a = 1.87 are about 2% larger than those measured for the compressed crystal at the critical pressure of 7 GPa. On the other hand, the calculations of Ref. [27](#page-12-10) predict that the magnetic order of the β phase is AFM, in striking contrast with our results. Also their calculated msat(Mn) = 3.8µ<sup>B</sup> is substantially smaller than our 4.6µB. The origin of these discrepancies is not clear, but it may be due to the different exchange-correlation functionals used, and/or to application of the +U(Mn) correction in our calculations (which can affect the results.[31](#page-12-14))
The calculated total energy of the FM β–CuMnSb relative to the AFM α–CuMnSb is higher by 102 meV per f.u. This energy difference is not large, being comparable to the growth temperature, which implies that the β–CuMnSb polymorph can indeed form during epitaxy. We also stress that stoichiometry of the α and β phases is the same, which facilitates formation of β–CuMnSb. Finally, the observed β–CuMnSb inclusions are coherent, i.e., lattice matched, with the host structure. This agrees with the fact that the calculated excess elastic energy of matching the lattice parameters of the β phase to the host α phase is very low and ranges from 3 meV per f.u. (when the tetragonal a parameter constrained to the cubic a = 6.105 ˚A) to 20 meV per f.u. (the tetragonal c parameter constrained to the cubic a).
The second considered possibility, Cu3Mn2Sb<sup>2</sup> shown in Fig. [2](#page-3-0) (c), is higher in energy by 0.37 eV per f.u. in the Cu–rich conditions than the ideal CuMnSb, i.e., by 0.27 eV per f.u. than β–CuMnSb, its stoichiometry is markedly different, and thus we can eliminate this structure from considerations.
# D. Energy band structures of α–CuMnSb and β–CuMnSb
Figure [7](#page-8-1) (a) shows the energy bands and DOS of the AFM001 α–CuMnSb. We see that this phase has a metallic character, however DOS at the Fermi level is low. The states close to E<sup>F</sup> are built from s, p and d states of all ions with similar weights. The low DOS(EF) makes CuMnSb almost semimetallic with a low electrical conductivity. Compatible with the small DOS(EF) is the high resistivity measured in Ref. [41](#page-12-25) and [55.](#page-13-10)
Since the system is antiferromagnetically ordered, the total DOSs of spin-up and spin-down states are the same. In Fig. [7](#page-8-1) only contributions of the 3d(Mn) and 3d(Cu) orbitals are presented to reveal magnetic properties. We see that the exchange spin splitting of the d(Mn) shell is large, about 5 eV. The closely spaced levels contributing to the DOS maxima centered at 4 eV below the Fermi energy are composed mainly of the d states of both Cu and Mn. Spin-up and spin-down 3d(Cu) orbitals are almost
completely occupied, and thus Cu ions are non-magnetic. In turn, the majority spin states of the 3d(Mn) orbitals are completely occupied, while the minority spin states at 1 eV above the Fermi energy are partially filled thanks to a small overlap with spin up states. As a result, a single Mn ion is in between the d <sup>5</sup> and d 6 configuration, with the saturation magnetic moment of 4.6µ<sup>B</sup> consistent with Tab. [II.](#page-6-1) Our results for α–CuMnSb are close to those of Ref. [31.](#page-12-14) A similar electronic configuration takes place in CuMnAs, where the spin-down Mn states are partially filled.[56](#page-13-11)
The overall band structure of the FM β–CuMnSb displayed in Fig. [7](#page-8-1) (b) is close to that of α–CuMnSb, which is particularly clear when comparing partial DOS of both phases. In particular, msat(Mn) is about 4.5µ<sup>B</sup> in both phases, and energies of both d(Mn)- and d(Cu)-related bands are largely independent of the actual crystal structure. This similarity can be due to the fact that the MnSb (001) planes play a dominant role, and the exact locations of the Cu ions are less important.
On the other hand, the calculated DOS(EF) for the α phase is 0.35 states per spin and f.u., while for the β phase we find 1.26 states per spin and f.u., which is 3.6 times higher. As a consequence, α–CuMnSb is semimetallic, and the AFM order is dominant, while β phase is more metallic in character, which in turn favors the RKKY-type coupling and the FM order. This feature can explain the different magnetic phases of the α and β polymorphs.
Analysis of the calculated electronic structure of Heusler and half-Heusler CuMnZ led Sasioglu et al.[17](#page-12-0) to the conclusion that when the spin polarization of conduction electrons is large, and the d(Mn) spin down states are far above EF, then the RKKY coupling is dominant, and one should expect the FM order, otherwise the short range AFM coupling is dominant. Our results do not confirm this conclusion, and indicate that the important
## <span id="page-8-0"></span>E. Point native defects in α–CuMnSb
where E(CuMnSb) and E(CuMnSb : D) are the total energies of a supercell without and with a defect, and n<sup>i</sup> = +1(−1) corresponds to the removal (addition) of one ith atom. µis are the variable chemical potentials of atoms in the solid, which in general are different from the chemical potentials µi(bulk) of the standard state of elements, i.e., Cu, Mn and Sb bulk. Details of calculations of chemical potentials are given in Appendix [A.](#page-10-0)
The point native defects considered here are vacancies VX, interstitials X<sup>i</sup> , and antisites X<sup>Y</sup> (where X and Y are Cu, Mn, or Sb) for all three sublattices. As it was mentioned above, the Cu sublattice is "half- empty" compared to the MnSb sublattice. Consequently, we consider here formation of interstitials at the empty sites of the Cu sublattice only, and neglect other possibilities, expected to have higher formation energies Eform. Thus, the set of defects considered here only partially overlaps with that of Ref. [35.](#page-12-18) Of particular interest to the present study are defects involving Mn ions, since they can influence magnetic properties of α–CuMnSb .[35](#page-12-18) This is why we consider them more extensively, after briefly analyzing the non-magnetic defects. The calculated formation energies are summarized in Tab. [III.](#page-9-0) Because of the magnetic coupling, formation energies of the Mn-related defects depend on the spin direction relative to the spins of the host Mn neighbors. We consider possible spin configurations shown in Fig. [8](#page-9-1) (b).
<span id="page-9-0"></span>TABLE III. Formation energies (in eV) of isolated point defects in the Mn-rich conditions. In parentheses are Mn-related values corrected for ∆H<sup>f</sup> (MnSb) = 0.48 eV, which correspond to the Mn-poor case.
where k<sup>B</sup> is the Boltzmann constant and N<sup>0</sup> is the density of the relevant lattice sites. Details of the calculations of Eform are provided in Supporting Information. To put the calculated formation energies into a proper context, we note that if the growth temperatrure Tgrowth = 2500C and Eform = 0.1 eV, then exp(−Eform/kBTgrowth) = 0.1, which corresponds to a high 10 atomic per cent concentration of this defect on the considered sublattice. On the other hand, if Eform = 1 eV, then exp(−Eform/kBTgrowth) = 9 × 10<sup>−</sup><sup>11</sup>, which implies a negligible defect concentration.
Sb sublattice. The prohibitively high values of Eform demonstrate that VSb and Sb<sup>i</sup> should not form. Similarly, formation energies of SbCu, SbMn, CuSb and MnSb antisites exceed 1 eV, and those defects are not expected to be present at high concentrations. Consequently, the Sb sublattice is thermodynamically stable, robust, and constitutes a defect-free back-bone of CuMnSb.
(ii) Formation energy of Cu interstitials at the Cu sublattice, Eform(Cui) = 1 eV, is relatively high, and their concentrations are negligible. Additionally, the high formation energy of Cu<sup>i</sup> interstitials is consistent with the sparse character of the Cu sublattice in α–CuMnSb.
(iii) Formation of Mn<sup>i</sup> interstitials at the Cu sublattice is characterized by Eform = 0.7-1.4 eV, depending on the spin direction and conditions of growth, and therefore they are not expected to be present at high concentrations, especially in the Mn-poor conditions.
In brief, low formation energies are found for three defects, namely the VCu and VMn vacancies and the MnCu antisite, particularly at the Mn-rich growth conditions. This indicates that a Cu deficit on the Cu sublattice is possible, affecting stoichiometry. Significantly, MnCu antisites make the Cu sublattice magnetic, and also they can participate in the magnetic coupling between the adjacent MnSb (001) planes, thus influencing magnetic properties, as it will be discussed in more detail below. In contrast, SbCu antisites are present in negligible concentrations. Our results are in a reasonable agreement with those of Ref. [35,](#page-12-18) especially given their neglect of spin effects and a somewhat different theoretical approach. Interestingly, formation energies of native defects in CuMnAs calculated in Ref. [56](#page-13-11) are close to the present results in spite of the different anion.
## F. Defect-induced magnetic coupling
There are two Mn-related point defects, Mn<sup>i</sup> and MnCu, both situated on the Cu sublattice. When present at high concentrations, they affect magnetism of α– CuMnSb. Their coupling with host Mn ions is different than the Mn-Mn coupling between the host Mn because of the different local coordination. Energetics of both defects is complex and rich, since the total energy of the system (and thus formation energies) depends on their spin orientations relative to the neighborhood. At both substitutional and interstitial sites in the Cu layer, a Mn ion has 4 Mn nearest neighbors arranged in a tetrahedral configuration, 2 in the upper and 2 in the lower MnSb layer. The Mni–MnMn distance is shorter than that of
MnMn–MnMn, and equal to (<sup>√</sup> 3/4)a.
The possible local spin configurations are reduced to small clusters of 5 Mn ions, shown in Fig. [8.](#page-9-1) The Mn spin-up and spin-down (001) MnSb layers are denoted by in pink and blue, respectively, reflecting the calculated (001) AFM magnetic ground state. The central MnCu (or Mni) ion of such a cluster provides an additional channel of magnetic coupling between two adjacent MnSb layers. The corresponding formation energies are given in Fig. [8.](#page-9-1)
As it was pointed out, in ideal α–CuMnSb, the Mn ions are second neighbors only, separated either by Sb (i.e., the Mn-Sb-Mn "bridge" in the MnSb(001) plane), or by Cu (forming a Mn-Cu-Mn "bridge" linking 3 consecutive (001) planes.) Thus, the short range magnetic coupling in ideal α–CuMnSb is successfully modelled in Sec. [III B](#page-5-2) by the interaction between two Mn second neighbors, situated either in the same MnSb layer, or in two adjacent ones. In contrast, the 4 host Mn ions in the cluster are the first neighbors of a Mn<sup>i</sup> or a MnCu defect. Thus, one can expect that this coupling is stronger than the intrinsic one in the ideal host, and indeed, the differences in energy between various configurations in Fig. [8](#page-9-1) are about 100 meV, which is too high to be explained by the estimated Jsr = 0.4 meV.
As it follows from Fig. [8,](#page-9-1) 5-atom clusters are magnetically frustrated. In particular, the lowest energy case denoted as 4AFM favors the local FM orientation of spins in two adjacent (001) planes, which is opposite to the global host magnetic order. Our results do not confirm the conclusion of Ref. [56](#page-13-11) who find that the 3AFM configuration has the lowest energy, and thus it promotes the global AFM111 order. Instead, we rather expect that Mn-related point defects induce disorder of the host AFM phase, possibly leading to formation of a spin glass.[57](#page-13-12)
#### IV. SUMMARY
CuMnSb films were epitaxially grown on GaSb substrates. Magnetic measurements reveal the presence of two magnetic subsystems. The dominant magnetic order is AFM with the N´eel temperature of 62 K, which is the same as in bulk CuMnSb. It co-exists with a FM phase, characterized by the Curie temperature of about 100 K.
These findings go in hand with transmission electron microscopy and selective area diffraction measurements, which demonstrate coexistence of two structural polymorphs of the same stoichiometry. The dominant one is the cubic half-Heusler α–CuMnSb, which is the equilibrium structure of bulk samples. The second component is a tetragonal β–CuMnSb polymorph, which forms 10-100 nm long elongated inclusions.
(i) The β–CuMnSb phase is metastable, and its total energy is higher by 0.1 eV per f.u. only than that of the equilibrium α–CuMnSb. Lattice parameters of the β phase differ from those of α–CuMnSb by about 4 per cent. This lattice misfit between the two structures does not prevent the pseudomorphic coexistence of both phases, since the calculated misfit strain energy is below 20 meV per f.u.
(ii) In agreement with experiment, α–CuMnSb is AFM, and the FM order is 19 meV per f.u. higher in energy. In contrast, the magnetic ground state of β– CuMnSb is FM, which is more stable than AFM by 11 meV per f.u. This indicates that indeed the β–CuMnSb inclusions are responsible for the FM signal.
(iii) The different magnetic orders of the α and β phases originate in their somewhat different band structures. In particular, critical for magnetic order is the DOS at the Fermi level, which is about 4 times higher in β–CuMnSb than in the α phase. This shows that the β phase is more metallic in character, which in turn favors the FM order driven by the Ruderman-Kittel-Kasuya-Yoshida interaction.
(iv) Our calculations predict the saturated magnetic moment of Mn msat = 4.6µ<sup>B</sup> and 4.5µ<sup>B</sup> for the α and the β phase, respectively. This corresponds to the effective moment of 5.6µB, in good agreement with the measured 5.5µB.
(v) The calculated formation energies of point native defects indicate that the most probable are the MnCu antisites with low formation energies of 0–0.2 eV. However, their presence is expected to disorder the host magnetic AFM phase rather than to induce a transition to the FM configuration.
(vi) Regarding the properties of the CuMnX series we see that their structural stability is relatively weak, as they crystallize in a variety of structures. In particular, unlike the bulk orthorhombic CuMnAs, epitaxial films of CuMnAs are tetragonal, but both structures are AFM. In the case of CuMnSb, polymorphism comprises also the equilibrium magnetic structure, AFM in the bulk specimens, and FM in epitaxial films.
#### ACKNOWLEDGMENTS
LS, CG, JK and LWM thank M. Zipf for technical assistance. Our work was funded by the Deutsche Forschungsgemeinschaft (DFG,German Research Foundation) No. 397861849, by the Free State of Bavaria (Institute for Topological Insulators) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC2147 ct.qmat (Project-Id 390858490).
#### <span id="page-10-0"></span>Appendix A:
The highest possible value of µ<sup>i</sup> is µi(bulk), which implies that the studied system is in equilibrium with the given bulk source of atoms and δµ<sup>i</sup> = 0, otherwise δµ<sup>i</sup> < 0.
Chemical potentials of the components in the standard state are given by the total energies per atom of elemental solids. The calculated cohesive energies Ecoh of the face centered cubic Cu, the face centered cubic Mn with the AFM magnetic order, and the triclinic Sb are, respectively, 3.40 (3.49), 2.65 (2.92) and 2.68 (2.75) eV/atom. They compare reasonably well with the experimental values given in parentheses.[58](#page-13-13)
Chemical potentials of the involved atomic species depend on possible formation of compounds. The ranges of variations of chemical potentials are determined by conditions of equilibrium between various phases, i.e., Cu2Sb, MnSb and CuMnSb. Thermodynamic equilibrium requires that
$$\begin{aligned} \delta\mu(\text{Cu}) + 2\delta\mu(\text{Sb}) &= \Delta H\_f(\text{Cu}\_2\text{Sb}), \\ \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{MnSb}), \\ \delta\mu(\text{Cu}) + \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{CuMnSb}), \end{aligned} \quad \text{(A2)}$$
The calculated values ∆H<sup>f</sup> (Cu2Sb) = −0.03 eV per f.u., ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u., and ∆H<sup>f</sup> (CuMnSb) = −0.42 eV per f.u. The very low ∆H<sup>f</sup> (Cu2Sb) is somewhat unexpected, since Cu2Sb is a stable compound which crystallizes in the tetragonal phase.[43](#page-12-26) Next, our result ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u. agrees well with both the previous value -0.52 eV per f.u. calculated in Ref. [59,](#page-13-14) and the experimental - 0.52 eV per f.u.[60](#page-13-15) Assuming that the accuracy of the calculated values is 0.03 eV per f.u., the set of Equation [A2](#page-11-15) is consistent if we assume ∆H<sup>f</sup> (Cu2Sb) = 0, and ∆H<sup>f</sup> (MnSb) = ∆H<sup>f</sup> (CuMnSb) = −0.45 eV per f.u. This in turn implies that δµ(Cu) = δµ(Sb) = 0, and δµ(Mn) = −0.45 eV. Consequently, the allowed window of the Mn chemical potential is
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| |
FIG. 8. All possible spin orientations of Mn ions in α–CuMnSb AFM001. In the ground state configuration, the Mn spins are parallel within each MnSb (001) layer, and the consecutive MnSb (001) layers are AFM, as shown in (a). (b) Mn MnCu antisites and Mnⁱ interstitials can assume 5 different local spin configurations. The corresponding spin dependent formation energies in eV are given by the numbers below.
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# Coexistence of Antiferromagnetic Cubic and Ferromagnetic Tetragonal Polymorphs in Epitaxial CuMnSb
High-resolution transmission electron microscopy and superconducting quantum interference device magnetometry shows that epitaxial CuMnSb films exhibit a coexistence of two magnetic phases, coherently intertwined in nanometric scales. The dominant α phase is half-Heusler cubic antiferromagnet with the N´eel temperature of 62 K, the equilibrium structure of bulk CuMnSb. The secondary phase is its ferromagnetic tetragonal β polymorph with the Curie temperature of about 100 K. First principles calculations provide a consistent interpretation of experiment, since (i) total energy of β–CuMnSb is higher than that of α–CuMnSb only by 0.12 eV per formula unit, which allows for epitaxial stabilization of this phase, (ii) the metallic character of β–CuMnSb favors the Ruderman-Kittel-Kasuya-Yoshida ferromagnetic coupling, and (iii) the calculated effective Curie-Weiss magnetic moment of Mn ions in both phases is about 5.5 µB, favorably close to the measured value. Calculated properties of all point native defects indicate that the most likely to occur are MnCu antisites. They affect magnetic properties of epilayers, but they cannot induce the ferromagnetic order in CuMnSb. Combined, the findings highlight a practical route towards fabrication of functional materials in which coexisting polymorphs provide complementing functionalities in one host.
#### I. INTRODUCTION
One of the most challenging and long-standing problems in fundamental magnetism is a competition between ferromagnetic and antiferromagnetic phases. Their interplay at the interface results in a well known effect of the exchange bias,[1](#page-11-1)[,2](#page-11-2) which fuels now a rapid development of spintronics[3](#page-11-3) and unconventional computing.[4](#page-11-4) The material class of Heusler alloys was previously used to study the origin of the transition between magnetic phases because it offers a wide spectrum of functionalities.[5](#page-11-5) Indeed, Heusler alloys exhibit ferromagnetic (FM), antiferromagnetic (AFM), and canted ferromagnetic order. This indicates that different types of magnetic coupling are competing in this family. Moreover, some of its members display structural polymorphism, which allows studying relationships between the crystalline phase, the magnetic phase, and the corresponding electronic structure.
Heusler alloys incorporate full-Heusler (X2YZ) and half-Heusler (XYZ) variants, where X and Y stand for transition metals, whereas Z denotes anions from the main group. In this class, qualitative changes in material characteristics can be achieved by chemical substitution on either the transition metal cation or on the anion sublattice. Typically, the change of the cation does not change the crystal structure, but it can induce a crossover between the AFM and the FM magnetic phases. A rarely met complete solubility with only marginally affected crystallinity of the otherwise chemically homogenous systems allowed to study the FM-AFM phase competition in detail. The prominent examples are quaternary solid solutions such as Ru2Mn1−xFexSn[6–](#page-11-6)[8](#page-11-7)
Heuslers, and Co1−xNixMnSb,[9](#page-11-8)[,10](#page-11-9) Cu1−xNixMnSb,[11–](#page-11-10)[13](#page-11-11) Co1−xCuxMnSb,[14](#page-11-12) and Cu1−xPdxMnSb[15](#page-11-13) half-Heuslers. In the latter case, the crossover between AFM to FM phases is related to a change in the electronic structure from semimetallic to half-metallic.[16](#page-11-14)[,17](#page-12-0)
Cu–based CuMnZ compounds are antiferromagnets. This feature attracts attention given the recent progress achieved in the AFM spintronics.[18](#page-12-1) Of particular interest is CuMnAs, with a high N´eel temperature T<sup>N</sup> = 480 K.[19](#page-12-2) In this case, features essential for applications, such as anisotropic magnetoresistance,[20,](#page-12-3)[21](#page-12-4) current-induced electrical switching of the N´eel vector[22](#page-12-5) and of the magnetic domains,[23](#page-12-6) have been demonstrated.
The AFM order of CuMnZ is independent of the actual crystalline structure. The equilibrium structure of bulk CuMnP and CuMnAs is orthorhombic, while that of CuMnSb is half-Heusler cubic, referred to below as the α phase. On the other hand, epitaxial growth can stabilizes metastable phases. This is the case of epitaxial layers of CuMnAs, grown on both GaP[19](#page-12-2)[–21](#page-12-4)[,24](#page-12-7)[,25](#page-12-8) and GaAs[23](#page-12-6) substrates, which crystalize in the tetragonal structure, referred to below as the β phase. Theoretical investigations of the crystalline properties of CuMnZ series show that the total energy difference between the cubic and orthorhombic phase is about 1 eV per f.u. (formula unit) for CuMnP, and about 0.5 eV per f.u. for CuMnAs.[26](#page-12-9) This suggests that the orthorhombic phase of CuMnSb, the last member of the CuMnZ series, may not be stable, and indeed the stable structure is the α phase. However, as we show here, epitaxial stabilization of CuMnSb in the β phase is in principle possible, because the calculated energy difference between
Concerning the magnetic properties, the N´eel temperature of both orthorhombic CuMnAs and β–CuMnAs is well above the room temperature,[19](#page-12-2) whereas that of α– CuMnSb is lower, about 60 K.[28,](#page-12-11)[29](#page-12-12) Theory agrees with experiment, since according to Ref. [30,](#page-12-13) in the orthorhombic CuMnP and CuMnAs, the AFM order is more stable than the FM by about 250 meV/Mn. This energy difference is smaller in the cubic phase of CuMnZ compounds, for which the AFM order is lower in energy than FM one by about 50 meV per f.u.[30](#page-12-13)[,31](#page-12-14) Finally, the AFM order of α–CuMnSb is stable under applied magnetic field, as T<sup>N</sup> does not change up to 50 Tesla.[32](#page-12-15)
Turning to the electronic structure of the CuMnP-CuMnAs-CuMnSb series we observe that the character of the energy band gap depends on the anion. Similar to the case of e.g. zinc blende semiconductors, the band gap decreases with the increasing atomic number of the anion.[30](#page-12-13) Indeed, CuMnP is a semiconductor, CuMnAs has a practically vanishing band gap, and CuMnSb is a semimetal.[33](#page-12-16)
Here we experimentally confirm a puzzling coexistence of AFM and FM phases in epitaxial stoichiometric CuMnSb films, observed by us previously,[34](#page-12-17) and explain the underlying mechanism responsible for this effect. A fine analysis of transmission electron microscopy (TEM) images, Sec. [II B,](#page-2-0) points to the formation of tetragonal β–CuMnSb inclusions embedded coherently within the cubic α–CuMnSb host. The tetragonal structure of these inclusions is the same as that of the tetragonal β– CuMnAs. Magnetic properties of our films, Sec. [II C,](#page-4-0) demonstrate coexistence of two magnetic phases: apart from the dominant AFM one, expected for CuMnSb, the measurements reveal the presence of a FM contribution. This is an unexpected feature within the CuMnZ series, exhibiting the AFM order.
In Sec. [III,](#page-5-0) we employ calculations based on the density functional theory to assess properties of CuMnSb films. In agreement with the experiment, β–CuMnSb is weakly metastable, but its magnetic ground state is FM. Band structures of α and β polymorphs are close, but changes in the density of states at the Fermi level account for the change of the dominant mechanism of the magnetic coupling from AFM superexchange to FM Ruderman-Kittel- Kasuya-Yoshida (RKKY). Finally, in Sec. [III E](#page-8-0) native point defects in CuMnSb are examined to assess their possible influence on the magnetic properties.[35](#page-12-18) Our results indicate that the dominant native defects in α–CuMnSb are Mn antisites, and their presence in the films can possibly account for small differences between the measured and the calculated magnetic characteristics, but they do not stabilize the FM order of α–CuMnSb.
# II. EXPERIMENTAL RESULTS
## A. Experimental Methods
# Growth conditions.
CuMnSb layers about 200 nm thick are grown by molecular beam epitaxy. Separate growth chambers connected by an ultra-high vacuum transfer system are used for the growth of the individual layers. Low telluriumdoped epi-ready GaSb (001) wafers are used as substrates. Prior to the growth, the natural oxide layer is desorbed in an Sb atmosphere. Then, 150 nm thick GaSb buffer layers are grown on the substrates to ensure a high-quality interface for the growth of CuMnSb. The GaSb buffer layers are grown at a substrate temperature of 530◦C and a beam equivalent pressure of 4.0 × 10−<sup>6</sup> mbar and 5.3 × 10−<sup>7</sup> mbar for Sb and Ga, respectively. Sb supply is facilitated by a single-filament effusion cell, while Ga is provided by a double-filament effusion cell.
A substrate temperature of 250◦C is used for the growth of CuMnSb films. The corresponding beam equivalent pressures are as follows: BEPCu = 5.80 × 10<sup>−</sup><sup>9</sup> mbar, BEPMn = 9.03 × 10<sup>−</sup><sup>9</sup> mbar, and BEPSb = 4.23 × 10<sup>−</sup><sup>8</sup> mbar. Cu is supplied by a double filament effusion cell, while Mn and Sb are supplied by single filament effusion cells. Following the growth of CuMnSb, a 2.5 nm thick layer of Al2O<sup>3</sup> is deposited on the samples through a sequential process of aluminum DC magnetron sputtering and oxidation. Please, refer to Ref. [29](#page-12-12) for a comprehensive analysis of the growth process and physical properties of the CuMnSb layers produced using the methodology outlined above.
Transmission Electron Microscopy. Specimens for the transmission electron microscopy (TEM) investigations are prepared by the focused ion beam method in the form of lamellas cut along the [100] and [110] directions, i.e., perpendicularly to the surface (001) plane. Titan Cubed 80-300 electron transmission microscope operating with accelerating voltage 300 kV and equipped with energy-dispersive X-ray spectrometer (EDXS) is used for the study. Most of the investigations are done on Cu grids, but for EDXS elemental analysis a Mo grid is used to avoid interference of Cu fluorescence signal from the grid. This analysis yields percentage atomic concentration at 37(3) : 32(5) : 31(7) for Cu, Mn, and Sb, respectively, which, within the experimental errors (given in the parentheses), correspond to the expected stoichiometric ratio of 33 : 33 : 33.
SQUID Magnetometry. Magnetic characterization is performed in a commercial superconducting quantum interference device (SQUID) magnetometer MPMS XL7. The magnetic moment of antiferromagnetic layers is generally very weak and by far dominated by the magnetic response of the bulky semiconductor substrates. Therefore, to counter act the typical shortcomings of commercial magnetometers built around superconducting magnets[36](#page-12-19) and to minimize subtraction errors during
![<span id="page-2-1"></span>FIG. 1. (a) High-angle annular dark-field scanning transmission electron microscopy image of a CuMnSb layer in the [100] zone axis. The inset in the top-right corner brings up a part of the image in atomic resolution, where bright dots represent columns of Mn and Sb atoms. (b) Electron diffraction pattern of the layer. (c) Schematics of the positions of Bragg's spots from (b). Big bullets represent the main reflections from the cubic CuMnSb structure, whereas the open triangles mark the positions of the weak extra reflections. The orientation of the triangles follows from the analysis of the data in panels (d-g). (d-e) Blown up two regions from (a), in which either vertical or horizontal strips dominate. The corresponding Fourier transforms are showed in the top right corners of both panels. (f) Selected area electron diffraction pattern taken at the regions dominated by the vertically oriented strips. (g) Diffraction intensity profiles taken along the horizontal [010]\* and the vertical [001]\* lines passing through the center the diffraction pattern. The solid line corresponds to the horizontal [010]\* direction and the dashed one to the vertical [001]\* one in panel (f). Stars denote directions in the reciprocal space. The arrows α and β indicate the length of α–2g(002) and β–2g(002) diffraction vectors, respectively.](path)
data reduction we actively employ the in situ compensation.[37](#page-12-20) It allows us to reduce the coupling of the signal of the substrates to about 10% of their original strength. The actual effectiveness of the compensation depends on the mass of the sample and its orientation with respect to the SQUID pick-up coils.[36,](#page-12-19)[38](#page-12-21) We also strongly underline the importance of a thorough mechanical removal of the metallic MBE glue from the backside of the samples for any magnetic studies. Its strongly nonlinear magnetic contribution can be of the same magnitude as that of the layer of interest.[39](#page-12-22) To accurately establish the magnitude of magnetic moment specific to CuMnSb we measure a reference sample grown without the CuMnSb layer[29](#page-12-12) using the same sample holder and following exactly the
#### <span id="page-2-0"></span>B. Structural characterization
An exemplary atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF/STEM) image obtained for the [100] zone axis (the direction of the projection) is in Fig. [1](#page-2-1) (a). It confirms a high quality cubic constitution of the material, as it is underlined in the inset. However, at the contrast chosen here, the image in this field of view reveals the presence of stripe-like features, which are the main subject of this analysis. In this image, the apparent lengths and widths of the strips are about 40 nm and about 4 nm, respectively, running predominantly either vertically or horizontally in this particular projection. On other images, the strips exhibit a relatively wide distribution of lengths in the 10-100 nm window. Since similarly distributed shadowy stripes are observed also in the [110] zone axis, we conclude that they form along all three principal crystallographic directions without any particular preferences. The expected F43m cubic structure of α–CuMnSb is clearly confirmed by the fourfold symmetry of the dominant (bright) spots seen on electron diffraction pattern presented in Fig. [1](#page-2-1) (b).
Importantly, the diffraction pattern in Fig. [1](#page-2-1) (b) contains also a second set of much fainter reflections, situated halfway between two adjacent reflections of the main pattern. This indicates the presence of a second crystallographic β phase, which periodicity in the corresponding direction is doubled relative to that of α–CuMnSb, but otherwise coherent with this host structure. We bring all the Bragg's spots up in Fig. [1](#page-2-1) (c), in which the bullets represent the main reflections from α–CuMnSb, whereas the open triangles mark the positions of the weak ones, which are forbidden for this structure.
The presence of β–CuMnSb is further substantiated by the inspection of the two close-ups from Fig. [1](#page-2-1) (a), shown in Fig. [1](#page-2-1) (d) and (e). At this magnification they reveal that, on top of the otherwise cubic arrangement of atomic columns, the strips' brightness alternates every second {002} plane along the direction perpendicular to strip's long axis. The modulation is vertical in Fig. [1](#page-2-1) (d), whereas it goes horizontally in Fig. [1](#page-2-1) (e). The top right corners of these figures contain the corresponding Fourier transform of the parent image, and, similarly to Fig. [1](#page-2-1) (b), both patterns are dominated by the main reflections of α–CuMnSb. The additional spots are embedded either along vertical [Fig. [1](#page-2-1) (d)] or horizontal [Fig. [1](#page-2-1) (e)] lines, i.e., the presence of vertical and horizontal orientations is mutually exclusive. This feature is reflected in Fig. [1](#page-2-1) (c), where the additional spots are marked by differently oriented triangles. The triangles with apexes directed vertically correspond to the vertical orientation of the brightness modulation in Fig. [1](#page-2-1) (d), whereas the horizontal direction of apexes corresponds to the horizontal modulation.
Based on the data shown above we propose that the second phase of CuMnSb, present in our films in the form of strips, is a tetragonal structure, which also is the structure of epitaxial CuMnAs,[19–](#page-12-2)[21](#page-12-4)[,23](#page-12-6)[–25](#page-12-8) and of CuMnSb at high pressures.[27](#page-12-10) This β–CuMnSb polymorph is shown in the panel (b) of Fig. [2.](#page-3-0) The difference between α and β phases consists in the location of Cu ions: in the α phase every (001) plane between two consecutive MnSb planes is half-occupied by Cu, whereas in the β phase Cu ions completely fill up every second (001) plane, and the overall stoichiometry of the material is preserved.
![<span id="page-3-0"></span>FIG. 2. Crystal structures of (a) α–CuMnSb with the cubic lattice constant a, (b) tetragonal β–CuMnSb with the lattice constants a in the (x, y) plane and c in the [001] direction, and (c) Cu3Mn2Sb2.](path)
regions with different orientations of the strips. Diffraction pattern of an area dominated by the vertically oriented strips is shown in more detail in Fig. [1](#page-2-1) (f). In agreement with the Fourier transforms, SAED shows the occurrence of specific reflections corresponding to this particular orientation. The reflections common to both the cubic α and the tetragonal β polymorphs are split along the [010]\* direction, i.e., orthogonal to the strip's axis, whereas the weak spots of the β phase are not split and are commensurate with the cubic phase. (A star denotes a direction in the reciprocal space.)
We quantify the effect analyzing intensity profiles taken along lines passing through the center of diffraction. The profiles are superimposed, and presented in Fig. [1](#page-2-1) (g). The profile along the [001]\* direction reflects the periodicity of α–CuMnSb, while that along [010]\* is additionally split. From the Figure it follows that in our specimens the c lattice parameter of the β–CuMnSb strips is equal to that of the host α–CuMnSb, 6.2(1) ˚A, whereas the a and b parameters of the β phase, 5.8(1) ˚A, are smaller by about 7%. Analogous features are observed for the [010]-oriented strips.
The existence of such a significant strain is confirmed by the calculation of strain maps. We apply the geometrical phase analysis method[40](#page-12-23) for the main image presented in Fig. [1](#page-2-1) (a), and the results are presented in Fig. [3](#page-4-1) (a) and (b) for the horizontal, ϵxx, and the vertical, ϵzz, components of strain, respectively. It is seen that stripes' strain is negative (dark shade) perpendicular to strips and almost zero along the strips. For example, on the horizontal strain map [Fig. [3](#page-4-1) (a)] only vertical strips are visible because they are compressed horizontally, whereas the horizontal strips are invisible because they are not deformed in the horizontal direction.
 (a). (a) The horizontal component of strain ϵxx, and (b) the vertical one, ϵzz. Geometrical phase analysis method has been applied.[40](#page-12-23)](path)
The calculated properties of β–CuMnSb, such as its lattice parameters, stability, and magnetic properties, are discussed in detail in Sec. [III C.](#page-7-0) Anticipating, we mention that they are consistent with experiment. We have also considered a second possible structure which is (almost) compatible with the TEM data, Cu3Mn2Sb2, depicted in Fig. [2](#page-3-0) (c). However, this compound is higher in energy than the β phase, and was dropped from further considerations.
#### <span id="page-4-0"></span>C. Magnetic properties
The temperature T dependence of magnetization, M(T), of the 200 nm thick layer of CuMnSb, is depicted in Fig. [4](#page-4-2) (a). The clear kink on M(T) at T<sup>N</sup> = 62 K marks the position of the paramagnetic to antiferromagnetic N´eel transition in the layer. This value corresponds precisely to the values of T<sup>N</sup> established previously for CuMnSb/GaSb layers of the thickness t ≥ 200 nm, what, indirectly, indicates stoichiometric material composition of this layer.[29](#page-12-12)
More specific information about the magnetic state of that sample is obtained from the examination of the temperature dependence of the inverse magnetic susceptibility, χ −1 (T), shown in Fig. [4](#page-4-2) (b). We take here χ(T) = M(T)/H, where H = 10 kOe is the external magnetic field applied during the measurements. χ −1 (T) can be approximated by two straight lines. The abscissa of the first one, which approximates χ −1 (T) above 200 K (the solid orange line in Fig. [4\)](#page-4-2), yields exactly the same magnitude of the Curie-Weiss temperature TCW = −100(5) K as that established previously for a thicker 510 nm layer, for which χ −1 (T) formed a single straight line above T<sup>N</sup> at the same experimental conditions.[29](#page-12-12) Also the slope of this line yields the value of the effective magnetic moment meff = 5.4(1)µ<sup>B</sup> per f.u., which is very close to that found previously, meff = 5.6µ<sup>B</sup> per f.u.[29](#page-12-12) This correspondence indicates that the high temperature part of χ −1 (T) is determined predominantly by AFM excitations in the paramagnetic matrix of CuMnSb.
The abscissa of the second straight line, which approximates the experimental data between T<sup>N</sup> and about 200 K (marked as the dashed orange line in Fig. [4\)](#page-4-2), yields a more positive value of the Curie-Weiss temperature, T ′ CW = −10(10) K. This clear positive shift of TCW indicates the existence of a ferromagnetic contribution to the overall antiferromagnetic phase of the material, and that these FM excitations gain in importance below about 200 K. Interestingly, a somewhat stronger effect, characterized by a change of sign of TCW to T ′ CW = +60(10) K, was noted in 40 nm CuMnSb layer grown on InAs.[34](#page-12-17) In accordance with the findings of structural characterization we propose that the by far stronger AFM component originates from the dominant α phase, whereas the FM one is brought about by β–CuMnSb polymorph.
<span id="page-5-1"></span>TABLE I. Experimental N´eel temperature TN, effective Curie-Weiss magnetic moment of Mn ions meff (Mn), and Curie-Weiss temperature TCW of α–CuMnSb. Measured orientation of the AFM axis is also given (n.e. = not established). Refs. [42](#page-12-24) and [41](#page-12-25) report the saturation Mn moment.
Turning now to the magnetic characteristics established here for α–CuMnSb we note that they are close to those reported previously, as shown in Tab. [I.](#page-5-1) The published data exhibit a certain distribution, which may indicate that other factors, such as a weak crystalline disorder, may be at work. In particular, either additional Mn interstitial ions or CuMn-MnCu antisite pairs are likely to form.[35](#page-12-18) The presence of such defects was suggested to stabilize the experimentally observed AFM {111}-oriented phase of α–CuMnSb.[35](#page-12-18) Finally, we do not observe a canted AFM order at low temperatures[41](#page-12-25) in any of our samples.
#### <span id="page-5-0"></span>III. THEORY
## A. Theoretical Methods
Calculations are performed within the density functional theory[46,](#page-13-2)[47](#page-13-3) in the generalized gradient approximation of the exchange-correlation potential proposed by Perdew, Burke and Ernzerhof.[48](#page-13-4) To improve description of 3d electrons, the Hubbard-type +U correction on Mn is added.[49–](#page-13-5)[51](#page-13-6) The parameter U(Mn) = 1 eV reproduces the known formation energy of the intermetallic CuMn alloy and gives a reasonable value of the Mn cohesive energy. We use the pseudopotential method implemented in the Quantum ESPRESSO code,[52](#page-13-7) with the valence atomic configuration 4s <sup>1</sup>.<sup>5</sup>p <sup>0</sup>3d 9.5 for Cu,
3s 2p <sup>6</sup>4s 2p <sup>0</sup>3d 5 for Mn and 5s 2p 3 for Sb ions. The planewaves kinetic energy cutoffs of 50 Ry for wave functions and 250 Ry for charge density are employed. Finally, geometry relaxations are performed with a 0.05 GPa convergence criterion for pressure. In defected crystals ionic positions are optimized until the forces acting on ions become smaller than 0.02 eV/˚A.
The properties of defected α–CuMnSb are examined using cubic 2a×2a×2a supercells with 96 atoms (i.e., 32 f.u.), while magnetic order of ideal crystals are checked using the smallest possible supercells. Here a is the equilibrium lattice parameter. The k-space summations are performed with a 6 × 6 × 6 k-point grid for the largest supercell, and correspondingly denser grids are used for smaller cells.
Magnetic interactions and magnetic order depend on several factors, such as the exchange spin splitting of the d(TM) shells, charge states of TM ions, concentration of free carriers and their spin polarization, and the density of states (DOS) at the Fermi energy EF. These factors are interrelated, and are calculated self-consistently within ab initio approach.
Considering first the localized magnetic moments we note that spin polarization of Co, Ni, and Cu ions in XMnZ compounds practically vanishes, while that of the d(Mn) shell is substantial.[16,](#page-11-14)[17](#page-12-0)[,31](#page-12-14) The robustness of the Mn magnetic moment results from the large, 3 – 5 eV, spin splitting of the 3d(Mn) states. In fact, in XMnZ the d(Mn) spin up channel is occupied, while most of the spin down d(Mn) states lay above the Fermi level. Here, one can observe that spin polarization of the d(TM) electrons in free atoms depends on the difference in the number of spin up and spin down electrons, which is the highest in the case of Mn. Consequently, the Mn spin polarization persists in XMnZ. On the other hand, spin splitting of d electrons of Co and Ni atoms is smaller, and thus it vanishes in XMnSb hosts, see the analysis for TM dopants in ZnO.[53](#page-13-8)
In CuMnSb, the magnetic sublattice consists of Mn ions, which are second neighbors distant by 4.3 ˚A. Therefore, the direct exchange coupling between two Mn ions, given by overlaps of their d(Mn) orbitals, is negligibly small. The remaining indirect exchange coupling is the sum of two contributions, and the exchange constant Jindirect = Jsr + JRKKY . [16](#page-11-14)[,17](#page-12-0)[,54](#page-13-9) The first term Jsr has a short-range AFM character, and it is inversely proportional to the energy distance between the unoccupied d(Mn) states and EF. The second coupling channel is of RKKY type mediated by free carriers. This channel depends on the detailed electronic structure in the vicinity of EF, and JRKKY is proportional to DOS(EF). In particular, CoMnSb and NiMnSb half-metals are FM, while CuMnP and CuMnAs insulators are AFM. As we show here, CuMnSb is the border case.
#### <span id="page-5-2"></span>B. Crystal and magnetic properties of α–CuMnSb
A rhombohedral primitive cell of α–CuMnSb contains one formula unit. This structure consist in four interpenetrating fcc sublattices, one of them being empty. The consecutive (001) MnSb planes are followed by the "halfempty" Cu planes, in which the planar atomic density is twice lower. The cubic unit cell is presented in Fig. [2](#page-3-0) (a). Local coordination of Mn ions can be relevant from the point of view of magnetic interactions. With this respect we notice that the magnetic coordination of an Mn ion consists in 12 equidistant Mn atoms at a/<sup>√</sup> 2. More-
We consider four magnetic phases of α–CuMnSb. The corresponding supercells are shown in Fig. [5.](#page-6-0) Antiferromagnetic order with parallel Mn spins in the (001) planes, AFM001, is calculated using the cubic a×a×a cell with 4 f.u. (12 atoms), and shown in Fig. [5](#page-6-0) (a). The AFM order with a period doubled in the [001] direction with parallel Mn spins in each (001) plane, denoted as AFM002, is shown in Fig. [5](#page-6-0) (b). The corresponding a×a×2a cell contains 8 f.u., and is one of the possible supercells in which this phase can be realized. In the AFM111 phase, the Mn spins are parallel in each (111) plane, but the consecutive (111) planes are AFM, as shown in Fig. [5](#page-6-0) (c), and the corresponding rhombohedral unit cell a √ 2 × a √ 2 × a √ 2 contains 8 primitive cells with 24 atoms. Finally, the FM phase requires a primitive cell a/<sup>√</sup> 2×a/<sup>√</sup> 2×a/<sup>√</sup> 2 with 1 f.u., presented in Fig. [5](#page-6-0) (d).
<span id="page-6-1"></span>TABLE II. The calculated lattice parameter a, the saturation Mn magnetic moment, msat, and the energy of the given magnetic order relative to α–CuMnSb in the AFM001 ground state, ∆Etot. All energies are per one formula unit. Our measured TEM values are also given.
higher in energy. The least stable is the FM order, higher in energy than AFM001 by about 20 meV per f.u. The equilibrium lattice parameters a ≈ 6.1 ˚A are practically independent of the magnetic order, and close to the experimental value 6.088 ˚A.[42](#page-12-24) Some phases are characterized by a small distortion of the cubic symmetry caused by different bond lengths between ferromagnetically and antiferromagnetically oriented Mn ions. Differences in the lattice parameters between various magnetic phases are below 0.01 ˚A, and are not reported in the Table. Similar results for the AFM001 order were obtained in Ref. [35,](#page-12-18) while in Refs [16](#page-11-14) and [31](#page-12-14) the AFM order is more stable than FM by 50 and 90 meV per Mn, respectively.
The last property reported in Tab. [II](#page-6-1) is the saturation magnetic moment of Mn, which also is similar in all phases, and equal to about 4.6µB. This value corresponds to the Curie-Weiss moment of 5.5(1)µB, and compares favorably with the experimental values given in Tab. [I.](#page-5-1)
The obtained results allow estimating the relative roles of the short- and long-range contributions to the magnetic coupling. To this end, we assume the hamiltonian in the form Hex = −J/2 P i,j ⃗si⃗s<sup>j</sup> , where the short range interaction is limited to the Mn NNs neighbors, and the long-range term is neglected. The spin value, s<sup>i</sup> ≈ 2.3, is one half of the calculated magnetic moment of Mn.
The exchange constant J is positive (negative) for the FM (AFM) coupling, and is obtained by comparing energies of various magnetic orders. In the AFM001 phase, each Mn ion has 4 ferromagnetically oriented Mn NNs in the (001) plane and 8 antiferromagnetically oriented Mn NNs in the two adjacent planes. For the remaining magnetic phases, the energies calculated relative to the ground state E<sup>0</sup> ≡ EAFM001 depend on the magnetic order as shown in Tab. [II.](#page-6-1) These results give the coupling constant in the range −0.6 ≥ Jsr ≥ −0.2 meV. This spread is quite large and cannot be explained by (negligible) changes in atomic distances in cells with different magnetic ordering. Therefore, we conclude that the Heisenberg nearest neighbor model does not describe magnetic properties of bulk phases. Indeed, such a model is not appropriate for metallic or semimetallic systems such as α–CuMnSb, where the long-range RKKY coupling is present.
An opposite conclusion comes from the analysis of single spin excitations from the AFM001 ground state. We use a 2a×2a×2a supercell to calculate the energy differences ∆E for the following cases, in which we change (i) spin of one Mn ion, 1Mn ↑→ 1Mn ↓, called a single spin-flip, (ii) 2Mn↑→ 2Mn↓ for spins of two nearest Mn ions belonging to one layer and (iii) 2Mn ↑→ 2Mn ↓ for two distant Mn ions. In these processes the long-range coupling is not important, and indeed the calculated exchange constant consistently is Jsr ≈ −0.4 meV.
#### <span id="page-7-0"></span>C. Crystal and magnetic properties of β–CuMnSb
We now consider two possible structures of the secondary phase proposed based on the experimental results. They are characterized by doubling the periodicity in the [001] direction. The unit cell of β–CuMnSb, shown in Fig. [2,](#page-3-0) is tetragonally deformed relative to that of α–CuMnSb, with the corresponding lattice parameters a = 5.88 ˚A and c = 6.275 ˚A. They differ by about 3 per cent from our calculated cubic a(α– CuMnSb) = 6.105 ˚A. The two interlayer spacings between the consecutive MnSb planes in the [001] direction in the unit cell, shown in Fig. [2](#page-3-0) (b), are quite different, namely dinter<sup>1</sup> = 2.80 ˚A (no Cu), and dinter<sup>2</sup> = 3.48 ˚A (with Cu). Turing to the magnetic order of β–CuMnSb, we find that the FM phase constitutes the ground state with msat = 4.6µ<sup>B</sup> and is lower than the AFM phase by 11 meV per f.u., as indicated in Tab. [II.](#page-6-1) Thus, the
The experimental[27](#page-12-10) lattice parameters of β–CuMnSb reasonably agree with our values, i.e., the calculated a = 6.28 ˚A and c/a = 1.87 are about 2% larger than those measured for the compressed crystal at the critical pressure of 7 GPa. On the other hand, the calculations of Ref. [27](#page-12-10) predict that the magnetic order of the β phase is AFM, in striking contrast with our results. Also their calculated msat(Mn) = 3.8µ<sup>B</sup> is substantially smaller than our 4.6µB. The origin of these discrepancies is not clear, but it may be due to the different exchange-correlation functionals used, and/or to application of the +U(Mn) correction in our calculations (which can affect the results.[31](#page-12-14))
The calculated total energy of the FM β–CuMnSb relative to the AFM α–CuMnSb is higher by 102 meV per f.u. This energy difference is not large, being comparable to the growth temperature, which implies that the β–CuMnSb polymorph can indeed form during epitaxy. We also stress that stoichiometry of the α and β phases is the same, which facilitates formation of β–CuMnSb. Finally, the observed β–CuMnSb inclusions are coherent, i.e., lattice matched, with the host structure. This agrees with the fact that the calculated excess elastic energy of matching the lattice parameters of the β phase to the host α phase is very low and ranges from 3 meV per f.u. (when the tetragonal a parameter constrained to the cubic a = 6.105 ˚A) to 20 meV per f.u. (the tetragonal c parameter constrained to the cubic a).
The second considered possibility, Cu3Mn2Sb<sup>2</sup> shown in Fig. [2](#page-3-0) (c), is higher in energy by 0.37 eV per f.u. in the Cu–rich conditions than the ideal CuMnSb, i.e., by 0.27 eV per f.u. than β–CuMnSb, its stoichiometry is markedly different, and thus we can eliminate this structure from considerations.
# D. Energy band structures of α–CuMnSb and β–CuMnSb
Figure [7](#page-8-1) (a) shows the energy bands and DOS of the AFM001 α–CuMnSb. We see that this phase has a metallic character, however DOS at the Fermi level is low. The states close to E<sup>F</sup> are built from s, p and d states of all ions with similar weights. The low DOS(EF) makes CuMnSb almost semimetallic with a low electrical conductivity. Compatible with the small DOS(EF) is the high resistivity measured in Ref. [41](#page-12-25) and [55.](#page-13-10)
Since the system is antiferromagnetically ordered, the total DOSs of spin-up and spin-down states are the same. In Fig. [7](#page-8-1) only contributions of the 3d(Mn) and 3d(Cu) orbitals are presented to reveal magnetic properties. We see that the exchange spin splitting of the d(Mn) shell is large, about 5 eV. The closely spaced levels contributing to the DOS maxima centered at 4 eV below the Fermi energy are composed mainly of the d states of both Cu and Mn. Spin-up and spin-down 3d(Cu) orbitals are almost
completely occupied, and thus Cu ions are non-magnetic. In turn, the majority spin states of the 3d(Mn) orbitals are completely occupied, while the minority spin states at 1 eV above the Fermi energy are partially filled thanks to a small overlap with spin up states. As a result, a single Mn ion is in between the d <sup>5</sup> and d 6 configuration, with the saturation magnetic moment of 4.6µ<sup>B</sup> consistent with Tab. [II.](#page-6-1) Our results for α–CuMnSb are close to those of Ref. [31.](#page-12-14) A similar electronic configuration takes place in CuMnAs, where the spin-down Mn states are partially filled.[56](#page-13-11)
The overall band structure of the FM β–CuMnSb displayed in Fig. [7](#page-8-1) (b) is close to that of α–CuMnSb, which is particularly clear when comparing partial DOS of both phases. In particular, msat(Mn) is about 4.5µ<sup>B</sup> in both phases, and energies of both d(Mn)- and d(Cu)-related bands are largely independent of the actual crystal structure. This similarity can be due to the fact that the MnSb (001) planes play a dominant role, and the exact locations of the Cu ions are less important.
On the other hand, the calculated DOS(EF) for the α phase is 0.35 states per spin and f.u., while for the β phase we find 1.26 states per spin and f.u., which is 3.6 times higher. As a consequence, α–CuMnSb is semimetallic, and the AFM order is dominant, while β phase is more metallic in character, which in turn favors the RKKY-type coupling and the FM order. This feature can explain the different magnetic phases of the α and β polymorphs.
Analysis of the calculated electronic structure of Heusler and half-Heusler CuMnZ led Sasioglu et al.[17](#page-12-0) to the conclusion that when the spin polarization of conduction electrons is large, and the d(Mn) spin down states are far above EF, then the RKKY coupling is dominant, and one should expect the FM order, otherwise the short range AFM coupling is dominant. Our results do not confirm this conclusion, and indicate that the important
## <span id="page-8-0"></span>E. Point native defects in α–CuMnSb
where E(CuMnSb) and E(CuMnSb : D) are the total energies of a supercell without and with a defect, and n<sup>i</sup> = +1(−1) corresponds to the removal (addition) of one ith atom. µis are the variable chemical potentials of atoms in the solid, which in general are different from the chemical potentials µi(bulk) of the standard state of elements, i.e., Cu, Mn and Sb bulk. Details of calculations of chemical potentials are given in Appendix [A.](#page-10-0)
The point native defects considered here are vacancies VX, interstitials X<sup>i</sup> , and antisites X<sup>Y</sup> (where X and Y are Cu, Mn, or Sb) for all three sublattices. As it was mentioned above, the Cu sublattice is "half- empty" compared to the MnSb sublattice. Consequently, we consider here formation of interstitials at the empty sites of the Cu sublattice only, and neglect other possibilities, expected to have higher formation energies Eform. Thus, the set of defects considered here only partially overlaps with that of Ref. [35.](#page-12-18) Of particular interest to the present study are defects involving Mn ions, since they can influence magnetic properties of α–CuMnSb .[35](#page-12-18) This is why we consider them more extensively, after briefly analyzing the non-magnetic defects. The calculated formation energies are summarized in Tab. [III.](#page-9-0) Because of the magnetic coupling, formation energies of the Mn-related defects depend on the spin direction relative to the spins of the host Mn neighbors. We consider possible spin configurations shown in Fig. [8](#page-9-1) (b).
<span id="page-9-0"></span>TABLE III. Formation energies (in eV) of isolated point defects in the Mn-rich conditions. In parentheses are Mn-related values corrected for ∆H<sup>f</sup> (MnSb) = 0.48 eV, which correspond to the Mn-poor case.
where k<sup>B</sup> is the Boltzmann constant and N<sup>0</sup> is the density of the relevant lattice sites. Details of the calculations of Eform are provided in Supporting Information. To put the calculated formation energies into a proper context, we note that if the growth temperatrure Tgrowth = 2500C and Eform = 0.1 eV, then exp(−Eform/kBTgrowth) = 0.1, which corresponds to a high 10 atomic per cent concentration of this defect on the considered sublattice. On the other hand, if Eform = 1 eV, then exp(−Eform/kBTgrowth) = 9 × 10<sup>−</sup><sup>11</sup>, which implies a negligible defect concentration.
Sb sublattice. The prohibitively high values of Eform demonstrate that VSb and Sb<sup>i</sup> should not form. Similarly, formation energies of SbCu, SbMn, CuSb and MnSb antisites exceed 1 eV, and those defects are not expected to be present at high concentrations. Consequently, the Sb sublattice is thermodynamically stable, robust, and constitutes a defect-free back-bone of CuMnSb.
(ii) Formation energy of Cu interstitials at the Cu sublattice, Eform(Cui) = 1 eV, is relatively high, and their concentrations are negligible. Additionally, the high formation energy of Cu<sup>i</sup> interstitials is consistent with the sparse character of the Cu sublattice in α–CuMnSb.
(iii) Formation of Mn<sup>i</sup> interstitials at the Cu sublattice is characterized by Eform = 0.7-1.4 eV, depending on the spin direction and conditions of growth, and therefore they are not expected to be present at high concentrations, especially in the Mn-poor conditions.
In brief, low formation energies are found for three defects, namely the VCu and VMn vacancies and the MnCu antisite, particularly at the Mn-rich growth conditions. This indicates that a Cu deficit on the Cu sublattice is possible, affecting stoichiometry. Significantly, MnCu antisites make the Cu sublattice magnetic, and also they can participate in the magnetic coupling between the adjacent MnSb (001) planes, thus influencing magnetic properties, as it will be discussed in more detail below. In contrast, SbCu antisites are present in negligible concentrations. Our results are in a reasonable agreement with those of Ref. [35,](#page-12-18) especially given their neglect of spin effects and a somewhat different theoretical approach. Interestingly, formation energies of native defects in CuMnAs calculated in Ref. [56](#page-13-11) are close to the present results in spite of the different anion.
## F. Defect-induced magnetic coupling
There are two Mn-related point defects, Mn<sup>i</sup> and MnCu, both situated on the Cu sublattice. When present at high concentrations, they affect magnetism of α– CuMnSb. Their coupling with host Mn ions is different than the Mn-Mn coupling between the host Mn because of the different local coordination. Energetics of both defects is complex and rich, since the total energy of the system (and thus formation energies) depends on their spin orientations relative to the neighborhood. At both substitutional and interstitial sites in the Cu layer, a Mn ion has 4 Mn nearest neighbors arranged in a tetrahedral configuration, 2 in the upper and 2 in the lower MnSb layer. The Mni–MnMn distance is shorter than that of
MnMn–MnMn, and equal to (<sup>√</sup> 3/4)a.
The possible local spin configurations are reduced to small clusters of 5 Mn ions, shown in Fig. [8.](#page-9-1) The Mn spin-up and spin-down (001) MnSb layers are denoted by in pink and blue, respectively, reflecting the calculated (001) AFM magnetic ground state. The central MnCu (or Mni) ion of such a cluster provides an additional channel of magnetic coupling between two adjacent MnSb layers. The corresponding formation energies are given in Fig. [8.](#page-9-1)
As it was pointed out, in ideal α–CuMnSb, the Mn ions are second neighbors only, separated either by Sb (i.e., the Mn-Sb-Mn "bridge" in the MnSb(001) plane), or by Cu (forming a Mn-Cu-Mn "bridge" linking 3 consecutive (001) planes.) Thus, the short range magnetic coupling in ideal α–CuMnSb is successfully modelled in Sec. [III B](#page-5-2) by the interaction between two Mn second neighbors, situated either in the same MnSb layer, or in two adjacent ones. In contrast, the 4 host Mn ions in the cluster are the first neighbors of a Mn<sup>i</sup> or a MnCu defect. Thus, one can expect that this coupling is stronger than the intrinsic one in the ideal host, and indeed, the differences in energy between various configurations in Fig. [8](#page-9-1) are about 100 meV, which is too high to be explained by the estimated Jsr = 0.4 meV.
As it follows from Fig. [8,](#page-9-1) 5-atom clusters are magnetically frustrated. In particular, the lowest energy case denoted as 4AFM favors the local FM orientation of spins in two adjacent (001) planes, which is opposite to the global host magnetic order. Our results do not confirm the conclusion of Ref. [56](#page-13-11) who find that the 3AFM configuration has the lowest energy, and thus it promotes the global AFM111 order. Instead, we rather expect that Mn-related point defects induce disorder of the host AFM phase, possibly leading to formation of a spin glass.[57](#page-13-12)
#### IV. SUMMARY
CuMnSb films were epitaxially grown on GaSb substrates. Magnetic measurements reveal the presence of two magnetic subsystems. The dominant magnetic order is AFM with the N´eel temperature of 62 K, which is the same as in bulk CuMnSb. It co-exists with a FM phase, characterized by the Curie temperature of about 100 K.
These findings go in hand with transmission electron microscopy and selective area diffraction measurements, which demonstrate coexistence of two structural polymorphs of the same stoichiometry. The dominant one is the cubic half-Heusler α–CuMnSb, which is the equilibrium structure of bulk samples. The second component is a tetragonal β–CuMnSb polymorph, which forms 10-100 nm long elongated inclusions.
(i) The β–CuMnSb phase is metastable, and its total energy is higher by 0.1 eV per f.u. only than that of the equilibrium α–CuMnSb. Lattice parameters of the β phase differ from those of α–CuMnSb by about 4 per cent. This lattice misfit between the two structures does not prevent the pseudomorphic coexistence of both phases, since the calculated misfit strain energy is below 20 meV per f.u.
(ii) In agreement with experiment, α–CuMnSb is AFM, and the FM order is 19 meV per f.u. higher in energy. In contrast, the magnetic ground state of β– CuMnSb is FM, which is more stable than AFM by 11 meV per f.u. This indicates that indeed the β–CuMnSb inclusions are responsible for the FM signal.
(iii) The different magnetic orders of the α and β phases originate in their somewhat different band structures. In particular, critical for magnetic order is the DOS at the Fermi level, which is about 4 times higher in β–CuMnSb than in the α phase. This shows that the β phase is more metallic in character, which in turn favors the FM order driven by the Ruderman-Kittel-Kasuya-Yoshida interaction.
(iv) Our calculations predict the saturated magnetic moment of Mn msat = 4.6µ<sup>B</sup> and 4.5µ<sup>B</sup> for the α and the β phase, respectively. This corresponds to the effective moment of 5.6µB, in good agreement with the measured 5.5µB.
(v) The calculated formation energies of point native defects indicate that the most probable are the MnCu antisites with low formation energies of 0–0.2 eV. However, their presence is expected to disorder the host magnetic AFM phase rather than to induce a transition to the FM configuration.
(vi) Regarding the properties of the CuMnX series we see that their structural stability is relatively weak, as they crystallize in a variety of structures. In particular, unlike the bulk orthorhombic CuMnAs, epitaxial films of CuMnAs are tetragonal, but both structures are AFM. In the case of CuMnSb, polymorphism comprises also the equilibrium magnetic structure, AFM in the bulk specimens, and FM in epitaxial films.
#### ACKNOWLEDGMENTS
LS, CG, JK and LWM thank M. Zipf for technical assistance. Our work was funded by the Deutsche Forschungsgemeinschaft (DFG,German Research Foundation) No. 397861849, by the Free State of Bavaria (Institute for Topological Insulators) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC2147 ct.qmat (Project-Id 390858490).
#### <span id="page-10-0"></span>Appendix A:
The highest possible value of µ<sup>i</sup> is µi(bulk), which implies that the studied system is in equilibrium with the given bulk source of atoms and δµ<sup>i</sup> = 0, otherwise δµ<sup>i</sup> < 0.
Chemical potentials of the components in the standard state are given by the total energies per atom of elemental solids. The calculated cohesive energies Ecoh of the face centered cubic Cu, the face centered cubic Mn with the AFM magnetic order, and the triclinic Sb are, respectively, 3.40 (3.49), 2.65 (2.92) and 2.68 (2.75) eV/atom. They compare reasonably well with the experimental values given in parentheses.[58](#page-13-13)
Chemical potentials of the involved atomic species depend on possible formation of compounds. The ranges of variations of chemical potentials are determined by conditions of equilibrium between various phases, i.e., Cu2Sb, MnSb and CuMnSb. Thermodynamic equilibrium requires that
$$\begin{aligned} \delta\mu(\text{Cu}) + 2\delta\mu(\text{Sb}) &= \Delta H\_f(\text{Cu}\_2\text{Sb}), \\ \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{MnSb}), \\ \delta\mu(\text{Cu}) + \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{CuMnSb}), \end{aligned} \quad \text{(A2)}$$
The calculated values ∆H<sup>f</sup> (Cu2Sb) = −0.03 eV per f.u., ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u., and ∆H<sup>f</sup> (CuMnSb) = −0.42 eV per f.u. The very low ∆H<sup>f</sup> (Cu2Sb) is somewhat unexpected, since Cu2Sb is a stable compound which crystallizes in the tetragonal phase.[43](#page-12-26) Next, our result ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u. agrees well with both the previous value -0.52 eV per f.u. calculated in Ref. [59,](#page-13-14) and the experimental - 0.52 eV per f.u.[60](#page-13-15) Assuming that the accuracy of the calculated values is 0.03 eV per f.u., the set of Equation [A2](#page-11-15) is consistent if we assume ∆H<sup>f</sup> (Cu2Sb) = 0, and ∆H<sup>f</sup> (MnSb) = ∆H<sup>f</sup> (CuMnSb) = −0.45 eV per f.u. This in turn implies that δµ(Cu) = δµ(Sb) = 0, and δµ(Mn) = −0.45 eV. Consequently, the allowed window of the Mn chemical potential is
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| |
FIG. 1. (a) High-angle annular dark-field scanning transmission electron microscopy image of a CuMnSb layer in the [100] zone axis. The inset in the top-right corner brings up a part of the image in atomic resolution, where bright dots represent columns of Mn and Sb atoms. (b) Electron diffraction pattern of the layer. (c) Schematics of the positions of Bragg's spots from (b). Big bullets represent the main reflections from the cubic CuMnSb structure, whereas the open triangles mark the positions of the weak extra reflections. The orientation of the triangles follows from the analysis of the data in panels (d-g). (d-e) Blown up two regions from (a), in which either vertical or horizontal strips dominate. The corresponding Fourier transforms are showed in the top right corners of both panels. (f) Selected area electron diffraction pattern taken at the regions dominated by the vertically oriented strips. (g) Diffraction intensity profiles taken along the horizontal [010]* and the vertical [001]* lines passing through the center the diffraction pattern. The solid line corresponds to the horizontal [010]* direction and the dashed one to the vertical [001]* one in panel (f). Stars denote directions in the reciprocal space. The arrows α and β indicate the length of α–2g(002) and β–2g(002) diffraction vectors, respectively.
|
# Coexistence of Antiferromagnetic Cubic and Ferromagnetic Tetragonal Polymorphs in Epitaxial CuMnSb
High-resolution transmission electron microscopy and superconducting quantum interference device magnetometry shows that epitaxial CuMnSb films exhibit a coexistence of two magnetic phases, coherently intertwined in nanometric scales. The dominant α phase is half-Heusler cubic antiferromagnet with the N´eel temperature of 62 K, the equilibrium structure of bulk CuMnSb. The secondary phase is its ferromagnetic tetragonal β polymorph with the Curie temperature of about 100 K. First principles calculations provide a consistent interpretation of experiment, since (i) total energy of β–CuMnSb is higher than that of α–CuMnSb only by 0.12 eV per formula unit, which allows for epitaxial stabilization of this phase, (ii) the metallic character of β–CuMnSb favors the Ruderman-Kittel-Kasuya-Yoshida ferromagnetic coupling, and (iii) the calculated effective Curie-Weiss magnetic moment of Mn ions in both phases is about 5.5 µB, favorably close to the measured value. Calculated properties of all point native defects indicate that the most likely to occur are MnCu antisites. They affect magnetic properties of epilayers, but they cannot induce the ferromagnetic order in CuMnSb. Combined, the findings highlight a practical route towards fabrication of functional materials in which coexisting polymorphs provide complementing functionalities in one host.
#### I. INTRODUCTION
One of the most challenging and long-standing problems in fundamental magnetism is a competition between ferromagnetic and antiferromagnetic phases. Their interplay at the interface results in a well known effect of the exchange bias,[1](#page-11-1)[,2](#page-11-2) which fuels now a rapid development of spintronics[3](#page-11-3) and unconventional computing.[4](#page-11-4) The material class of Heusler alloys was previously used to study the origin of the transition between magnetic phases because it offers a wide spectrum of functionalities.[5](#page-11-5) Indeed, Heusler alloys exhibit ferromagnetic (FM), antiferromagnetic (AFM), and canted ferromagnetic order. This indicates that different types of magnetic coupling are competing in this family. Moreover, some of its members display structural polymorphism, which allows studying relationships between the crystalline phase, the magnetic phase, and the corresponding electronic structure.
Heusler alloys incorporate full-Heusler (X2YZ) and half-Heusler (XYZ) variants, where X and Y stand for transition metals, whereas Z denotes anions from the main group. In this class, qualitative changes in material characteristics can be achieved by chemical substitution on either the transition metal cation or on the anion sublattice. Typically, the change of the cation does not change the crystal structure, but it can induce a crossover between the AFM and the FM magnetic phases. A rarely met complete solubility with only marginally affected crystallinity of the otherwise chemically homogenous systems allowed to study the FM-AFM phase competition in detail. The prominent examples are quaternary solid solutions such as Ru2Mn1−xFexSn[6–](#page-11-6)[8](#page-11-7)
Heuslers, and Co1−xNixMnSb,[9](#page-11-8)[,10](#page-11-9) Cu1−xNixMnSb,[11–](#page-11-10)[13](#page-11-11) Co1−xCuxMnSb,[14](#page-11-12) and Cu1−xPdxMnSb[15](#page-11-13) half-Heuslers. In the latter case, the crossover between AFM to FM phases is related to a change in the electronic structure from semimetallic to half-metallic.[16](#page-11-14)[,17](#page-12-0)
Cu–based CuMnZ compounds are antiferromagnets. This feature attracts attention given the recent progress achieved in the AFM spintronics.[18](#page-12-1) Of particular interest is CuMnAs, with a high N´eel temperature T<sup>N</sup> = 480 K.[19](#page-12-2) In this case, features essential for applications, such as anisotropic magnetoresistance,[20,](#page-12-3)[21](#page-12-4) current-induced electrical switching of the N´eel vector[22](#page-12-5) and of the magnetic domains,[23](#page-12-6) have been demonstrated.
The AFM order of CuMnZ is independent of the actual crystalline structure. The equilibrium structure of bulk CuMnP and CuMnAs is orthorhombic, while that of CuMnSb is half-Heusler cubic, referred to below as the α phase. On the other hand, epitaxial growth can stabilizes metastable phases. This is the case of epitaxial layers of CuMnAs, grown on both GaP[19](#page-12-2)[–21](#page-12-4)[,24](#page-12-7)[,25](#page-12-8) and GaAs[23](#page-12-6) substrates, which crystalize in the tetragonal structure, referred to below as the β phase. Theoretical investigations of the crystalline properties of CuMnZ series show that the total energy difference between the cubic and orthorhombic phase is about 1 eV per f.u. (formula unit) for CuMnP, and about 0.5 eV per f.u. for CuMnAs.[26](#page-12-9) This suggests that the orthorhombic phase of CuMnSb, the last member of the CuMnZ series, may not be stable, and indeed the stable structure is the α phase. However, as we show here, epitaxial stabilization of CuMnSb in the β phase is in principle possible, because the calculated energy difference between
Concerning the magnetic properties, the N´eel temperature of both orthorhombic CuMnAs and β–CuMnAs is well above the room temperature,[19](#page-12-2) whereas that of α– CuMnSb is lower, about 60 K.[28,](#page-12-11)[29](#page-12-12) Theory agrees with experiment, since according to Ref. [30,](#page-12-13) in the orthorhombic CuMnP and CuMnAs, the AFM order is more stable than the FM by about 250 meV/Mn. This energy difference is smaller in the cubic phase of CuMnZ compounds, for which the AFM order is lower in energy than FM one by about 50 meV per f.u.[30](#page-12-13)[,31](#page-12-14) Finally, the AFM order of α–CuMnSb is stable under applied magnetic field, as T<sup>N</sup> does not change up to 50 Tesla.[32](#page-12-15)
Turning to the electronic structure of the CuMnP-CuMnAs-CuMnSb series we observe that the character of the energy band gap depends on the anion. Similar to the case of e.g. zinc blende semiconductors, the band gap decreases with the increasing atomic number of the anion.[30](#page-12-13) Indeed, CuMnP is a semiconductor, CuMnAs has a practically vanishing band gap, and CuMnSb is a semimetal.[33](#page-12-16)
Here we experimentally confirm a puzzling coexistence of AFM and FM phases in epitaxial stoichiometric CuMnSb films, observed by us previously,[34](#page-12-17) and explain the underlying mechanism responsible for this effect. A fine analysis of transmission electron microscopy (TEM) images, Sec. [II B,](#page-2-0) points to the formation of tetragonal β–CuMnSb inclusions embedded coherently within the cubic α–CuMnSb host. The tetragonal structure of these inclusions is the same as that of the tetragonal β– CuMnAs. Magnetic properties of our films, Sec. [II C,](#page-4-0) demonstrate coexistence of two magnetic phases: apart from the dominant AFM one, expected for CuMnSb, the measurements reveal the presence of a FM contribution. This is an unexpected feature within the CuMnZ series, exhibiting the AFM order.
In Sec. [III,](#page-5-0) we employ calculations based on the density functional theory to assess properties of CuMnSb films. In agreement with the experiment, β–CuMnSb is weakly metastable, but its magnetic ground state is FM. Band structures of α and β polymorphs are close, but changes in the density of states at the Fermi level account for the change of the dominant mechanism of the magnetic coupling from AFM superexchange to FM Ruderman-Kittel- Kasuya-Yoshida (RKKY). Finally, in Sec. [III E](#page-8-0) native point defects in CuMnSb are examined to assess their possible influence on the magnetic properties.[35](#page-12-18) Our results indicate that the dominant native defects in α–CuMnSb are Mn antisites, and their presence in the films can possibly account for small differences between the measured and the calculated magnetic characteristics, but they do not stabilize the FM order of α–CuMnSb.
# II. EXPERIMENTAL RESULTS
## A. Experimental Methods
# Growth conditions.
CuMnSb layers about 200 nm thick are grown by molecular beam epitaxy. Separate growth chambers connected by an ultra-high vacuum transfer system are used for the growth of the individual layers. Low telluriumdoped epi-ready GaSb (001) wafers are used as substrates. Prior to the growth, the natural oxide layer is desorbed in an Sb atmosphere. Then, 150 nm thick GaSb buffer layers are grown on the substrates to ensure a high-quality interface for the growth of CuMnSb. The GaSb buffer layers are grown at a substrate temperature of 530◦C and a beam equivalent pressure of 4.0 × 10−<sup>6</sup> mbar and 5.3 × 10−<sup>7</sup> mbar for Sb and Ga, respectively. Sb supply is facilitated by a single-filament effusion cell, while Ga is provided by a double-filament effusion cell.
A substrate temperature of 250◦C is used for the growth of CuMnSb films. The corresponding beam equivalent pressures are as follows: BEPCu = 5.80 × 10<sup>−</sup><sup>9</sup> mbar, BEPMn = 9.03 × 10<sup>−</sup><sup>9</sup> mbar, and BEPSb = 4.23 × 10<sup>−</sup><sup>8</sup> mbar. Cu is supplied by a double filament effusion cell, while Mn and Sb are supplied by single filament effusion cells. Following the growth of CuMnSb, a 2.5 nm thick layer of Al2O<sup>3</sup> is deposited on the samples through a sequential process of aluminum DC magnetron sputtering and oxidation. Please, refer to Ref. [29](#page-12-12) for a comprehensive analysis of the growth process and physical properties of the CuMnSb layers produced using the methodology outlined above.
Transmission Electron Microscopy. Specimens for the transmission electron microscopy (TEM) investigations are prepared by the focused ion beam method in the form of lamellas cut along the [100] and [110] directions, i.e., perpendicularly to the surface (001) plane. Titan Cubed 80-300 electron transmission microscope operating with accelerating voltage 300 kV and equipped with energy-dispersive X-ray spectrometer (EDXS) is used for the study. Most of the investigations are done on Cu grids, but for EDXS elemental analysis a Mo grid is used to avoid interference of Cu fluorescence signal from the grid. This analysis yields percentage atomic concentration at 37(3) : 32(5) : 31(7) for Cu, Mn, and Sb, respectively, which, within the experimental errors (given in the parentheses), correspond to the expected stoichiometric ratio of 33 : 33 : 33.
SQUID Magnetometry. Magnetic characterization is performed in a commercial superconducting quantum interference device (SQUID) magnetometer MPMS XL7. The magnetic moment of antiferromagnetic layers is generally very weak and by far dominated by the magnetic response of the bulky semiconductor substrates. Therefore, to counter act the typical shortcomings of commercial magnetometers built around superconducting magnets[36](#page-12-19) and to minimize subtraction errors during
![<span id="page-2-1"></span>FIG. 1. (a) High-angle annular dark-field scanning transmission electron microscopy image of a CuMnSb layer in the [100] zone axis. The inset in the top-right corner brings up a part of the image in atomic resolution, where bright dots represent columns of Mn and Sb atoms. (b) Electron diffraction pattern of the layer. (c) Schematics of the positions of Bragg's spots from (b). Big bullets represent the main reflections from the cubic CuMnSb structure, whereas the open triangles mark the positions of the weak extra reflections. The orientation of the triangles follows from the analysis of the data in panels (d-g). (d-e) Blown up two regions from (a), in which either vertical or horizontal strips dominate. The corresponding Fourier transforms are showed in the top right corners of both panels. (f) Selected area electron diffraction pattern taken at the regions dominated by the vertically oriented strips. (g) Diffraction intensity profiles taken along the horizontal [010]\* and the vertical [001]\* lines passing through the center the diffraction pattern. The solid line corresponds to the horizontal [010]\* direction and the dashed one to the vertical [001]\* one in panel (f). Stars denote directions in the reciprocal space. The arrows α and β indicate the length of α–2g(002) and β–2g(002) diffraction vectors, respectively.](path)
data reduction we actively employ the in situ compensation.[37](#page-12-20) It allows us to reduce the coupling of the signal of the substrates to about 10% of their original strength. The actual effectiveness of the compensation depends on the mass of the sample and its orientation with respect to the SQUID pick-up coils.[36,](#page-12-19)[38](#page-12-21) We also strongly underline the importance of a thorough mechanical removal of the metallic MBE glue from the backside of the samples for any magnetic studies. Its strongly nonlinear magnetic contribution can be of the same magnitude as that of the layer of interest.[39](#page-12-22) To accurately establish the magnitude of magnetic moment specific to CuMnSb we measure a reference sample grown without the CuMnSb layer[29](#page-12-12) using the same sample holder and following exactly the
#### <span id="page-2-0"></span>B. Structural characterization
An exemplary atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF/STEM) image obtained for the [100] zone axis (the direction of the projection) is in Fig. [1](#page-2-1) (a). It confirms a high quality cubic constitution of the material, as it is underlined in the inset. However, at the contrast chosen here, the image in this field of view reveals the presence of stripe-like features, which are the main subject of this analysis. In this image, the apparent lengths and widths of the strips are about 40 nm and about 4 nm, respectively, running predominantly either vertically or horizontally in this particular projection. On other images, the strips exhibit a relatively wide distribution of lengths in the 10-100 nm window. Since similarly distributed shadowy stripes are observed also in the [110] zone axis, we conclude that they form along all three principal crystallographic directions without any particular preferences. The expected F43m cubic structure of α–CuMnSb is clearly confirmed by the fourfold symmetry of the dominant (bright) spots seen on electron diffraction pattern presented in Fig. [1](#page-2-1) (b).
Importantly, the diffraction pattern in Fig. [1](#page-2-1) (b) contains also a second set of much fainter reflections, situated halfway between two adjacent reflections of the main pattern. This indicates the presence of a second crystallographic β phase, which periodicity in the corresponding direction is doubled relative to that of α–CuMnSb, but otherwise coherent with this host structure. We bring all the Bragg's spots up in Fig. [1](#page-2-1) (c), in which the bullets represent the main reflections from α–CuMnSb, whereas the open triangles mark the positions of the weak ones, which are forbidden for this structure.
The presence of β–CuMnSb is further substantiated by the inspection of the two close-ups from Fig. [1](#page-2-1) (a), shown in Fig. [1](#page-2-1) (d) and (e). At this magnification they reveal that, on top of the otherwise cubic arrangement of atomic columns, the strips' brightness alternates every second {002} plane along the direction perpendicular to strip's long axis. The modulation is vertical in Fig. [1](#page-2-1) (d), whereas it goes horizontally in Fig. [1](#page-2-1) (e). The top right corners of these figures contain the corresponding Fourier transform of the parent image, and, similarly to Fig. [1](#page-2-1) (b), both patterns are dominated by the main reflections of α–CuMnSb. The additional spots are embedded either along vertical [Fig. [1](#page-2-1) (d)] or horizontal [Fig. [1](#page-2-1) (e)] lines, i.e., the presence of vertical and horizontal orientations is mutually exclusive. This feature is reflected in Fig. [1](#page-2-1) (c), where the additional spots are marked by differently oriented triangles. The triangles with apexes directed vertically correspond to the vertical orientation of the brightness modulation in Fig. [1](#page-2-1) (d), whereas the horizontal direction of apexes corresponds to the horizontal modulation.
Based on the data shown above we propose that the second phase of CuMnSb, present in our films in the form of strips, is a tetragonal structure, which also is the structure of epitaxial CuMnAs,[19–](#page-12-2)[21](#page-12-4)[,23](#page-12-6)[–25](#page-12-8) and of CuMnSb at high pressures.[27](#page-12-10) This β–CuMnSb polymorph is shown in the panel (b) of Fig. [2.](#page-3-0) The difference between α and β phases consists in the location of Cu ions: in the α phase every (001) plane between two consecutive MnSb planes is half-occupied by Cu, whereas in the β phase Cu ions completely fill up every second (001) plane, and the overall stoichiometry of the material is preserved.
![<span id="page-3-0"></span>FIG. 2. Crystal structures of (a) α–CuMnSb with the cubic lattice constant a, (b) tetragonal β–CuMnSb with the lattice constants a in the (x, y) plane and c in the [001] direction, and (c) Cu3Mn2Sb2.](path)
regions with different orientations of the strips. Diffraction pattern of an area dominated by the vertically oriented strips is shown in more detail in Fig. [1](#page-2-1) (f). In agreement with the Fourier transforms, SAED shows the occurrence of specific reflections corresponding to this particular orientation. The reflections common to both the cubic α and the tetragonal β polymorphs are split along the [010]\* direction, i.e., orthogonal to the strip's axis, whereas the weak spots of the β phase are not split and are commensurate with the cubic phase. (A star denotes a direction in the reciprocal space.)
We quantify the effect analyzing intensity profiles taken along lines passing through the center of diffraction. The profiles are superimposed, and presented in Fig. [1](#page-2-1) (g). The profile along the [001]\* direction reflects the periodicity of α–CuMnSb, while that along [010]\* is additionally split. From the Figure it follows that in our specimens the c lattice parameter of the β–CuMnSb strips is equal to that of the host α–CuMnSb, 6.2(1) ˚A, whereas the a and b parameters of the β phase, 5.8(1) ˚A, are smaller by about 7%. Analogous features are observed for the [010]-oriented strips.
The existence of such a significant strain is confirmed by the calculation of strain maps. We apply the geometrical phase analysis method[40](#page-12-23) for the main image presented in Fig. [1](#page-2-1) (a), and the results are presented in Fig. [3](#page-4-1) (a) and (b) for the horizontal, ϵxx, and the vertical, ϵzz, components of strain, respectively. It is seen that stripes' strain is negative (dark shade) perpendicular to strips and almost zero along the strips. For example, on the horizontal strain map [Fig. [3](#page-4-1) (a)] only vertical strips are visible because they are compressed horizontally, whereas the horizontal strips are invisible because they are not deformed in the horizontal direction.
 (a). (a) The horizontal component of strain ϵxx, and (b) the vertical one, ϵzz. Geometrical phase analysis method has been applied.[40](#page-12-23)](path)
The calculated properties of β–CuMnSb, such as its lattice parameters, stability, and magnetic properties, are discussed in detail in Sec. [III C.](#page-7-0) Anticipating, we mention that they are consistent with experiment. We have also considered a second possible structure which is (almost) compatible with the TEM data, Cu3Mn2Sb2, depicted in Fig. [2](#page-3-0) (c). However, this compound is higher in energy than the β phase, and was dropped from further considerations.
#### <span id="page-4-0"></span>C. Magnetic properties
The temperature T dependence of magnetization, M(T), of the 200 nm thick layer of CuMnSb, is depicted in Fig. [4](#page-4-2) (a). The clear kink on M(T) at T<sup>N</sup> = 62 K marks the position of the paramagnetic to antiferromagnetic N´eel transition in the layer. This value corresponds precisely to the values of T<sup>N</sup> established previously for CuMnSb/GaSb layers of the thickness t ≥ 200 nm, what, indirectly, indicates stoichiometric material composition of this layer.[29](#page-12-12)
More specific information about the magnetic state of that sample is obtained from the examination of the temperature dependence of the inverse magnetic susceptibility, χ −1 (T), shown in Fig. [4](#page-4-2) (b). We take here χ(T) = M(T)/H, where H = 10 kOe is the external magnetic field applied during the measurements. χ −1 (T) can be approximated by two straight lines. The abscissa of the first one, which approximates χ −1 (T) above 200 K (the solid orange line in Fig. [4\)](#page-4-2), yields exactly the same magnitude of the Curie-Weiss temperature TCW = −100(5) K as that established previously for a thicker 510 nm layer, for which χ −1 (T) formed a single straight line above T<sup>N</sup> at the same experimental conditions.[29](#page-12-12) Also the slope of this line yields the value of the effective magnetic moment meff = 5.4(1)µ<sup>B</sup> per f.u., which is very close to that found previously, meff = 5.6µ<sup>B</sup> per f.u.[29](#page-12-12) This correspondence indicates that the high temperature part of χ −1 (T) is determined predominantly by AFM excitations in the paramagnetic matrix of CuMnSb.
The abscissa of the second straight line, which approximates the experimental data between T<sup>N</sup> and about 200 K (marked as the dashed orange line in Fig. [4\)](#page-4-2), yields a more positive value of the Curie-Weiss temperature, T ′ CW = −10(10) K. This clear positive shift of TCW indicates the existence of a ferromagnetic contribution to the overall antiferromagnetic phase of the material, and that these FM excitations gain in importance below about 200 K. Interestingly, a somewhat stronger effect, characterized by a change of sign of TCW to T ′ CW = +60(10) K, was noted in 40 nm CuMnSb layer grown on InAs.[34](#page-12-17) In accordance with the findings of structural characterization we propose that the by far stronger AFM component originates from the dominant α phase, whereas the FM one is brought about by β–CuMnSb polymorph.
<span id="page-5-1"></span>TABLE I. Experimental N´eel temperature TN, effective Curie-Weiss magnetic moment of Mn ions meff (Mn), and Curie-Weiss temperature TCW of α–CuMnSb. Measured orientation of the AFM axis is also given (n.e. = not established). Refs. [42](#page-12-24) and [41](#page-12-25) report the saturation Mn moment.
Turning now to the magnetic characteristics established here for α–CuMnSb we note that they are close to those reported previously, as shown in Tab. [I.](#page-5-1) The published data exhibit a certain distribution, which may indicate that other factors, such as a weak crystalline disorder, may be at work. In particular, either additional Mn interstitial ions or CuMn-MnCu antisite pairs are likely to form.[35](#page-12-18) The presence of such defects was suggested to stabilize the experimentally observed AFM {111}-oriented phase of α–CuMnSb.[35](#page-12-18) Finally, we do not observe a canted AFM order at low temperatures[41](#page-12-25) in any of our samples.
#### <span id="page-5-0"></span>III. THEORY
## A. Theoretical Methods
Calculations are performed within the density functional theory[46,](#page-13-2)[47](#page-13-3) in the generalized gradient approximation of the exchange-correlation potential proposed by Perdew, Burke and Ernzerhof.[48](#page-13-4) To improve description of 3d electrons, the Hubbard-type +U correction on Mn is added.[49–](#page-13-5)[51](#page-13-6) The parameter U(Mn) = 1 eV reproduces the known formation energy of the intermetallic CuMn alloy and gives a reasonable value of the Mn cohesive energy. We use the pseudopotential method implemented in the Quantum ESPRESSO code,[52](#page-13-7) with the valence atomic configuration 4s <sup>1</sup>.<sup>5</sup>p <sup>0</sup>3d 9.5 for Cu,
3s 2p <sup>6</sup>4s 2p <sup>0</sup>3d 5 for Mn and 5s 2p 3 for Sb ions. The planewaves kinetic energy cutoffs of 50 Ry for wave functions and 250 Ry for charge density are employed. Finally, geometry relaxations are performed with a 0.05 GPa convergence criterion for pressure. In defected crystals ionic positions are optimized until the forces acting on ions become smaller than 0.02 eV/˚A.
The properties of defected α–CuMnSb are examined using cubic 2a×2a×2a supercells with 96 atoms (i.e., 32 f.u.), while magnetic order of ideal crystals are checked using the smallest possible supercells. Here a is the equilibrium lattice parameter. The k-space summations are performed with a 6 × 6 × 6 k-point grid for the largest supercell, and correspondingly denser grids are used for smaller cells.
Magnetic interactions and magnetic order depend on several factors, such as the exchange spin splitting of the d(TM) shells, charge states of TM ions, concentration of free carriers and their spin polarization, and the density of states (DOS) at the Fermi energy EF. These factors are interrelated, and are calculated self-consistently within ab initio approach.
Considering first the localized magnetic moments we note that spin polarization of Co, Ni, and Cu ions in XMnZ compounds practically vanishes, while that of the d(Mn) shell is substantial.[16,](#page-11-14)[17](#page-12-0)[,31](#page-12-14) The robustness of the Mn magnetic moment results from the large, 3 – 5 eV, spin splitting of the 3d(Mn) states. In fact, in XMnZ the d(Mn) spin up channel is occupied, while most of the spin down d(Mn) states lay above the Fermi level. Here, one can observe that spin polarization of the d(TM) electrons in free atoms depends on the difference in the number of spin up and spin down electrons, which is the highest in the case of Mn. Consequently, the Mn spin polarization persists in XMnZ. On the other hand, spin splitting of d electrons of Co and Ni atoms is smaller, and thus it vanishes in XMnSb hosts, see the analysis for TM dopants in ZnO.[53](#page-13-8)
In CuMnSb, the magnetic sublattice consists of Mn ions, which are second neighbors distant by 4.3 ˚A. Therefore, the direct exchange coupling between two Mn ions, given by overlaps of their d(Mn) orbitals, is negligibly small. The remaining indirect exchange coupling is the sum of two contributions, and the exchange constant Jindirect = Jsr + JRKKY . [16](#page-11-14)[,17](#page-12-0)[,54](#page-13-9) The first term Jsr has a short-range AFM character, and it is inversely proportional to the energy distance between the unoccupied d(Mn) states and EF. The second coupling channel is of RKKY type mediated by free carriers. This channel depends on the detailed electronic structure in the vicinity of EF, and JRKKY is proportional to DOS(EF). In particular, CoMnSb and NiMnSb half-metals are FM, while CuMnP and CuMnAs insulators are AFM. As we show here, CuMnSb is the border case.
#### <span id="page-5-2"></span>B. Crystal and magnetic properties of α–CuMnSb
A rhombohedral primitive cell of α–CuMnSb contains one formula unit. This structure consist in four interpenetrating fcc sublattices, one of them being empty. The consecutive (001) MnSb planes are followed by the "halfempty" Cu planes, in which the planar atomic density is twice lower. The cubic unit cell is presented in Fig. [2](#page-3-0) (a). Local coordination of Mn ions can be relevant from the point of view of magnetic interactions. With this respect we notice that the magnetic coordination of an Mn ion consists in 12 equidistant Mn atoms at a/<sup>√</sup> 2. More-
We consider four magnetic phases of α–CuMnSb. The corresponding supercells are shown in Fig. [5.](#page-6-0) Antiferromagnetic order with parallel Mn spins in the (001) planes, AFM001, is calculated using the cubic a×a×a cell with 4 f.u. (12 atoms), and shown in Fig. [5](#page-6-0) (a). The AFM order with a period doubled in the [001] direction with parallel Mn spins in each (001) plane, denoted as AFM002, is shown in Fig. [5](#page-6-0) (b). The corresponding a×a×2a cell contains 8 f.u., and is one of the possible supercells in which this phase can be realized. In the AFM111 phase, the Mn spins are parallel in each (111) plane, but the consecutive (111) planes are AFM, as shown in Fig. [5](#page-6-0) (c), and the corresponding rhombohedral unit cell a √ 2 × a √ 2 × a √ 2 contains 8 primitive cells with 24 atoms. Finally, the FM phase requires a primitive cell a/<sup>√</sup> 2×a/<sup>√</sup> 2×a/<sup>√</sup> 2 with 1 f.u., presented in Fig. [5](#page-6-0) (d).
<span id="page-6-1"></span>TABLE II. The calculated lattice parameter a, the saturation Mn magnetic moment, msat, and the energy of the given magnetic order relative to α–CuMnSb in the AFM001 ground state, ∆Etot. All energies are per one formula unit. Our measured TEM values are also given.
higher in energy. The least stable is the FM order, higher in energy than AFM001 by about 20 meV per f.u. The equilibrium lattice parameters a ≈ 6.1 ˚A are practically independent of the magnetic order, and close to the experimental value 6.088 ˚A.[42](#page-12-24) Some phases are characterized by a small distortion of the cubic symmetry caused by different bond lengths between ferromagnetically and antiferromagnetically oriented Mn ions. Differences in the lattice parameters between various magnetic phases are below 0.01 ˚A, and are not reported in the Table. Similar results for the AFM001 order were obtained in Ref. [35,](#page-12-18) while in Refs [16](#page-11-14) and [31](#page-12-14) the AFM order is more stable than FM by 50 and 90 meV per Mn, respectively.
The last property reported in Tab. [II](#page-6-1) is the saturation magnetic moment of Mn, which also is similar in all phases, and equal to about 4.6µB. This value corresponds to the Curie-Weiss moment of 5.5(1)µB, and compares favorably with the experimental values given in Tab. [I.](#page-5-1)
The obtained results allow estimating the relative roles of the short- and long-range contributions to the magnetic coupling. To this end, we assume the hamiltonian in the form Hex = −J/2 P i,j ⃗si⃗s<sup>j</sup> , where the short range interaction is limited to the Mn NNs neighbors, and the long-range term is neglected. The spin value, s<sup>i</sup> ≈ 2.3, is one half of the calculated magnetic moment of Mn.
The exchange constant J is positive (negative) for the FM (AFM) coupling, and is obtained by comparing energies of various magnetic orders. In the AFM001 phase, each Mn ion has 4 ferromagnetically oriented Mn NNs in the (001) plane and 8 antiferromagnetically oriented Mn NNs in the two adjacent planes. For the remaining magnetic phases, the energies calculated relative to the ground state E<sup>0</sup> ≡ EAFM001 depend on the magnetic order as shown in Tab. [II.](#page-6-1) These results give the coupling constant in the range −0.6 ≥ Jsr ≥ −0.2 meV. This spread is quite large and cannot be explained by (negligible) changes in atomic distances in cells with different magnetic ordering. Therefore, we conclude that the Heisenberg nearest neighbor model does not describe magnetic properties of bulk phases. Indeed, such a model is not appropriate for metallic or semimetallic systems such as α–CuMnSb, where the long-range RKKY coupling is present.
An opposite conclusion comes from the analysis of single spin excitations from the AFM001 ground state. We use a 2a×2a×2a supercell to calculate the energy differences ∆E for the following cases, in which we change (i) spin of one Mn ion, 1Mn ↑→ 1Mn ↓, called a single spin-flip, (ii) 2Mn↑→ 2Mn↓ for spins of two nearest Mn ions belonging to one layer and (iii) 2Mn ↑→ 2Mn ↓ for two distant Mn ions. In these processes the long-range coupling is not important, and indeed the calculated exchange constant consistently is Jsr ≈ −0.4 meV.
#### <span id="page-7-0"></span>C. Crystal and magnetic properties of β–CuMnSb
We now consider two possible structures of the secondary phase proposed based on the experimental results. They are characterized by doubling the periodicity in the [001] direction. The unit cell of β–CuMnSb, shown in Fig. [2,](#page-3-0) is tetragonally deformed relative to that of α–CuMnSb, with the corresponding lattice parameters a = 5.88 ˚A and c = 6.275 ˚A. They differ by about 3 per cent from our calculated cubic a(α– CuMnSb) = 6.105 ˚A. The two interlayer spacings between the consecutive MnSb planes in the [001] direction in the unit cell, shown in Fig. [2](#page-3-0) (b), are quite different, namely dinter<sup>1</sup> = 2.80 ˚A (no Cu), and dinter<sup>2</sup> = 3.48 ˚A (with Cu). Turing to the magnetic order of β–CuMnSb, we find that the FM phase constitutes the ground state with msat = 4.6µ<sup>B</sup> and is lower than the AFM phase by 11 meV per f.u., as indicated in Tab. [II.](#page-6-1) Thus, the
The experimental[27](#page-12-10) lattice parameters of β–CuMnSb reasonably agree with our values, i.e., the calculated a = 6.28 ˚A and c/a = 1.87 are about 2% larger than those measured for the compressed crystal at the critical pressure of 7 GPa. On the other hand, the calculations of Ref. [27](#page-12-10) predict that the magnetic order of the β phase is AFM, in striking contrast with our results. Also their calculated msat(Mn) = 3.8µ<sup>B</sup> is substantially smaller than our 4.6µB. The origin of these discrepancies is not clear, but it may be due to the different exchange-correlation functionals used, and/or to application of the +U(Mn) correction in our calculations (which can affect the results.[31](#page-12-14))
The calculated total energy of the FM β–CuMnSb relative to the AFM α–CuMnSb is higher by 102 meV per f.u. This energy difference is not large, being comparable to the growth temperature, which implies that the β–CuMnSb polymorph can indeed form during epitaxy. We also stress that stoichiometry of the α and β phases is the same, which facilitates formation of β–CuMnSb. Finally, the observed β–CuMnSb inclusions are coherent, i.e., lattice matched, with the host structure. This agrees with the fact that the calculated excess elastic energy of matching the lattice parameters of the β phase to the host α phase is very low and ranges from 3 meV per f.u. (when the tetragonal a parameter constrained to the cubic a = 6.105 ˚A) to 20 meV per f.u. (the tetragonal c parameter constrained to the cubic a).
The second considered possibility, Cu3Mn2Sb<sup>2</sup> shown in Fig. [2](#page-3-0) (c), is higher in energy by 0.37 eV per f.u. in the Cu–rich conditions than the ideal CuMnSb, i.e., by 0.27 eV per f.u. than β–CuMnSb, its stoichiometry is markedly different, and thus we can eliminate this structure from considerations.
# D. Energy band structures of α–CuMnSb and β–CuMnSb
Figure [7](#page-8-1) (a) shows the energy bands and DOS of the AFM001 α–CuMnSb. We see that this phase has a metallic character, however DOS at the Fermi level is low. The states close to E<sup>F</sup> are built from s, p and d states of all ions with similar weights. The low DOS(EF) makes CuMnSb almost semimetallic with a low electrical conductivity. Compatible with the small DOS(EF) is the high resistivity measured in Ref. [41](#page-12-25) and [55.](#page-13-10)
Since the system is antiferromagnetically ordered, the total DOSs of spin-up and spin-down states are the same. In Fig. [7](#page-8-1) only contributions of the 3d(Mn) and 3d(Cu) orbitals are presented to reveal magnetic properties. We see that the exchange spin splitting of the d(Mn) shell is large, about 5 eV. The closely spaced levels contributing to the DOS maxima centered at 4 eV below the Fermi energy are composed mainly of the d states of both Cu and Mn. Spin-up and spin-down 3d(Cu) orbitals are almost
completely occupied, and thus Cu ions are non-magnetic. In turn, the majority spin states of the 3d(Mn) orbitals are completely occupied, while the minority spin states at 1 eV above the Fermi energy are partially filled thanks to a small overlap with spin up states. As a result, a single Mn ion is in between the d <sup>5</sup> and d 6 configuration, with the saturation magnetic moment of 4.6µ<sup>B</sup> consistent with Tab. [II.](#page-6-1) Our results for α–CuMnSb are close to those of Ref. [31.](#page-12-14) A similar electronic configuration takes place in CuMnAs, where the spin-down Mn states are partially filled.[56](#page-13-11)
The overall band structure of the FM β–CuMnSb displayed in Fig. [7](#page-8-1) (b) is close to that of α–CuMnSb, which is particularly clear when comparing partial DOS of both phases. In particular, msat(Mn) is about 4.5µ<sup>B</sup> in both phases, and energies of both d(Mn)- and d(Cu)-related bands are largely independent of the actual crystal structure. This similarity can be due to the fact that the MnSb (001) planes play a dominant role, and the exact locations of the Cu ions are less important.
On the other hand, the calculated DOS(EF) for the α phase is 0.35 states per spin and f.u., while for the β phase we find 1.26 states per spin and f.u., which is 3.6 times higher. As a consequence, α–CuMnSb is semimetallic, and the AFM order is dominant, while β phase is more metallic in character, which in turn favors the RKKY-type coupling and the FM order. This feature can explain the different magnetic phases of the α and β polymorphs.
Analysis of the calculated electronic structure of Heusler and half-Heusler CuMnZ led Sasioglu et al.[17](#page-12-0) to the conclusion that when the spin polarization of conduction electrons is large, and the d(Mn) spin down states are far above EF, then the RKKY coupling is dominant, and one should expect the FM order, otherwise the short range AFM coupling is dominant. Our results do not confirm this conclusion, and indicate that the important
## <span id="page-8-0"></span>E. Point native defects in α–CuMnSb
where E(CuMnSb) and E(CuMnSb : D) are the total energies of a supercell without and with a defect, and n<sup>i</sup> = +1(−1) corresponds to the removal (addition) of one ith atom. µis are the variable chemical potentials of atoms in the solid, which in general are different from the chemical potentials µi(bulk) of the standard state of elements, i.e., Cu, Mn and Sb bulk. Details of calculations of chemical potentials are given in Appendix [A.](#page-10-0)
The point native defects considered here are vacancies VX, interstitials X<sup>i</sup> , and antisites X<sup>Y</sup> (where X and Y are Cu, Mn, or Sb) for all three sublattices. As it was mentioned above, the Cu sublattice is "half- empty" compared to the MnSb sublattice. Consequently, we consider here formation of interstitials at the empty sites of the Cu sublattice only, and neglect other possibilities, expected to have higher formation energies Eform. Thus, the set of defects considered here only partially overlaps with that of Ref. [35.](#page-12-18) Of particular interest to the present study are defects involving Mn ions, since they can influence magnetic properties of α–CuMnSb .[35](#page-12-18) This is why we consider them more extensively, after briefly analyzing the non-magnetic defects. The calculated formation energies are summarized in Tab. [III.](#page-9-0) Because of the magnetic coupling, formation energies of the Mn-related defects depend on the spin direction relative to the spins of the host Mn neighbors. We consider possible spin configurations shown in Fig. [8](#page-9-1) (b).
<span id="page-9-0"></span>TABLE III. Formation energies (in eV) of isolated point defects in the Mn-rich conditions. In parentheses are Mn-related values corrected for ∆H<sup>f</sup> (MnSb) = 0.48 eV, which correspond to the Mn-poor case.
where k<sup>B</sup> is the Boltzmann constant and N<sup>0</sup> is the density of the relevant lattice sites. Details of the calculations of Eform are provided in Supporting Information. To put the calculated formation energies into a proper context, we note that if the growth temperatrure Tgrowth = 2500C and Eform = 0.1 eV, then exp(−Eform/kBTgrowth) = 0.1, which corresponds to a high 10 atomic per cent concentration of this defect on the considered sublattice. On the other hand, if Eform = 1 eV, then exp(−Eform/kBTgrowth) = 9 × 10<sup>−</sup><sup>11</sup>, which implies a negligible defect concentration.
Sb sublattice. The prohibitively high values of Eform demonstrate that VSb and Sb<sup>i</sup> should not form. Similarly, formation energies of SbCu, SbMn, CuSb and MnSb antisites exceed 1 eV, and those defects are not expected to be present at high concentrations. Consequently, the Sb sublattice is thermodynamically stable, robust, and constitutes a defect-free back-bone of CuMnSb.
(ii) Formation energy of Cu interstitials at the Cu sublattice, Eform(Cui) = 1 eV, is relatively high, and their concentrations are negligible. Additionally, the high formation energy of Cu<sup>i</sup> interstitials is consistent with the sparse character of the Cu sublattice in α–CuMnSb.
(iii) Formation of Mn<sup>i</sup> interstitials at the Cu sublattice is characterized by Eform = 0.7-1.4 eV, depending on the spin direction and conditions of growth, and therefore they are not expected to be present at high concentrations, especially in the Mn-poor conditions.
In brief, low formation energies are found for three defects, namely the VCu and VMn vacancies and the MnCu antisite, particularly at the Mn-rich growth conditions. This indicates that a Cu deficit on the Cu sublattice is possible, affecting stoichiometry. Significantly, MnCu antisites make the Cu sublattice magnetic, and also they can participate in the magnetic coupling between the adjacent MnSb (001) planes, thus influencing magnetic properties, as it will be discussed in more detail below. In contrast, SbCu antisites are present in negligible concentrations. Our results are in a reasonable agreement with those of Ref. [35,](#page-12-18) especially given their neglect of spin effects and a somewhat different theoretical approach. Interestingly, formation energies of native defects in CuMnAs calculated in Ref. [56](#page-13-11) are close to the present results in spite of the different anion.
## F. Defect-induced magnetic coupling
There are two Mn-related point defects, Mn<sup>i</sup> and MnCu, both situated on the Cu sublattice. When present at high concentrations, they affect magnetism of α– CuMnSb. Their coupling with host Mn ions is different than the Mn-Mn coupling between the host Mn because of the different local coordination. Energetics of both defects is complex and rich, since the total energy of the system (and thus formation energies) depends on their spin orientations relative to the neighborhood. At both substitutional and interstitial sites in the Cu layer, a Mn ion has 4 Mn nearest neighbors arranged in a tetrahedral configuration, 2 in the upper and 2 in the lower MnSb layer. The Mni–MnMn distance is shorter than that of
MnMn–MnMn, and equal to (<sup>√</sup> 3/4)a.
The possible local spin configurations are reduced to small clusters of 5 Mn ions, shown in Fig. [8.](#page-9-1) The Mn spin-up and spin-down (001) MnSb layers are denoted by in pink and blue, respectively, reflecting the calculated (001) AFM magnetic ground state. The central MnCu (or Mni) ion of such a cluster provides an additional channel of magnetic coupling between two adjacent MnSb layers. The corresponding formation energies are given in Fig. [8.](#page-9-1)
As it was pointed out, in ideal α–CuMnSb, the Mn ions are second neighbors only, separated either by Sb (i.e., the Mn-Sb-Mn "bridge" in the MnSb(001) plane), or by Cu (forming a Mn-Cu-Mn "bridge" linking 3 consecutive (001) planes.) Thus, the short range magnetic coupling in ideal α–CuMnSb is successfully modelled in Sec. [III B](#page-5-2) by the interaction between two Mn second neighbors, situated either in the same MnSb layer, or in two adjacent ones. In contrast, the 4 host Mn ions in the cluster are the first neighbors of a Mn<sup>i</sup> or a MnCu defect. Thus, one can expect that this coupling is stronger than the intrinsic one in the ideal host, and indeed, the differences in energy between various configurations in Fig. [8](#page-9-1) are about 100 meV, which is too high to be explained by the estimated Jsr = 0.4 meV.
As it follows from Fig. [8,](#page-9-1) 5-atom clusters are magnetically frustrated. In particular, the lowest energy case denoted as 4AFM favors the local FM orientation of spins in two adjacent (001) planes, which is opposite to the global host magnetic order. Our results do not confirm the conclusion of Ref. [56](#page-13-11) who find that the 3AFM configuration has the lowest energy, and thus it promotes the global AFM111 order. Instead, we rather expect that Mn-related point defects induce disorder of the host AFM phase, possibly leading to formation of a spin glass.[57](#page-13-12)
#### IV. SUMMARY
CuMnSb films were epitaxially grown on GaSb substrates. Magnetic measurements reveal the presence of two magnetic subsystems. The dominant magnetic order is AFM with the N´eel temperature of 62 K, which is the same as in bulk CuMnSb. It co-exists with a FM phase, characterized by the Curie temperature of about 100 K.
These findings go in hand with transmission electron microscopy and selective area diffraction measurements, which demonstrate coexistence of two structural polymorphs of the same stoichiometry. The dominant one is the cubic half-Heusler α–CuMnSb, which is the equilibrium structure of bulk samples. The second component is a tetragonal β–CuMnSb polymorph, which forms 10-100 nm long elongated inclusions.
(i) The β–CuMnSb phase is metastable, and its total energy is higher by 0.1 eV per f.u. only than that of the equilibrium α–CuMnSb. Lattice parameters of the β phase differ from those of α–CuMnSb by about 4 per cent. This lattice misfit between the two structures does not prevent the pseudomorphic coexistence of both phases, since the calculated misfit strain energy is below 20 meV per f.u.
(ii) In agreement with experiment, α–CuMnSb is AFM, and the FM order is 19 meV per f.u. higher in energy. In contrast, the magnetic ground state of β– CuMnSb is FM, which is more stable than AFM by 11 meV per f.u. This indicates that indeed the β–CuMnSb inclusions are responsible for the FM signal.
(iii) The different magnetic orders of the α and β phases originate in their somewhat different band structures. In particular, critical for magnetic order is the DOS at the Fermi level, which is about 4 times higher in β–CuMnSb than in the α phase. This shows that the β phase is more metallic in character, which in turn favors the FM order driven by the Ruderman-Kittel-Kasuya-Yoshida interaction.
(iv) Our calculations predict the saturated magnetic moment of Mn msat = 4.6µ<sup>B</sup> and 4.5µ<sup>B</sup> for the α and the β phase, respectively. This corresponds to the effective moment of 5.6µB, in good agreement with the measured 5.5µB.
(v) The calculated formation energies of point native defects indicate that the most probable are the MnCu antisites with low formation energies of 0–0.2 eV. However, their presence is expected to disorder the host magnetic AFM phase rather than to induce a transition to the FM configuration.
(vi) Regarding the properties of the CuMnX series we see that their structural stability is relatively weak, as they crystallize in a variety of structures. In particular, unlike the bulk orthorhombic CuMnAs, epitaxial films of CuMnAs are tetragonal, but both structures are AFM. In the case of CuMnSb, polymorphism comprises also the equilibrium magnetic structure, AFM in the bulk specimens, and FM in epitaxial films.
#### ACKNOWLEDGMENTS
LS, CG, JK and LWM thank M. Zipf for technical assistance. Our work was funded by the Deutsche Forschungsgemeinschaft (DFG,German Research Foundation) No. 397861849, by the Free State of Bavaria (Institute for Topological Insulators) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC2147 ct.qmat (Project-Id 390858490).
#### <span id="page-10-0"></span>Appendix A:
The highest possible value of µ<sup>i</sup> is µi(bulk), which implies that the studied system is in equilibrium with the given bulk source of atoms and δµ<sup>i</sup> = 0, otherwise δµ<sup>i</sup> < 0.
Chemical potentials of the components in the standard state are given by the total energies per atom of elemental solids. The calculated cohesive energies Ecoh of the face centered cubic Cu, the face centered cubic Mn with the AFM magnetic order, and the triclinic Sb are, respectively, 3.40 (3.49), 2.65 (2.92) and 2.68 (2.75) eV/atom. They compare reasonably well with the experimental values given in parentheses.[58](#page-13-13)
Chemical potentials of the involved atomic species depend on possible formation of compounds. The ranges of variations of chemical potentials are determined by conditions of equilibrium between various phases, i.e., Cu2Sb, MnSb and CuMnSb. Thermodynamic equilibrium requires that
$$\begin{aligned} \delta\mu(\text{Cu}) + 2\delta\mu(\text{Sb}) &= \Delta H\_f(\text{Cu}\_2\text{Sb}), \\ \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{MnSb}), \\ \delta\mu(\text{Cu}) + \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{CuMnSb}), \end{aligned} \quad \text{(A2)}$$
The calculated values ∆H<sup>f</sup> (Cu2Sb) = −0.03 eV per f.u., ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u., and ∆H<sup>f</sup> (CuMnSb) = −0.42 eV per f.u. The very low ∆H<sup>f</sup> (Cu2Sb) is somewhat unexpected, since Cu2Sb is a stable compound which crystallizes in the tetragonal phase.[43](#page-12-26) Next, our result ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u. agrees well with both the previous value -0.52 eV per f.u. calculated in Ref. [59,](#page-13-14) and the experimental - 0.52 eV per f.u.[60](#page-13-15) Assuming that the accuracy of the calculated values is 0.03 eV per f.u., the set of Equation [A2](#page-11-15) is consistent if we assume ∆H<sup>f</sup> (Cu2Sb) = 0, and ∆H<sup>f</sup> (MnSb) = ∆H<sup>f</sup> (CuMnSb) = −0.45 eV per f.u. This in turn implies that δµ(Cu) = δµ(Sb) = 0, and δµ(Mn) = −0.45 eV. Consequently, the allowed window of the Mn chemical potential is
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| |
FIG. 7. Bands and partial DOSs for (a) the AFM001 of α–CuMnSb and for (b) the FM state of β–CuMnSb obtained using the a × a × c cell. The right panels show the partial DOSs for Cu and Mn ions, and thus different contributions to spin-up and spin-down density of Mn↑ are exposed also in AFM case. In (b) the spin degeneracy is lifted.
|
# Coexistence of Antiferromagnetic Cubic and Ferromagnetic Tetragonal Polymorphs in Epitaxial CuMnSb
High-resolution transmission electron microscopy and superconducting quantum interference device magnetometry shows that epitaxial CuMnSb films exhibit a coexistence of two magnetic phases, coherently intertwined in nanometric scales. The dominant α phase is half-Heusler cubic antiferromagnet with the N´eel temperature of 62 K, the equilibrium structure of bulk CuMnSb. The secondary phase is its ferromagnetic tetragonal β polymorph with the Curie temperature of about 100 K. First principles calculations provide a consistent interpretation of experiment, since (i) total energy of β–CuMnSb is higher than that of α–CuMnSb only by 0.12 eV per formula unit, which allows for epitaxial stabilization of this phase, (ii) the metallic character of β–CuMnSb favors the Ruderman-Kittel-Kasuya-Yoshida ferromagnetic coupling, and (iii) the calculated effective Curie-Weiss magnetic moment of Mn ions in both phases is about 5.5 µB, favorably close to the measured value. Calculated properties of all point native defects indicate that the most likely to occur are MnCu antisites. They affect magnetic properties of epilayers, but they cannot induce the ferromagnetic order in CuMnSb. Combined, the findings highlight a practical route towards fabrication of functional materials in which coexisting polymorphs provide complementing functionalities in one host.
#### I. INTRODUCTION
One of the most challenging and long-standing problems in fundamental magnetism is a competition between ferromagnetic and antiferromagnetic phases. Their interplay at the interface results in a well known effect of the exchange bias,[1](#page-11-1)[,2](#page-11-2) which fuels now a rapid development of spintronics[3](#page-11-3) and unconventional computing.[4](#page-11-4) The material class of Heusler alloys was previously used to study the origin of the transition between magnetic phases because it offers a wide spectrum of functionalities.[5](#page-11-5) Indeed, Heusler alloys exhibit ferromagnetic (FM), antiferromagnetic (AFM), and canted ferromagnetic order. This indicates that different types of magnetic coupling are competing in this family. Moreover, some of its members display structural polymorphism, which allows studying relationships between the crystalline phase, the magnetic phase, and the corresponding electronic structure.
Heusler alloys incorporate full-Heusler (X2YZ) and half-Heusler (XYZ) variants, where X and Y stand for transition metals, whereas Z denotes anions from the main group. In this class, qualitative changes in material characteristics can be achieved by chemical substitution on either the transition metal cation or on the anion sublattice. Typically, the change of the cation does not change the crystal structure, but it can induce a crossover between the AFM and the FM magnetic phases. A rarely met complete solubility with only marginally affected crystallinity of the otherwise chemically homogenous systems allowed to study the FM-AFM phase competition in detail. The prominent examples are quaternary solid solutions such as Ru2Mn1−xFexSn[6–](#page-11-6)[8](#page-11-7)
Heuslers, and Co1−xNixMnSb,[9](#page-11-8)[,10](#page-11-9) Cu1−xNixMnSb,[11–](#page-11-10)[13](#page-11-11) Co1−xCuxMnSb,[14](#page-11-12) and Cu1−xPdxMnSb[15](#page-11-13) half-Heuslers. In the latter case, the crossover between AFM to FM phases is related to a change in the electronic structure from semimetallic to half-metallic.[16](#page-11-14)[,17](#page-12-0)
Cu–based CuMnZ compounds are antiferromagnets. This feature attracts attention given the recent progress achieved in the AFM spintronics.[18](#page-12-1) Of particular interest is CuMnAs, with a high N´eel temperature T<sup>N</sup> = 480 K.[19](#page-12-2) In this case, features essential for applications, such as anisotropic magnetoresistance,[20,](#page-12-3)[21](#page-12-4) current-induced electrical switching of the N´eel vector[22](#page-12-5) and of the magnetic domains,[23](#page-12-6) have been demonstrated.
The AFM order of CuMnZ is independent of the actual crystalline structure. The equilibrium structure of bulk CuMnP and CuMnAs is orthorhombic, while that of CuMnSb is half-Heusler cubic, referred to below as the α phase. On the other hand, epitaxial growth can stabilizes metastable phases. This is the case of epitaxial layers of CuMnAs, grown on both GaP[19](#page-12-2)[–21](#page-12-4)[,24](#page-12-7)[,25](#page-12-8) and GaAs[23](#page-12-6) substrates, which crystalize in the tetragonal structure, referred to below as the β phase. Theoretical investigations of the crystalline properties of CuMnZ series show that the total energy difference between the cubic and orthorhombic phase is about 1 eV per f.u. (formula unit) for CuMnP, and about 0.5 eV per f.u. for CuMnAs.[26](#page-12-9) This suggests that the orthorhombic phase of CuMnSb, the last member of the CuMnZ series, may not be stable, and indeed the stable structure is the α phase. However, as we show here, epitaxial stabilization of CuMnSb in the β phase is in principle possible, because the calculated energy difference between
Concerning the magnetic properties, the N´eel temperature of both orthorhombic CuMnAs and β–CuMnAs is well above the room temperature,[19](#page-12-2) whereas that of α– CuMnSb is lower, about 60 K.[28,](#page-12-11)[29](#page-12-12) Theory agrees with experiment, since according to Ref. [30,](#page-12-13) in the orthorhombic CuMnP and CuMnAs, the AFM order is more stable than the FM by about 250 meV/Mn. This energy difference is smaller in the cubic phase of CuMnZ compounds, for which the AFM order is lower in energy than FM one by about 50 meV per f.u.[30](#page-12-13)[,31](#page-12-14) Finally, the AFM order of α–CuMnSb is stable under applied magnetic field, as T<sup>N</sup> does not change up to 50 Tesla.[32](#page-12-15)
Turning to the electronic structure of the CuMnP-CuMnAs-CuMnSb series we observe that the character of the energy band gap depends on the anion. Similar to the case of e.g. zinc blende semiconductors, the band gap decreases with the increasing atomic number of the anion.[30](#page-12-13) Indeed, CuMnP is a semiconductor, CuMnAs has a practically vanishing band gap, and CuMnSb is a semimetal.[33](#page-12-16)
Here we experimentally confirm a puzzling coexistence of AFM and FM phases in epitaxial stoichiometric CuMnSb films, observed by us previously,[34](#page-12-17) and explain the underlying mechanism responsible for this effect. A fine analysis of transmission electron microscopy (TEM) images, Sec. [II B,](#page-2-0) points to the formation of tetragonal β–CuMnSb inclusions embedded coherently within the cubic α–CuMnSb host. The tetragonal structure of these inclusions is the same as that of the tetragonal β– CuMnAs. Magnetic properties of our films, Sec. [II C,](#page-4-0) demonstrate coexistence of two magnetic phases: apart from the dominant AFM one, expected for CuMnSb, the measurements reveal the presence of a FM contribution. This is an unexpected feature within the CuMnZ series, exhibiting the AFM order.
In Sec. [III,](#page-5-0) we employ calculations based on the density functional theory to assess properties of CuMnSb films. In agreement with the experiment, β–CuMnSb is weakly metastable, but its magnetic ground state is FM. Band structures of α and β polymorphs are close, but changes in the density of states at the Fermi level account for the change of the dominant mechanism of the magnetic coupling from AFM superexchange to FM Ruderman-Kittel- Kasuya-Yoshida (RKKY). Finally, in Sec. [III E](#page-8-0) native point defects in CuMnSb are examined to assess their possible influence on the magnetic properties.[35](#page-12-18) Our results indicate that the dominant native defects in α–CuMnSb are Mn antisites, and their presence in the films can possibly account for small differences between the measured and the calculated magnetic characteristics, but they do not stabilize the FM order of α–CuMnSb.
# II. EXPERIMENTAL RESULTS
## A. Experimental Methods
# Growth conditions.
CuMnSb layers about 200 nm thick are grown by molecular beam epitaxy. Separate growth chambers connected by an ultra-high vacuum transfer system are used for the growth of the individual layers. Low telluriumdoped epi-ready GaSb (001) wafers are used as substrates. Prior to the growth, the natural oxide layer is desorbed in an Sb atmosphere. Then, 150 nm thick GaSb buffer layers are grown on the substrates to ensure a high-quality interface for the growth of CuMnSb. The GaSb buffer layers are grown at a substrate temperature of 530◦C and a beam equivalent pressure of 4.0 × 10−<sup>6</sup> mbar and 5.3 × 10−<sup>7</sup> mbar for Sb and Ga, respectively. Sb supply is facilitated by a single-filament effusion cell, while Ga is provided by a double-filament effusion cell.
A substrate temperature of 250◦C is used for the growth of CuMnSb films. The corresponding beam equivalent pressures are as follows: BEPCu = 5.80 × 10<sup>−</sup><sup>9</sup> mbar, BEPMn = 9.03 × 10<sup>−</sup><sup>9</sup> mbar, and BEPSb = 4.23 × 10<sup>−</sup><sup>8</sup> mbar. Cu is supplied by a double filament effusion cell, while Mn and Sb are supplied by single filament effusion cells. Following the growth of CuMnSb, a 2.5 nm thick layer of Al2O<sup>3</sup> is deposited on the samples through a sequential process of aluminum DC magnetron sputtering and oxidation. Please, refer to Ref. [29](#page-12-12) for a comprehensive analysis of the growth process and physical properties of the CuMnSb layers produced using the methodology outlined above.
Transmission Electron Microscopy. Specimens for the transmission electron microscopy (TEM) investigations are prepared by the focused ion beam method in the form of lamellas cut along the [100] and [110] directions, i.e., perpendicularly to the surface (001) plane. Titan Cubed 80-300 electron transmission microscope operating with accelerating voltage 300 kV and equipped with energy-dispersive X-ray spectrometer (EDXS) is used for the study. Most of the investigations are done on Cu grids, but for EDXS elemental analysis a Mo grid is used to avoid interference of Cu fluorescence signal from the grid. This analysis yields percentage atomic concentration at 37(3) : 32(5) : 31(7) for Cu, Mn, and Sb, respectively, which, within the experimental errors (given in the parentheses), correspond to the expected stoichiometric ratio of 33 : 33 : 33.
SQUID Magnetometry. Magnetic characterization is performed in a commercial superconducting quantum interference device (SQUID) magnetometer MPMS XL7. The magnetic moment of antiferromagnetic layers is generally very weak and by far dominated by the magnetic response of the bulky semiconductor substrates. Therefore, to counter act the typical shortcomings of commercial magnetometers built around superconducting magnets[36](#page-12-19) and to minimize subtraction errors during
![<span id="page-2-1"></span>FIG. 1. (a) High-angle annular dark-field scanning transmission electron microscopy image of a CuMnSb layer in the [100] zone axis. The inset in the top-right corner brings up a part of the image in atomic resolution, where bright dots represent columns of Mn and Sb atoms. (b) Electron diffraction pattern of the layer. (c) Schematics of the positions of Bragg's spots from (b). Big bullets represent the main reflections from the cubic CuMnSb structure, whereas the open triangles mark the positions of the weak extra reflections. The orientation of the triangles follows from the analysis of the data in panels (d-g). (d-e) Blown up two regions from (a), in which either vertical or horizontal strips dominate. The corresponding Fourier transforms are showed in the top right corners of both panels. (f) Selected area electron diffraction pattern taken at the regions dominated by the vertically oriented strips. (g) Diffraction intensity profiles taken along the horizontal [010]\* and the vertical [001]\* lines passing through the center the diffraction pattern. The solid line corresponds to the horizontal [010]\* direction and the dashed one to the vertical [001]\* one in panel (f). Stars denote directions in the reciprocal space. The arrows α and β indicate the length of α–2g(002) and β–2g(002) diffraction vectors, respectively.](path)
data reduction we actively employ the in situ compensation.[37](#page-12-20) It allows us to reduce the coupling of the signal of the substrates to about 10% of their original strength. The actual effectiveness of the compensation depends on the mass of the sample and its orientation with respect to the SQUID pick-up coils.[36,](#page-12-19)[38](#page-12-21) We also strongly underline the importance of a thorough mechanical removal of the metallic MBE glue from the backside of the samples for any magnetic studies. Its strongly nonlinear magnetic contribution can be of the same magnitude as that of the layer of interest.[39](#page-12-22) To accurately establish the magnitude of magnetic moment specific to CuMnSb we measure a reference sample grown without the CuMnSb layer[29](#page-12-12) using the same sample holder and following exactly the
#### <span id="page-2-0"></span>B. Structural characterization
An exemplary atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF/STEM) image obtained for the [100] zone axis (the direction of the projection) is in Fig. [1](#page-2-1) (a). It confirms a high quality cubic constitution of the material, as it is underlined in the inset. However, at the contrast chosen here, the image in this field of view reveals the presence of stripe-like features, which are the main subject of this analysis. In this image, the apparent lengths and widths of the strips are about 40 nm and about 4 nm, respectively, running predominantly either vertically or horizontally in this particular projection. On other images, the strips exhibit a relatively wide distribution of lengths in the 10-100 nm window. Since similarly distributed shadowy stripes are observed also in the [110] zone axis, we conclude that they form along all three principal crystallographic directions without any particular preferences. The expected F43m cubic structure of α–CuMnSb is clearly confirmed by the fourfold symmetry of the dominant (bright) spots seen on electron diffraction pattern presented in Fig. [1](#page-2-1) (b).
Importantly, the diffraction pattern in Fig. [1](#page-2-1) (b) contains also a second set of much fainter reflections, situated halfway between two adjacent reflections of the main pattern. This indicates the presence of a second crystallographic β phase, which periodicity in the corresponding direction is doubled relative to that of α–CuMnSb, but otherwise coherent with this host structure. We bring all the Bragg's spots up in Fig. [1](#page-2-1) (c), in which the bullets represent the main reflections from α–CuMnSb, whereas the open triangles mark the positions of the weak ones, which are forbidden for this structure.
The presence of β–CuMnSb is further substantiated by the inspection of the two close-ups from Fig. [1](#page-2-1) (a), shown in Fig. [1](#page-2-1) (d) and (e). At this magnification they reveal that, on top of the otherwise cubic arrangement of atomic columns, the strips' brightness alternates every second {002} plane along the direction perpendicular to strip's long axis. The modulation is vertical in Fig. [1](#page-2-1) (d), whereas it goes horizontally in Fig. [1](#page-2-1) (e). The top right corners of these figures contain the corresponding Fourier transform of the parent image, and, similarly to Fig. [1](#page-2-1) (b), both patterns are dominated by the main reflections of α–CuMnSb. The additional spots are embedded either along vertical [Fig. [1](#page-2-1) (d)] or horizontal [Fig. [1](#page-2-1) (e)] lines, i.e., the presence of vertical and horizontal orientations is mutually exclusive. This feature is reflected in Fig. [1](#page-2-1) (c), where the additional spots are marked by differently oriented triangles. The triangles with apexes directed vertically correspond to the vertical orientation of the brightness modulation in Fig. [1](#page-2-1) (d), whereas the horizontal direction of apexes corresponds to the horizontal modulation.
Based on the data shown above we propose that the second phase of CuMnSb, present in our films in the form of strips, is a tetragonal structure, which also is the structure of epitaxial CuMnAs,[19–](#page-12-2)[21](#page-12-4)[,23](#page-12-6)[–25](#page-12-8) and of CuMnSb at high pressures.[27](#page-12-10) This β–CuMnSb polymorph is shown in the panel (b) of Fig. [2.](#page-3-0) The difference between α and β phases consists in the location of Cu ions: in the α phase every (001) plane between two consecutive MnSb planes is half-occupied by Cu, whereas in the β phase Cu ions completely fill up every second (001) plane, and the overall stoichiometry of the material is preserved.
![<span id="page-3-0"></span>FIG. 2. Crystal structures of (a) α–CuMnSb with the cubic lattice constant a, (b) tetragonal β–CuMnSb with the lattice constants a in the (x, y) plane and c in the [001] direction, and (c) Cu3Mn2Sb2.](path)
regions with different orientations of the strips. Diffraction pattern of an area dominated by the vertically oriented strips is shown in more detail in Fig. [1](#page-2-1) (f). In agreement with the Fourier transforms, SAED shows the occurrence of specific reflections corresponding to this particular orientation. The reflections common to both the cubic α and the tetragonal β polymorphs are split along the [010]\* direction, i.e., orthogonal to the strip's axis, whereas the weak spots of the β phase are not split and are commensurate with the cubic phase. (A star denotes a direction in the reciprocal space.)
We quantify the effect analyzing intensity profiles taken along lines passing through the center of diffraction. The profiles are superimposed, and presented in Fig. [1](#page-2-1) (g). The profile along the [001]\* direction reflects the periodicity of α–CuMnSb, while that along [010]\* is additionally split. From the Figure it follows that in our specimens the c lattice parameter of the β–CuMnSb strips is equal to that of the host α–CuMnSb, 6.2(1) ˚A, whereas the a and b parameters of the β phase, 5.8(1) ˚A, are smaller by about 7%. Analogous features are observed for the [010]-oriented strips.
The existence of such a significant strain is confirmed by the calculation of strain maps. We apply the geometrical phase analysis method[40](#page-12-23) for the main image presented in Fig. [1](#page-2-1) (a), and the results are presented in Fig. [3](#page-4-1) (a) and (b) for the horizontal, ϵxx, and the vertical, ϵzz, components of strain, respectively. It is seen that stripes' strain is negative (dark shade) perpendicular to strips and almost zero along the strips. For example, on the horizontal strain map [Fig. [3](#page-4-1) (a)] only vertical strips are visible because they are compressed horizontally, whereas the horizontal strips are invisible because they are not deformed in the horizontal direction.
 (a). (a) The horizontal component of strain ϵxx, and (b) the vertical one, ϵzz. Geometrical phase analysis method has been applied.[40](#page-12-23)](path)
The calculated properties of β–CuMnSb, such as its lattice parameters, stability, and magnetic properties, are discussed in detail in Sec. [III C.](#page-7-0) Anticipating, we mention that they are consistent with experiment. We have also considered a second possible structure which is (almost) compatible with the TEM data, Cu3Mn2Sb2, depicted in Fig. [2](#page-3-0) (c). However, this compound is higher in energy than the β phase, and was dropped from further considerations.
#### <span id="page-4-0"></span>C. Magnetic properties
The temperature T dependence of magnetization, M(T), of the 200 nm thick layer of CuMnSb, is depicted in Fig. [4](#page-4-2) (a). The clear kink on M(T) at T<sup>N</sup> = 62 K marks the position of the paramagnetic to antiferromagnetic N´eel transition in the layer. This value corresponds precisely to the values of T<sup>N</sup> established previously for CuMnSb/GaSb layers of the thickness t ≥ 200 nm, what, indirectly, indicates stoichiometric material composition of this layer.[29](#page-12-12)
More specific information about the magnetic state of that sample is obtained from the examination of the temperature dependence of the inverse magnetic susceptibility, χ −1 (T), shown in Fig. [4](#page-4-2) (b). We take here χ(T) = M(T)/H, where H = 10 kOe is the external magnetic field applied during the measurements. χ −1 (T) can be approximated by two straight lines. The abscissa of the first one, which approximates χ −1 (T) above 200 K (the solid orange line in Fig. [4\)](#page-4-2), yields exactly the same magnitude of the Curie-Weiss temperature TCW = −100(5) K as that established previously for a thicker 510 nm layer, for which χ −1 (T) formed a single straight line above T<sup>N</sup> at the same experimental conditions.[29](#page-12-12) Also the slope of this line yields the value of the effective magnetic moment meff = 5.4(1)µ<sup>B</sup> per f.u., which is very close to that found previously, meff = 5.6µ<sup>B</sup> per f.u.[29](#page-12-12) This correspondence indicates that the high temperature part of χ −1 (T) is determined predominantly by AFM excitations in the paramagnetic matrix of CuMnSb.
The abscissa of the second straight line, which approximates the experimental data between T<sup>N</sup> and about 200 K (marked as the dashed orange line in Fig. [4\)](#page-4-2), yields a more positive value of the Curie-Weiss temperature, T ′ CW = −10(10) K. This clear positive shift of TCW indicates the existence of a ferromagnetic contribution to the overall antiferromagnetic phase of the material, and that these FM excitations gain in importance below about 200 K. Interestingly, a somewhat stronger effect, characterized by a change of sign of TCW to T ′ CW = +60(10) K, was noted in 40 nm CuMnSb layer grown on InAs.[34](#page-12-17) In accordance with the findings of structural characterization we propose that the by far stronger AFM component originates from the dominant α phase, whereas the FM one is brought about by β–CuMnSb polymorph.
<span id="page-5-1"></span>TABLE I. Experimental N´eel temperature TN, effective Curie-Weiss magnetic moment of Mn ions meff (Mn), and Curie-Weiss temperature TCW of α–CuMnSb. Measured orientation of the AFM axis is also given (n.e. = not established). Refs. [42](#page-12-24) and [41](#page-12-25) report the saturation Mn moment.
Turning now to the magnetic characteristics established here for α–CuMnSb we note that they are close to those reported previously, as shown in Tab. [I.](#page-5-1) The published data exhibit a certain distribution, which may indicate that other factors, such as a weak crystalline disorder, may be at work. In particular, either additional Mn interstitial ions or CuMn-MnCu antisite pairs are likely to form.[35](#page-12-18) The presence of such defects was suggested to stabilize the experimentally observed AFM {111}-oriented phase of α–CuMnSb.[35](#page-12-18) Finally, we do not observe a canted AFM order at low temperatures[41](#page-12-25) in any of our samples.
#### <span id="page-5-0"></span>III. THEORY
## A. Theoretical Methods
Calculations are performed within the density functional theory[46,](#page-13-2)[47](#page-13-3) in the generalized gradient approximation of the exchange-correlation potential proposed by Perdew, Burke and Ernzerhof.[48](#page-13-4) To improve description of 3d electrons, the Hubbard-type +U correction on Mn is added.[49–](#page-13-5)[51](#page-13-6) The parameter U(Mn) = 1 eV reproduces the known formation energy of the intermetallic CuMn alloy and gives a reasonable value of the Mn cohesive energy. We use the pseudopotential method implemented in the Quantum ESPRESSO code,[52](#page-13-7) with the valence atomic configuration 4s <sup>1</sup>.<sup>5</sup>p <sup>0</sup>3d 9.5 for Cu,
3s 2p <sup>6</sup>4s 2p <sup>0</sup>3d 5 for Mn and 5s 2p 3 for Sb ions. The planewaves kinetic energy cutoffs of 50 Ry for wave functions and 250 Ry for charge density are employed. Finally, geometry relaxations are performed with a 0.05 GPa convergence criterion for pressure. In defected crystals ionic positions are optimized until the forces acting on ions become smaller than 0.02 eV/˚A.
The properties of defected α–CuMnSb are examined using cubic 2a×2a×2a supercells with 96 atoms (i.e., 32 f.u.), while magnetic order of ideal crystals are checked using the smallest possible supercells. Here a is the equilibrium lattice parameter. The k-space summations are performed with a 6 × 6 × 6 k-point grid for the largest supercell, and correspondingly denser grids are used for smaller cells.
Magnetic interactions and magnetic order depend on several factors, such as the exchange spin splitting of the d(TM) shells, charge states of TM ions, concentration of free carriers and their spin polarization, and the density of states (DOS) at the Fermi energy EF. These factors are interrelated, and are calculated self-consistently within ab initio approach.
Considering first the localized magnetic moments we note that spin polarization of Co, Ni, and Cu ions in XMnZ compounds practically vanishes, while that of the d(Mn) shell is substantial.[16,](#page-11-14)[17](#page-12-0)[,31](#page-12-14) The robustness of the Mn magnetic moment results from the large, 3 – 5 eV, spin splitting of the 3d(Mn) states. In fact, in XMnZ the d(Mn) spin up channel is occupied, while most of the spin down d(Mn) states lay above the Fermi level. Here, one can observe that spin polarization of the d(TM) electrons in free atoms depends on the difference in the number of spin up and spin down electrons, which is the highest in the case of Mn. Consequently, the Mn spin polarization persists in XMnZ. On the other hand, spin splitting of d electrons of Co and Ni atoms is smaller, and thus it vanishes in XMnSb hosts, see the analysis for TM dopants in ZnO.[53](#page-13-8)
In CuMnSb, the magnetic sublattice consists of Mn ions, which are second neighbors distant by 4.3 ˚A. Therefore, the direct exchange coupling between two Mn ions, given by overlaps of their d(Mn) orbitals, is negligibly small. The remaining indirect exchange coupling is the sum of two contributions, and the exchange constant Jindirect = Jsr + JRKKY . [16](#page-11-14)[,17](#page-12-0)[,54](#page-13-9) The first term Jsr has a short-range AFM character, and it is inversely proportional to the energy distance between the unoccupied d(Mn) states and EF. The second coupling channel is of RKKY type mediated by free carriers. This channel depends on the detailed electronic structure in the vicinity of EF, and JRKKY is proportional to DOS(EF). In particular, CoMnSb and NiMnSb half-metals are FM, while CuMnP and CuMnAs insulators are AFM. As we show here, CuMnSb is the border case.
#### <span id="page-5-2"></span>B. Crystal and magnetic properties of α–CuMnSb
A rhombohedral primitive cell of α–CuMnSb contains one formula unit. This structure consist in four interpenetrating fcc sublattices, one of them being empty. The consecutive (001) MnSb planes are followed by the "halfempty" Cu planes, in which the planar atomic density is twice lower. The cubic unit cell is presented in Fig. [2](#page-3-0) (a). Local coordination of Mn ions can be relevant from the point of view of magnetic interactions. With this respect we notice that the magnetic coordination of an Mn ion consists in 12 equidistant Mn atoms at a/<sup>√</sup> 2. More-
We consider four magnetic phases of α–CuMnSb. The corresponding supercells are shown in Fig. [5.](#page-6-0) Antiferromagnetic order with parallel Mn spins in the (001) planes, AFM001, is calculated using the cubic a×a×a cell with 4 f.u. (12 atoms), and shown in Fig. [5](#page-6-0) (a). The AFM order with a period doubled in the [001] direction with parallel Mn spins in each (001) plane, denoted as AFM002, is shown in Fig. [5](#page-6-0) (b). The corresponding a×a×2a cell contains 8 f.u., and is one of the possible supercells in which this phase can be realized. In the AFM111 phase, the Mn spins are parallel in each (111) plane, but the consecutive (111) planes are AFM, as shown in Fig. [5](#page-6-0) (c), and the corresponding rhombohedral unit cell a √ 2 × a √ 2 × a √ 2 contains 8 primitive cells with 24 atoms. Finally, the FM phase requires a primitive cell a/<sup>√</sup> 2×a/<sup>√</sup> 2×a/<sup>√</sup> 2 with 1 f.u., presented in Fig. [5](#page-6-0) (d).
<span id="page-6-1"></span>TABLE II. The calculated lattice parameter a, the saturation Mn magnetic moment, msat, and the energy of the given magnetic order relative to α–CuMnSb in the AFM001 ground state, ∆Etot. All energies are per one formula unit. Our measured TEM values are also given.
higher in energy. The least stable is the FM order, higher in energy than AFM001 by about 20 meV per f.u. The equilibrium lattice parameters a ≈ 6.1 ˚A are practically independent of the magnetic order, and close to the experimental value 6.088 ˚A.[42](#page-12-24) Some phases are characterized by a small distortion of the cubic symmetry caused by different bond lengths between ferromagnetically and antiferromagnetically oriented Mn ions. Differences in the lattice parameters between various magnetic phases are below 0.01 ˚A, and are not reported in the Table. Similar results for the AFM001 order were obtained in Ref. [35,](#page-12-18) while in Refs [16](#page-11-14) and [31](#page-12-14) the AFM order is more stable than FM by 50 and 90 meV per Mn, respectively.
The last property reported in Tab. [II](#page-6-1) is the saturation magnetic moment of Mn, which also is similar in all phases, and equal to about 4.6µB. This value corresponds to the Curie-Weiss moment of 5.5(1)µB, and compares favorably with the experimental values given in Tab. [I.](#page-5-1)
The obtained results allow estimating the relative roles of the short- and long-range contributions to the magnetic coupling. To this end, we assume the hamiltonian in the form Hex = −J/2 P i,j ⃗si⃗s<sup>j</sup> , where the short range interaction is limited to the Mn NNs neighbors, and the long-range term is neglected. The spin value, s<sup>i</sup> ≈ 2.3, is one half of the calculated magnetic moment of Mn.
The exchange constant J is positive (negative) for the FM (AFM) coupling, and is obtained by comparing energies of various magnetic orders. In the AFM001 phase, each Mn ion has 4 ferromagnetically oriented Mn NNs in the (001) plane and 8 antiferromagnetically oriented Mn NNs in the two adjacent planes. For the remaining magnetic phases, the energies calculated relative to the ground state E<sup>0</sup> ≡ EAFM001 depend on the magnetic order as shown in Tab. [II.](#page-6-1) These results give the coupling constant in the range −0.6 ≥ Jsr ≥ −0.2 meV. This spread is quite large and cannot be explained by (negligible) changes in atomic distances in cells with different magnetic ordering. Therefore, we conclude that the Heisenberg nearest neighbor model does not describe magnetic properties of bulk phases. Indeed, such a model is not appropriate for metallic or semimetallic systems such as α–CuMnSb, where the long-range RKKY coupling is present.
An opposite conclusion comes from the analysis of single spin excitations from the AFM001 ground state. We use a 2a×2a×2a supercell to calculate the energy differences ∆E for the following cases, in which we change (i) spin of one Mn ion, 1Mn ↑→ 1Mn ↓, called a single spin-flip, (ii) 2Mn↑→ 2Mn↓ for spins of two nearest Mn ions belonging to one layer and (iii) 2Mn ↑→ 2Mn ↓ for two distant Mn ions. In these processes the long-range coupling is not important, and indeed the calculated exchange constant consistently is Jsr ≈ −0.4 meV.
#### <span id="page-7-0"></span>C. Crystal and magnetic properties of β–CuMnSb
We now consider two possible structures of the secondary phase proposed based on the experimental results. They are characterized by doubling the periodicity in the [001] direction. The unit cell of β–CuMnSb, shown in Fig. [2,](#page-3-0) is tetragonally deformed relative to that of α–CuMnSb, with the corresponding lattice parameters a = 5.88 ˚A and c = 6.275 ˚A. They differ by about 3 per cent from our calculated cubic a(α– CuMnSb) = 6.105 ˚A. The two interlayer spacings between the consecutive MnSb planes in the [001] direction in the unit cell, shown in Fig. [2](#page-3-0) (b), are quite different, namely dinter<sup>1</sup> = 2.80 ˚A (no Cu), and dinter<sup>2</sup> = 3.48 ˚A (with Cu). Turing to the magnetic order of β–CuMnSb, we find that the FM phase constitutes the ground state with msat = 4.6µ<sup>B</sup> and is lower than the AFM phase by 11 meV per f.u., as indicated in Tab. [II.](#page-6-1) Thus, the
The experimental[27](#page-12-10) lattice parameters of β–CuMnSb reasonably agree with our values, i.e., the calculated a = 6.28 ˚A and c/a = 1.87 are about 2% larger than those measured for the compressed crystal at the critical pressure of 7 GPa. On the other hand, the calculations of Ref. [27](#page-12-10) predict that the magnetic order of the β phase is AFM, in striking contrast with our results. Also their calculated msat(Mn) = 3.8µ<sup>B</sup> is substantially smaller than our 4.6µB. The origin of these discrepancies is not clear, but it may be due to the different exchange-correlation functionals used, and/or to application of the +U(Mn) correction in our calculations (which can affect the results.[31](#page-12-14))
The calculated total energy of the FM β–CuMnSb relative to the AFM α–CuMnSb is higher by 102 meV per f.u. This energy difference is not large, being comparable to the growth temperature, which implies that the β–CuMnSb polymorph can indeed form during epitaxy. We also stress that stoichiometry of the α and β phases is the same, which facilitates formation of β–CuMnSb. Finally, the observed β–CuMnSb inclusions are coherent, i.e., lattice matched, with the host structure. This agrees with the fact that the calculated excess elastic energy of matching the lattice parameters of the β phase to the host α phase is very low and ranges from 3 meV per f.u. (when the tetragonal a parameter constrained to the cubic a = 6.105 ˚A) to 20 meV per f.u. (the tetragonal c parameter constrained to the cubic a).
The second considered possibility, Cu3Mn2Sb<sup>2</sup> shown in Fig. [2](#page-3-0) (c), is higher in energy by 0.37 eV per f.u. in the Cu–rich conditions than the ideal CuMnSb, i.e., by 0.27 eV per f.u. than β–CuMnSb, its stoichiometry is markedly different, and thus we can eliminate this structure from considerations.
# D. Energy band structures of α–CuMnSb and β–CuMnSb
Figure [7](#page-8-1) (a) shows the energy bands and DOS of the AFM001 α–CuMnSb. We see that this phase has a metallic character, however DOS at the Fermi level is low. The states close to E<sup>F</sup> are built from s, p and d states of all ions with similar weights. The low DOS(EF) makes CuMnSb almost semimetallic with a low electrical conductivity. Compatible with the small DOS(EF) is the high resistivity measured in Ref. [41](#page-12-25) and [55.](#page-13-10)
Since the system is antiferromagnetically ordered, the total DOSs of spin-up and spin-down states are the same. In Fig. [7](#page-8-1) only contributions of the 3d(Mn) and 3d(Cu) orbitals are presented to reveal magnetic properties. We see that the exchange spin splitting of the d(Mn) shell is large, about 5 eV. The closely spaced levels contributing to the DOS maxima centered at 4 eV below the Fermi energy are composed mainly of the d states of both Cu and Mn. Spin-up and spin-down 3d(Cu) orbitals are almost
completely occupied, and thus Cu ions are non-magnetic. In turn, the majority spin states of the 3d(Mn) orbitals are completely occupied, while the minority spin states at 1 eV above the Fermi energy are partially filled thanks to a small overlap with spin up states. As a result, a single Mn ion is in between the d <sup>5</sup> and d 6 configuration, with the saturation magnetic moment of 4.6µ<sup>B</sup> consistent with Tab. [II.](#page-6-1) Our results for α–CuMnSb are close to those of Ref. [31.](#page-12-14) A similar electronic configuration takes place in CuMnAs, where the spin-down Mn states are partially filled.[56](#page-13-11)
The overall band structure of the FM β–CuMnSb displayed in Fig. [7](#page-8-1) (b) is close to that of α–CuMnSb, which is particularly clear when comparing partial DOS of both phases. In particular, msat(Mn) is about 4.5µ<sup>B</sup> in both phases, and energies of both d(Mn)- and d(Cu)-related bands are largely independent of the actual crystal structure. This similarity can be due to the fact that the MnSb (001) planes play a dominant role, and the exact locations of the Cu ions are less important.
On the other hand, the calculated DOS(EF) for the α phase is 0.35 states per spin and f.u., while for the β phase we find 1.26 states per spin and f.u., which is 3.6 times higher. As a consequence, α–CuMnSb is semimetallic, and the AFM order is dominant, while β phase is more metallic in character, which in turn favors the RKKY-type coupling and the FM order. This feature can explain the different magnetic phases of the α and β polymorphs.
Analysis of the calculated electronic structure of Heusler and half-Heusler CuMnZ led Sasioglu et al.[17](#page-12-0) to the conclusion that when the spin polarization of conduction electrons is large, and the d(Mn) spin down states are far above EF, then the RKKY coupling is dominant, and one should expect the FM order, otherwise the short range AFM coupling is dominant. Our results do not confirm this conclusion, and indicate that the important
## <span id="page-8-0"></span>E. Point native defects in α–CuMnSb
where E(CuMnSb) and E(CuMnSb : D) are the total energies of a supercell without and with a defect, and n<sup>i</sup> = +1(−1) corresponds to the removal (addition) of one ith atom. µis are the variable chemical potentials of atoms in the solid, which in general are different from the chemical potentials µi(bulk) of the standard state of elements, i.e., Cu, Mn and Sb bulk. Details of calculations of chemical potentials are given in Appendix [A.](#page-10-0)
The point native defects considered here are vacancies VX, interstitials X<sup>i</sup> , and antisites X<sup>Y</sup> (where X and Y are Cu, Mn, or Sb) for all three sublattices. As it was mentioned above, the Cu sublattice is "half- empty" compared to the MnSb sublattice. Consequently, we consider here formation of interstitials at the empty sites of the Cu sublattice only, and neglect other possibilities, expected to have higher formation energies Eform. Thus, the set of defects considered here only partially overlaps with that of Ref. [35.](#page-12-18) Of particular interest to the present study are defects involving Mn ions, since they can influence magnetic properties of α–CuMnSb .[35](#page-12-18) This is why we consider them more extensively, after briefly analyzing the non-magnetic defects. The calculated formation energies are summarized in Tab. [III.](#page-9-0) Because of the magnetic coupling, formation energies of the Mn-related defects depend on the spin direction relative to the spins of the host Mn neighbors. We consider possible spin configurations shown in Fig. [8](#page-9-1) (b).
<span id="page-9-0"></span>TABLE III. Formation energies (in eV) of isolated point defects in the Mn-rich conditions. In parentheses are Mn-related values corrected for ∆H<sup>f</sup> (MnSb) = 0.48 eV, which correspond to the Mn-poor case.
where k<sup>B</sup> is the Boltzmann constant and N<sup>0</sup> is the density of the relevant lattice sites. Details of the calculations of Eform are provided in Supporting Information. To put the calculated formation energies into a proper context, we note that if the growth temperatrure Tgrowth = 2500C and Eform = 0.1 eV, then exp(−Eform/kBTgrowth) = 0.1, which corresponds to a high 10 atomic per cent concentration of this defect on the considered sublattice. On the other hand, if Eform = 1 eV, then exp(−Eform/kBTgrowth) = 9 × 10<sup>−</sup><sup>11</sup>, which implies a negligible defect concentration.
Sb sublattice. The prohibitively high values of Eform demonstrate that VSb and Sb<sup>i</sup> should not form. Similarly, formation energies of SbCu, SbMn, CuSb and MnSb antisites exceed 1 eV, and those defects are not expected to be present at high concentrations. Consequently, the Sb sublattice is thermodynamically stable, robust, and constitutes a defect-free back-bone of CuMnSb.
(ii) Formation energy of Cu interstitials at the Cu sublattice, Eform(Cui) = 1 eV, is relatively high, and their concentrations are negligible. Additionally, the high formation energy of Cu<sup>i</sup> interstitials is consistent with the sparse character of the Cu sublattice in α–CuMnSb.
(iii) Formation of Mn<sup>i</sup> interstitials at the Cu sublattice is characterized by Eform = 0.7-1.4 eV, depending on the spin direction and conditions of growth, and therefore they are not expected to be present at high concentrations, especially in the Mn-poor conditions.
In brief, low formation energies are found for three defects, namely the VCu and VMn vacancies and the MnCu antisite, particularly at the Mn-rich growth conditions. This indicates that a Cu deficit on the Cu sublattice is possible, affecting stoichiometry. Significantly, MnCu antisites make the Cu sublattice magnetic, and also they can participate in the magnetic coupling between the adjacent MnSb (001) planes, thus influencing magnetic properties, as it will be discussed in more detail below. In contrast, SbCu antisites are present in negligible concentrations. Our results are in a reasonable agreement with those of Ref. [35,](#page-12-18) especially given their neglect of spin effects and a somewhat different theoretical approach. Interestingly, formation energies of native defects in CuMnAs calculated in Ref. [56](#page-13-11) are close to the present results in spite of the different anion.
## F. Defect-induced magnetic coupling
There are two Mn-related point defects, Mn<sup>i</sup> and MnCu, both situated on the Cu sublattice. When present at high concentrations, they affect magnetism of α– CuMnSb. Their coupling with host Mn ions is different than the Mn-Mn coupling between the host Mn because of the different local coordination. Energetics of both defects is complex and rich, since the total energy of the system (and thus formation energies) depends on their spin orientations relative to the neighborhood. At both substitutional and interstitial sites in the Cu layer, a Mn ion has 4 Mn nearest neighbors arranged in a tetrahedral configuration, 2 in the upper and 2 in the lower MnSb layer. The Mni–MnMn distance is shorter than that of
MnMn–MnMn, and equal to (<sup>√</sup> 3/4)a.
The possible local spin configurations are reduced to small clusters of 5 Mn ions, shown in Fig. [8.](#page-9-1) The Mn spin-up and spin-down (001) MnSb layers are denoted by in pink and blue, respectively, reflecting the calculated (001) AFM magnetic ground state. The central MnCu (or Mni) ion of such a cluster provides an additional channel of magnetic coupling between two adjacent MnSb layers. The corresponding formation energies are given in Fig. [8.](#page-9-1)
As it was pointed out, in ideal α–CuMnSb, the Mn ions are second neighbors only, separated either by Sb (i.e., the Mn-Sb-Mn "bridge" in the MnSb(001) plane), or by Cu (forming a Mn-Cu-Mn "bridge" linking 3 consecutive (001) planes.) Thus, the short range magnetic coupling in ideal α–CuMnSb is successfully modelled in Sec. [III B](#page-5-2) by the interaction between two Mn second neighbors, situated either in the same MnSb layer, or in two adjacent ones. In contrast, the 4 host Mn ions in the cluster are the first neighbors of a Mn<sup>i</sup> or a MnCu defect. Thus, one can expect that this coupling is stronger than the intrinsic one in the ideal host, and indeed, the differences in energy between various configurations in Fig. [8](#page-9-1) are about 100 meV, which is too high to be explained by the estimated Jsr = 0.4 meV.
As it follows from Fig. [8,](#page-9-1) 5-atom clusters are magnetically frustrated. In particular, the lowest energy case denoted as 4AFM favors the local FM orientation of spins in two adjacent (001) planes, which is opposite to the global host magnetic order. Our results do not confirm the conclusion of Ref. [56](#page-13-11) who find that the 3AFM configuration has the lowest energy, and thus it promotes the global AFM111 order. Instead, we rather expect that Mn-related point defects induce disorder of the host AFM phase, possibly leading to formation of a spin glass.[57](#page-13-12)
#### IV. SUMMARY
CuMnSb films were epitaxially grown on GaSb substrates. Magnetic measurements reveal the presence of two magnetic subsystems. The dominant magnetic order is AFM with the N´eel temperature of 62 K, which is the same as in bulk CuMnSb. It co-exists with a FM phase, characterized by the Curie temperature of about 100 K.
These findings go in hand with transmission electron microscopy and selective area diffraction measurements, which demonstrate coexistence of two structural polymorphs of the same stoichiometry. The dominant one is the cubic half-Heusler α–CuMnSb, which is the equilibrium structure of bulk samples. The second component is a tetragonal β–CuMnSb polymorph, which forms 10-100 nm long elongated inclusions.
(i) The β–CuMnSb phase is metastable, and its total energy is higher by 0.1 eV per f.u. only than that of the equilibrium α–CuMnSb. Lattice parameters of the β phase differ from those of α–CuMnSb by about 4 per cent. This lattice misfit between the two structures does not prevent the pseudomorphic coexistence of both phases, since the calculated misfit strain energy is below 20 meV per f.u.
(ii) In agreement with experiment, α–CuMnSb is AFM, and the FM order is 19 meV per f.u. higher in energy. In contrast, the magnetic ground state of β– CuMnSb is FM, which is more stable than AFM by 11 meV per f.u. This indicates that indeed the β–CuMnSb inclusions are responsible for the FM signal.
(iii) The different magnetic orders of the α and β phases originate in their somewhat different band structures. In particular, critical for magnetic order is the DOS at the Fermi level, which is about 4 times higher in β–CuMnSb than in the α phase. This shows that the β phase is more metallic in character, which in turn favors the FM order driven by the Ruderman-Kittel-Kasuya-Yoshida interaction.
(iv) Our calculations predict the saturated magnetic moment of Mn msat = 4.6µ<sup>B</sup> and 4.5µ<sup>B</sup> for the α and the β phase, respectively. This corresponds to the effective moment of 5.6µB, in good agreement with the measured 5.5µB.
(v) The calculated formation energies of point native defects indicate that the most probable are the MnCu antisites with low formation energies of 0–0.2 eV. However, their presence is expected to disorder the host magnetic AFM phase rather than to induce a transition to the FM configuration.
(vi) Regarding the properties of the CuMnX series we see that their structural stability is relatively weak, as they crystallize in a variety of structures. In particular, unlike the bulk orthorhombic CuMnAs, epitaxial films of CuMnAs are tetragonal, but both structures are AFM. In the case of CuMnSb, polymorphism comprises also the equilibrium magnetic structure, AFM in the bulk specimens, and FM in epitaxial films.
#### ACKNOWLEDGMENTS
LS, CG, JK and LWM thank M. Zipf for technical assistance. Our work was funded by the Deutsche Forschungsgemeinschaft (DFG,German Research Foundation) No. 397861849, by the Free State of Bavaria (Institute for Topological Insulators) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC2147 ct.qmat (Project-Id 390858490).
#### <span id="page-10-0"></span>Appendix A:
The highest possible value of µ<sup>i</sup> is µi(bulk), which implies that the studied system is in equilibrium with the given bulk source of atoms and δµ<sup>i</sup> = 0, otherwise δµ<sup>i</sup> < 0.
Chemical potentials of the components in the standard state are given by the total energies per atom of elemental solids. The calculated cohesive energies Ecoh of the face centered cubic Cu, the face centered cubic Mn with the AFM magnetic order, and the triclinic Sb are, respectively, 3.40 (3.49), 2.65 (2.92) and 2.68 (2.75) eV/atom. They compare reasonably well with the experimental values given in parentheses.[58](#page-13-13)
Chemical potentials of the involved atomic species depend on possible formation of compounds. The ranges of variations of chemical potentials are determined by conditions of equilibrium between various phases, i.e., Cu2Sb, MnSb and CuMnSb. Thermodynamic equilibrium requires that
$$\begin{aligned} \delta\mu(\text{Cu}) + 2\delta\mu(\text{Sb}) &= \Delta H\_f(\text{Cu}\_2\text{Sb}), \\ \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{MnSb}), \\ \delta\mu(\text{Cu}) + \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{CuMnSb}), \end{aligned} \quad \text{(A2)}$$
The calculated values ∆H<sup>f</sup> (Cu2Sb) = −0.03 eV per f.u., ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u., and ∆H<sup>f</sup> (CuMnSb) = −0.42 eV per f.u. The very low ∆H<sup>f</sup> (Cu2Sb) is somewhat unexpected, since Cu2Sb is a stable compound which crystallizes in the tetragonal phase.[43](#page-12-26) Next, our result ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u. agrees well with both the previous value -0.52 eV per f.u. calculated in Ref. [59,](#page-13-14) and the experimental - 0.52 eV per f.u.[60](#page-13-15) Assuming that the accuracy of the calculated values is 0.03 eV per f.u., the set of Equation [A2](#page-11-15) is consistent if we assume ∆H<sup>f</sup> (Cu2Sb) = 0, and ∆H<sup>f</sup> (MnSb) = ∆H<sup>f</sup> (CuMnSb) = −0.45 eV per f.u. This in turn implies that δµ(Cu) = δµ(Sb) = 0, and δµ(Mn) = −0.45 eV. Consequently, the allowed window of the Mn chemical potential is
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| |
FIG. 4. Results of temperature dependent magnetic studies of 200 nm thick CuMnSb layer (green bullets). (a) Magnetization M established in a bias field of H = 10 kOe, and (b) the corresponding inverse of the molar magnetic susceptibility χ −1 <sup>m</sup> . The solid and dashed orange lines indicate the Curie-Weiss behavior of χ −1 <sup>m</sup> (T) for T > 200 K and for T<sup>N</sup> < T < 200 K, respectively. The arrows indicate the position of the N´eel temperature, T<sup>N</sup> = 62 K, on both panels.
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# Coexistence of Antiferromagnetic Cubic and Ferromagnetic Tetragonal Polymorphs in Epitaxial CuMnSb
High-resolution transmission electron microscopy and superconducting quantum interference device magnetometry shows that epitaxial CuMnSb films exhibit a coexistence of two magnetic phases, coherently intertwined in nanometric scales. The dominant α phase is half-Heusler cubic antiferromagnet with the N´eel temperature of 62 K, the equilibrium structure of bulk CuMnSb. The secondary phase is its ferromagnetic tetragonal β polymorph with the Curie temperature of about 100 K. First principles calculations provide a consistent interpretation of experiment, since (i) total energy of β–CuMnSb is higher than that of α–CuMnSb only by 0.12 eV per formula unit, which allows for epitaxial stabilization of this phase, (ii) the metallic character of β–CuMnSb favors the Ruderman-Kittel-Kasuya-Yoshida ferromagnetic coupling, and (iii) the calculated effective Curie-Weiss magnetic moment of Mn ions in both phases is about 5.5 µB, favorably close to the measured value. Calculated properties of all point native defects indicate that the most likely to occur are MnCu antisites. They affect magnetic properties of epilayers, but they cannot induce the ferromagnetic order in CuMnSb. Combined, the findings highlight a practical route towards fabrication of functional materials in which coexisting polymorphs provide complementing functionalities in one host.
#### I. INTRODUCTION
One of the most challenging and long-standing problems in fundamental magnetism is a competition between ferromagnetic and antiferromagnetic phases. Their interplay at the interface results in a well known effect of the exchange bias,[1](#page-11-1)[,2](#page-11-2) which fuels now a rapid development of spintronics[3](#page-11-3) and unconventional computing.[4](#page-11-4) The material class of Heusler alloys was previously used to study the origin of the transition between magnetic phases because it offers a wide spectrum of functionalities.[5](#page-11-5) Indeed, Heusler alloys exhibit ferromagnetic (FM), antiferromagnetic (AFM), and canted ferromagnetic order. This indicates that different types of magnetic coupling are competing in this family. Moreover, some of its members display structural polymorphism, which allows studying relationships between the crystalline phase, the magnetic phase, and the corresponding electronic structure.
Heusler alloys incorporate full-Heusler (X2YZ) and half-Heusler (XYZ) variants, where X and Y stand for transition metals, whereas Z denotes anions from the main group. In this class, qualitative changes in material characteristics can be achieved by chemical substitution on either the transition metal cation or on the anion sublattice. Typically, the change of the cation does not change the crystal structure, but it can induce a crossover between the AFM and the FM magnetic phases. A rarely met complete solubility with only marginally affected crystallinity of the otherwise chemically homogenous systems allowed to study the FM-AFM phase competition in detail. The prominent examples are quaternary solid solutions such as Ru2Mn1−xFexSn[6–](#page-11-6)[8](#page-11-7)
Heuslers, and Co1−xNixMnSb,[9](#page-11-8)[,10](#page-11-9) Cu1−xNixMnSb,[11–](#page-11-10)[13](#page-11-11) Co1−xCuxMnSb,[14](#page-11-12) and Cu1−xPdxMnSb[15](#page-11-13) half-Heuslers. In the latter case, the crossover between AFM to FM phases is related to a change in the electronic structure from semimetallic to half-metallic.[16](#page-11-14)[,17](#page-12-0)
Cu–based CuMnZ compounds are antiferromagnets. This feature attracts attention given the recent progress achieved in the AFM spintronics.[18](#page-12-1) Of particular interest is CuMnAs, with a high N´eel temperature T<sup>N</sup> = 480 K.[19](#page-12-2) In this case, features essential for applications, such as anisotropic magnetoresistance,[20,](#page-12-3)[21](#page-12-4) current-induced electrical switching of the N´eel vector[22](#page-12-5) and of the magnetic domains,[23](#page-12-6) have been demonstrated.
The AFM order of CuMnZ is independent of the actual crystalline structure. The equilibrium structure of bulk CuMnP and CuMnAs is orthorhombic, while that of CuMnSb is half-Heusler cubic, referred to below as the α phase. On the other hand, epitaxial growth can stabilizes metastable phases. This is the case of epitaxial layers of CuMnAs, grown on both GaP[19](#page-12-2)[–21](#page-12-4)[,24](#page-12-7)[,25](#page-12-8) and GaAs[23](#page-12-6) substrates, which crystalize in the tetragonal structure, referred to below as the β phase. Theoretical investigations of the crystalline properties of CuMnZ series show that the total energy difference between the cubic and orthorhombic phase is about 1 eV per f.u. (formula unit) for CuMnP, and about 0.5 eV per f.u. for CuMnAs.[26](#page-12-9) This suggests that the orthorhombic phase of CuMnSb, the last member of the CuMnZ series, may not be stable, and indeed the stable structure is the α phase. However, as we show here, epitaxial stabilization of CuMnSb in the β phase is in principle possible, because the calculated energy difference between
Concerning the magnetic properties, the N´eel temperature of both orthorhombic CuMnAs and β–CuMnAs is well above the room temperature,[19](#page-12-2) whereas that of α– CuMnSb is lower, about 60 K.[28,](#page-12-11)[29](#page-12-12) Theory agrees with experiment, since according to Ref. [30,](#page-12-13) in the orthorhombic CuMnP and CuMnAs, the AFM order is more stable than the FM by about 250 meV/Mn. This energy difference is smaller in the cubic phase of CuMnZ compounds, for which the AFM order is lower in energy than FM one by about 50 meV per f.u.[30](#page-12-13)[,31](#page-12-14) Finally, the AFM order of α–CuMnSb is stable under applied magnetic field, as T<sup>N</sup> does not change up to 50 Tesla.[32](#page-12-15)
Turning to the electronic structure of the CuMnP-CuMnAs-CuMnSb series we observe that the character of the energy band gap depends on the anion. Similar to the case of e.g. zinc blende semiconductors, the band gap decreases with the increasing atomic number of the anion.[30](#page-12-13) Indeed, CuMnP is a semiconductor, CuMnAs has a practically vanishing band gap, and CuMnSb is a semimetal.[33](#page-12-16)
Here we experimentally confirm a puzzling coexistence of AFM and FM phases in epitaxial stoichiometric CuMnSb films, observed by us previously,[34](#page-12-17) and explain the underlying mechanism responsible for this effect. A fine analysis of transmission electron microscopy (TEM) images, Sec. [II B,](#page-2-0) points to the formation of tetragonal β–CuMnSb inclusions embedded coherently within the cubic α–CuMnSb host. The tetragonal structure of these inclusions is the same as that of the tetragonal β– CuMnAs. Magnetic properties of our films, Sec. [II C,](#page-4-0) demonstrate coexistence of two magnetic phases: apart from the dominant AFM one, expected for CuMnSb, the measurements reveal the presence of a FM contribution. This is an unexpected feature within the CuMnZ series, exhibiting the AFM order.
In Sec. [III,](#page-5-0) we employ calculations based on the density functional theory to assess properties of CuMnSb films. In agreement with the experiment, β–CuMnSb is weakly metastable, but its magnetic ground state is FM. Band structures of α and β polymorphs are close, but changes in the density of states at the Fermi level account for the change of the dominant mechanism of the magnetic coupling from AFM superexchange to FM Ruderman-Kittel- Kasuya-Yoshida (RKKY). Finally, in Sec. [III E](#page-8-0) native point defects in CuMnSb are examined to assess their possible influence on the magnetic properties.[35](#page-12-18) Our results indicate that the dominant native defects in α–CuMnSb are Mn antisites, and their presence in the films can possibly account for small differences between the measured and the calculated magnetic characteristics, but they do not stabilize the FM order of α–CuMnSb.
# II. EXPERIMENTAL RESULTS
## A. Experimental Methods
# Growth conditions.
CuMnSb layers about 200 nm thick are grown by molecular beam epitaxy. Separate growth chambers connected by an ultra-high vacuum transfer system are used for the growth of the individual layers. Low telluriumdoped epi-ready GaSb (001) wafers are used as substrates. Prior to the growth, the natural oxide layer is desorbed in an Sb atmosphere. Then, 150 nm thick GaSb buffer layers are grown on the substrates to ensure a high-quality interface for the growth of CuMnSb. The GaSb buffer layers are grown at a substrate temperature of 530◦C and a beam equivalent pressure of 4.0 × 10−<sup>6</sup> mbar and 5.3 × 10−<sup>7</sup> mbar for Sb and Ga, respectively. Sb supply is facilitated by a single-filament effusion cell, while Ga is provided by a double-filament effusion cell.
A substrate temperature of 250◦C is used for the growth of CuMnSb films. The corresponding beam equivalent pressures are as follows: BEPCu = 5.80 × 10<sup>−</sup><sup>9</sup> mbar, BEPMn = 9.03 × 10<sup>−</sup><sup>9</sup> mbar, and BEPSb = 4.23 × 10<sup>−</sup><sup>8</sup> mbar. Cu is supplied by a double filament effusion cell, while Mn and Sb are supplied by single filament effusion cells. Following the growth of CuMnSb, a 2.5 nm thick layer of Al2O<sup>3</sup> is deposited on the samples through a sequential process of aluminum DC magnetron sputtering and oxidation. Please, refer to Ref. [29](#page-12-12) for a comprehensive analysis of the growth process and physical properties of the CuMnSb layers produced using the methodology outlined above.
Transmission Electron Microscopy. Specimens for the transmission electron microscopy (TEM) investigations are prepared by the focused ion beam method in the form of lamellas cut along the [100] and [110] directions, i.e., perpendicularly to the surface (001) plane. Titan Cubed 80-300 electron transmission microscope operating with accelerating voltage 300 kV and equipped with energy-dispersive X-ray spectrometer (EDXS) is used for the study. Most of the investigations are done on Cu grids, but for EDXS elemental analysis a Mo grid is used to avoid interference of Cu fluorescence signal from the grid. This analysis yields percentage atomic concentration at 37(3) : 32(5) : 31(7) for Cu, Mn, and Sb, respectively, which, within the experimental errors (given in the parentheses), correspond to the expected stoichiometric ratio of 33 : 33 : 33.
SQUID Magnetometry. Magnetic characterization is performed in a commercial superconducting quantum interference device (SQUID) magnetometer MPMS XL7. The magnetic moment of antiferromagnetic layers is generally very weak and by far dominated by the magnetic response of the bulky semiconductor substrates. Therefore, to counter act the typical shortcomings of commercial magnetometers built around superconducting magnets[36](#page-12-19) and to minimize subtraction errors during
![<span id="page-2-1"></span>FIG. 1. (a) High-angle annular dark-field scanning transmission electron microscopy image of a CuMnSb layer in the [100] zone axis. The inset in the top-right corner brings up a part of the image in atomic resolution, where bright dots represent columns of Mn and Sb atoms. (b) Electron diffraction pattern of the layer. (c) Schematics of the positions of Bragg's spots from (b). Big bullets represent the main reflections from the cubic CuMnSb structure, whereas the open triangles mark the positions of the weak extra reflections. The orientation of the triangles follows from the analysis of the data in panels (d-g). (d-e) Blown up two regions from (a), in which either vertical or horizontal strips dominate. The corresponding Fourier transforms are showed in the top right corners of both panels. (f) Selected area electron diffraction pattern taken at the regions dominated by the vertically oriented strips. (g) Diffraction intensity profiles taken along the horizontal [010]\* and the vertical [001]\* lines passing through the center the diffraction pattern. The solid line corresponds to the horizontal [010]\* direction and the dashed one to the vertical [001]\* one in panel (f). Stars denote directions in the reciprocal space. The arrows α and β indicate the length of α–2g(002) and β–2g(002) diffraction vectors, respectively.](path)
data reduction we actively employ the in situ compensation.[37](#page-12-20) It allows us to reduce the coupling of the signal of the substrates to about 10% of their original strength. The actual effectiveness of the compensation depends on the mass of the sample and its orientation with respect to the SQUID pick-up coils.[36,](#page-12-19)[38](#page-12-21) We also strongly underline the importance of a thorough mechanical removal of the metallic MBE glue from the backside of the samples for any magnetic studies. Its strongly nonlinear magnetic contribution can be of the same magnitude as that of the layer of interest.[39](#page-12-22) To accurately establish the magnitude of magnetic moment specific to CuMnSb we measure a reference sample grown without the CuMnSb layer[29](#page-12-12) using the same sample holder and following exactly the
#### <span id="page-2-0"></span>B. Structural characterization
An exemplary atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF/STEM) image obtained for the [100] zone axis (the direction of the projection) is in Fig. [1](#page-2-1) (a). It confirms a high quality cubic constitution of the material, as it is underlined in the inset. However, at the contrast chosen here, the image in this field of view reveals the presence of stripe-like features, which are the main subject of this analysis. In this image, the apparent lengths and widths of the strips are about 40 nm and about 4 nm, respectively, running predominantly either vertically or horizontally in this particular projection. On other images, the strips exhibit a relatively wide distribution of lengths in the 10-100 nm window. Since similarly distributed shadowy stripes are observed also in the [110] zone axis, we conclude that they form along all three principal crystallographic directions without any particular preferences. The expected F43m cubic structure of α–CuMnSb is clearly confirmed by the fourfold symmetry of the dominant (bright) spots seen on electron diffraction pattern presented in Fig. [1](#page-2-1) (b).
Importantly, the diffraction pattern in Fig. [1](#page-2-1) (b) contains also a second set of much fainter reflections, situated halfway between two adjacent reflections of the main pattern. This indicates the presence of a second crystallographic β phase, which periodicity in the corresponding direction is doubled relative to that of α–CuMnSb, but otherwise coherent with this host structure. We bring all the Bragg's spots up in Fig. [1](#page-2-1) (c), in which the bullets represent the main reflections from α–CuMnSb, whereas the open triangles mark the positions of the weak ones, which are forbidden for this structure.
The presence of β–CuMnSb is further substantiated by the inspection of the two close-ups from Fig. [1](#page-2-1) (a), shown in Fig. [1](#page-2-1) (d) and (e). At this magnification they reveal that, on top of the otherwise cubic arrangement of atomic columns, the strips' brightness alternates every second {002} plane along the direction perpendicular to strip's long axis. The modulation is vertical in Fig. [1](#page-2-1) (d), whereas it goes horizontally in Fig. [1](#page-2-1) (e). The top right corners of these figures contain the corresponding Fourier transform of the parent image, and, similarly to Fig. [1](#page-2-1) (b), both patterns are dominated by the main reflections of α–CuMnSb. The additional spots are embedded either along vertical [Fig. [1](#page-2-1) (d)] or horizontal [Fig. [1](#page-2-1) (e)] lines, i.e., the presence of vertical and horizontal orientations is mutually exclusive. This feature is reflected in Fig. [1](#page-2-1) (c), where the additional spots are marked by differently oriented triangles. The triangles with apexes directed vertically correspond to the vertical orientation of the brightness modulation in Fig. [1](#page-2-1) (d), whereas the horizontal direction of apexes corresponds to the horizontal modulation.
Based on the data shown above we propose that the second phase of CuMnSb, present in our films in the form of strips, is a tetragonal structure, which also is the structure of epitaxial CuMnAs,[19–](#page-12-2)[21](#page-12-4)[,23](#page-12-6)[–25](#page-12-8) and of CuMnSb at high pressures.[27](#page-12-10) This β–CuMnSb polymorph is shown in the panel (b) of Fig. [2.](#page-3-0) The difference between α and β phases consists in the location of Cu ions: in the α phase every (001) plane between two consecutive MnSb planes is half-occupied by Cu, whereas in the β phase Cu ions completely fill up every second (001) plane, and the overall stoichiometry of the material is preserved.
![<span id="page-3-0"></span>FIG. 2. Crystal structures of (a) α–CuMnSb with the cubic lattice constant a, (b) tetragonal β–CuMnSb with the lattice constants a in the (x, y) plane and c in the [001] direction, and (c) Cu3Mn2Sb2.](path)
regions with different orientations of the strips. Diffraction pattern of an area dominated by the vertically oriented strips is shown in more detail in Fig. [1](#page-2-1) (f). In agreement with the Fourier transforms, SAED shows the occurrence of specific reflections corresponding to this particular orientation. The reflections common to both the cubic α and the tetragonal β polymorphs are split along the [010]\* direction, i.e., orthogonal to the strip's axis, whereas the weak spots of the β phase are not split and are commensurate with the cubic phase. (A star denotes a direction in the reciprocal space.)
We quantify the effect analyzing intensity profiles taken along lines passing through the center of diffraction. The profiles are superimposed, and presented in Fig. [1](#page-2-1) (g). The profile along the [001]\* direction reflects the periodicity of α–CuMnSb, while that along [010]\* is additionally split. From the Figure it follows that in our specimens the c lattice parameter of the β–CuMnSb strips is equal to that of the host α–CuMnSb, 6.2(1) ˚A, whereas the a and b parameters of the β phase, 5.8(1) ˚A, are smaller by about 7%. Analogous features are observed for the [010]-oriented strips.
The existence of such a significant strain is confirmed by the calculation of strain maps. We apply the geometrical phase analysis method[40](#page-12-23) for the main image presented in Fig. [1](#page-2-1) (a), and the results are presented in Fig. [3](#page-4-1) (a) and (b) for the horizontal, ϵxx, and the vertical, ϵzz, components of strain, respectively. It is seen that stripes' strain is negative (dark shade) perpendicular to strips and almost zero along the strips. For example, on the horizontal strain map [Fig. [3](#page-4-1) (a)] only vertical strips are visible because they are compressed horizontally, whereas the horizontal strips are invisible because they are not deformed in the horizontal direction.
 (a). (a) The horizontal component of strain ϵxx, and (b) the vertical one, ϵzz. Geometrical phase analysis method has been applied.[40](#page-12-23)](path)
The calculated properties of β–CuMnSb, such as its lattice parameters, stability, and magnetic properties, are discussed in detail in Sec. [III C.](#page-7-0) Anticipating, we mention that they are consistent with experiment. We have also considered a second possible structure which is (almost) compatible with the TEM data, Cu3Mn2Sb2, depicted in Fig. [2](#page-3-0) (c). However, this compound is higher in energy than the β phase, and was dropped from further considerations.
#### <span id="page-4-0"></span>C. Magnetic properties
The temperature T dependence of magnetization, M(T), of the 200 nm thick layer of CuMnSb, is depicted in Fig. [4](#page-4-2) (a). The clear kink on M(T) at T<sup>N</sup> = 62 K marks the position of the paramagnetic to antiferromagnetic N´eel transition in the layer. This value corresponds precisely to the values of T<sup>N</sup> established previously for CuMnSb/GaSb layers of the thickness t ≥ 200 nm, what, indirectly, indicates stoichiometric material composition of this layer.[29](#page-12-12)
More specific information about the magnetic state of that sample is obtained from the examination of the temperature dependence of the inverse magnetic susceptibility, χ −1 (T), shown in Fig. [4](#page-4-2) (b). We take here χ(T) = M(T)/H, where H = 10 kOe is the external magnetic field applied during the measurements. χ −1 (T) can be approximated by two straight lines. The abscissa of the first one, which approximates χ −1 (T) above 200 K (the solid orange line in Fig. [4\)](#page-4-2), yields exactly the same magnitude of the Curie-Weiss temperature TCW = −100(5) K as that established previously for a thicker 510 nm layer, for which χ −1 (T) formed a single straight line above T<sup>N</sup> at the same experimental conditions.[29](#page-12-12) Also the slope of this line yields the value of the effective magnetic moment meff = 5.4(1)µ<sup>B</sup> per f.u., which is very close to that found previously, meff = 5.6µ<sup>B</sup> per f.u.[29](#page-12-12) This correspondence indicates that the high temperature part of χ −1 (T) is determined predominantly by AFM excitations in the paramagnetic matrix of CuMnSb.
The abscissa of the second straight line, which approximates the experimental data between T<sup>N</sup> and about 200 K (marked as the dashed orange line in Fig. [4\)](#page-4-2), yields a more positive value of the Curie-Weiss temperature, T ′ CW = −10(10) K. This clear positive shift of TCW indicates the existence of a ferromagnetic contribution to the overall antiferromagnetic phase of the material, and that these FM excitations gain in importance below about 200 K. Interestingly, a somewhat stronger effect, characterized by a change of sign of TCW to T ′ CW = +60(10) K, was noted in 40 nm CuMnSb layer grown on InAs.[34](#page-12-17) In accordance with the findings of structural characterization we propose that the by far stronger AFM component originates from the dominant α phase, whereas the FM one is brought about by β–CuMnSb polymorph.
<span id="page-5-1"></span>TABLE I. Experimental N´eel temperature TN, effective Curie-Weiss magnetic moment of Mn ions meff (Mn), and Curie-Weiss temperature TCW of α–CuMnSb. Measured orientation of the AFM axis is also given (n.e. = not established). Refs. [42](#page-12-24) and [41](#page-12-25) report the saturation Mn moment.
Turning now to the magnetic characteristics established here for α–CuMnSb we note that they are close to those reported previously, as shown in Tab. [I.](#page-5-1) The published data exhibit a certain distribution, which may indicate that other factors, such as a weak crystalline disorder, may be at work. In particular, either additional Mn interstitial ions or CuMn-MnCu antisite pairs are likely to form.[35](#page-12-18) The presence of such defects was suggested to stabilize the experimentally observed AFM {111}-oriented phase of α–CuMnSb.[35](#page-12-18) Finally, we do not observe a canted AFM order at low temperatures[41](#page-12-25) in any of our samples.
#### <span id="page-5-0"></span>III. THEORY
## A. Theoretical Methods
Calculations are performed within the density functional theory[46,](#page-13-2)[47](#page-13-3) in the generalized gradient approximation of the exchange-correlation potential proposed by Perdew, Burke and Ernzerhof.[48](#page-13-4) To improve description of 3d electrons, the Hubbard-type +U correction on Mn is added.[49–](#page-13-5)[51](#page-13-6) The parameter U(Mn) = 1 eV reproduces the known formation energy of the intermetallic CuMn alloy and gives a reasonable value of the Mn cohesive energy. We use the pseudopotential method implemented in the Quantum ESPRESSO code,[52](#page-13-7) with the valence atomic configuration 4s <sup>1</sup>.<sup>5</sup>p <sup>0</sup>3d 9.5 for Cu,
3s 2p <sup>6</sup>4s 2p <sup>0</sup>3d 5 for Mn and 5s 2p 3 for Sb ions. The planewaves kinetic energy cutoffs of 50 Ry for wave functions and 250 Ry for charge density are employed. Finally, geometry relaxations are performed with a 0.05 GPa convergence criterion for pressure. In defected crystals ionic positions are optimized until the forces acting on ions become smaller than 0.02 eV/˚A.
The properties of defected α–CuMnSb are examined using cubic 2a×2a×2a supercells with 96 atoms (i.e., 32 f.u.), while magnetic order of ideal crystals are checked using the smallest possible supercells. Here a is the equilibrium lattice parameter. The k-space summations are performed with a 6 × 6 × 6 k-point grid for the largest supercell, and correspondingly denser grids are used for smaller cells.
Magnetic interactions and magnetic order depend on several factors, such as the exchange spin splitting of the d(TM) shells, charge states of TM ions, concentration of free carriers and their spin polarization, and the density of states (DOS) at the Fermi energy EF. These factors are interrelated, and are calculated self-consistently within ab initio approach.
Considering first the localized magnetic moments we note that spin polarization of Co, Ni, and Cu ions in XMnZ compounds practically vanishes, while that of the d(Mn) shell is substantial.[16,](#page-11-14)[17](#page-12-0)[,31](#page-12-14) The robustness of the Mn magnetic moment results from the large, 3 – 5 eV, spin splitting of the 3d(Mn) states. In fact, in XMnZ the d(Mn) spin up channel is occupied, while most of the spin down d(Mn) states lay above the Fermi level. Here, one can observe that spin polarization of the d(TM) electrons in free atoms depends on the difference in the number of spin up and spin down electrons, which is the highest in the case of Mn. Consequently, the Mn spin polarization persists in XMnZ. On the other hand, spin splitting of d electrons of Co and Ni atoms is smaller, and thus it vanishes in XMnSb hosts, see the analysis for TM dopants in ZnO.[53](#page-13-8)
In CuMnSb, the magnetic sublattice consists of Mn ions, which are second neighbors distant by 4.3 ˚A. Therefore, the direct exchange coupling between two Mn ions, given by overlaps of their d(Mn) orbitals, is negligibly small. The remaining indirect exchange coupling is the sum of two contributions, and the exchange constant Jindirect = Jsr + JRKKY . [16](#page-11-14)[,17](#page-12-0)[,54](#page-13-9) The first term Jsr has a short-range AFM character, and it is inversely proportional to the energy distance between the unoccupied d(Mn) states and EF. The second coupling channel is of RKKY type mediated by free carriers. This channel depends on the detailed electronic structure in the vicinity of EF, and JRKKY is proportional to DOS(EF). In particular, CoMnSb and NiMnSb half-metals are FM, while CuMnP and CuMnAs insulators are AFM. As we show here, CuMnSb is the border case.
#### <span id="page-5-2"></span>B. Crystal and magnetic properties of α–CuMnSb
A rhombohedral primitive cell of α–CuMnSb contains one formula unit. This structure consist in four interpenetrating fcc sublattices, one of them being empty. The consecutive (001) MnSb planes are followed by the "halfempty" Cu planes, in which the planar atomic density is twice lower. The cubic unit cell is presented in Fig. [2](#page-3-0) (a). Local coordination of Mn ions can be relevant from the point of view of magnetic interactions. With this respect we notice that the magnetic coordination of an Mn ion consists in 12 equidistant Mn atoms at a/<sup>√</sup> 2. More-
We consider four magnetic phases of α–CuMnSb. The corresponding supercells are shown in Fig. [5.](#page-6-0) Antiferromagnetic order with parallel Mn spins in the (001) planes, AFM001, is calculated using the cubic a×a×a cell with 4 f.u. (12 atoms), and shown in Fig. [5](#page-6-0) (a). The AFM order with a period doubled in the [001] direction with parallel Mn spins in each (001) plane, denoted as AFM002, is shown in Fig. [5](#page-6-0) (b). The corresponding a×a×2a cell contains 8 f.u., and is one of the possible supercells in which this phase can be realized. In the AFM111 phase, the Mn spins are parallel in each (111) plane, but the consecutive (111) planes are AFM, as shown in Fig. [5](#page-6-0) (c), and the corresponding rhombohedral unit cell a √ 2 × a √ 2 × a √ 2 contains 8 primitive cells with 24 atoms. Finally, the FM phase requires a primitive cell a/<sup>√</sup> 2×a/<sup>√</sup> 2×a/<sup>√</sup> 2 with 1 f.u., presented in Fig. [5](#page-6-0) (d).
<span id="page-6-1"></span>TABLE II. The calculated lattice parameter a, the saturation Mn magnetic moment, msat, and the energy of the given magnetic order relative to α–CuMnSb in the AFM001 ground state, ∆Etot. All energies are per one formula unit. Our measured TEM values are also given.
higher in energy. The least stable is the FM order, higher in energy than AFM001 by about 20 meV per f.u. The equilibrium lattice parameters a ≈ 6.1 ˚A are practically independent of the magnetic order, and close to the experimental value 6.088 ˚A.[42](#page-12-24) Some phases are characterized by a small distortion of the cubic symmetry caused by different bond lengths between ferromagnetically and antiferromagnetically oriented Mn ions. Differences in the lattice parameters between various magnetic phases are below 0.01 ˚A, and are not reported in the Table. Similar results for the AFM001 order were obtained in Ref. [35,](#page-12-18) while in Refs [16](#page-11-14) and [31](#page-12-14) the AFM order is more stable than FM by 50 and 90 meV per Mn, respectively.
The last property reported in Tab. [II](#page-6-1) is the saturation magnetic moment of Mn, which also is similar in all phases, and equal to about 4.6µB. This value corresponds to the Curie-Weiss moment of 5.5(1)µB, and compares favorably with the experimental values given in Tab. [I.](#page-5-1)
The obtained results allow estimating the relative roles of the short- and long-range contributions to the magnetic coupling. To this end, we assume the hamiltonian in the form Hex = −J/2 P i,j ⃗si⃗s<sup>j</sup> , where the short range interaction is limited to the Mn NNs neighbors, and the long-range term is neglected. The spin value, s<sup>i</sup> ≈ 2.3, is one half of the calculated magnetic moment of Mn.
The exchange constant J is positive (negative) for the FM (AFM) coupling, and is obtained by comparing energies of various magnetic orders. In the AFM001 phase, each Mn ion has 4 ferromagnetically oriented Mn NNs in the (001) plane and 8 antiferromagnetically oriented Mn NNs in the two adjacent planes. For the remaining magnetic phases, the energies calculated relative to the ground state E<sup>0</sup> ≡ EAFM001 depend on the magnetic order as shown in Tab. [II.](#page-6-1) These results give the coupling constant in the range −0.6 ≥ Jsr ≥ −0.2 meV. This spread is quite large and cannot be explained by (negligible) changes in atomic distances in cells with different magnetic ordering. Therefore, we conclude that the Heisenberg nearest neighbor model does not describe magnetic properties of bulk phases. Indeed, such a model is not appropriate for metallic or semimetallic systems such as α–CuMnSb, where the long-range RKKY coupling is present.
An opposite conclusion comes from the analysis of single spin excitations from the AFM001 ground state. We use a 2a×2a×2a supercell to calculate the energy differences ∆E for the following cases, in which we change (i) spin of one Mn ion, 1Mn ↑→ 1Mn ↓, called a single spin-flip, (ii) 2Mn↑→ 2Mn↓ for spins of two nearest Mn ions belonging to one layer and (iii) 2Mn ↑→ 2Mn ↓ for two distant Mn ions. In these processes the long-range coupling is not important, and indeed the calculated exchange constant consistently is Jsr ≈ −0.4 meV.
#### <span id="page-7-0"></span>C. Crystal and magnetic properties of β–CuMnSb
We now consider two possible structures of the secondary phase proposed based on the experimental results. They are characterized by doubling the periodicity in the [001] direction. The unit cell of β–CuMnSb, shown in Fig. [2,](#page-3-0) is tetragonally deformed relative to that of α–CuMnSb, with the corresponding lattice parameters a = 5.88 ˚A and c = 6.275 ˚A. They differ by about 3 per cent from our calculated cubic a(α– CuMnSb) = 6.105 ˚A. The two interlayer spacings between the consecutive MnSb planes in the [001] direction in the unit cell, shown in Fig. [2](#page-3-0) (b), are quite different, namely dinter<sup>1</sup> = 2.80 ˚A (no Cu), and dinter<sup>2</sup> = 3.48 ˚A (with Cu). Turing to the magnetic order of β–CuMnSb, we find that the FM phase constitutes the ground state with msat = 4.6µ<sup>B</sup> and is lower than the AFM phase by 11 meV per f.u., as indicated in Tab. [II.](#page-6-1) Thus, the
The experimental[27](#page-12-10) lattice parameters of β–CuMnSb reasonably agree with our values, i.e., the calculated a = 6.28 ˚A and c/a = 1.87 are about 2% larger than those measured for the compressed crystal at the critical pressure of 7 GPa. On the other hand, the calculations of Ref. [27](#page-12-10) predict that the magnetic order of the β phase is AFM, in striking contrast with our results. Also their calculated msat(Mn) = 3.8µ<sup>B</sup> is substantially smaller than our 4.6µB. The origin of these discrepancies is not clear, but it may be due to the different exchange-correlation functionals used, and/or to application of the +U(Mn) correction in our calculations (which can affect the results.[31](#page-12-14))
The calculated total energy of the FM β–CuMnSb relative to the AFM α–CuMnSb is higher by 102 meV per f.u. This energy difference is not large, being comparable to the growth temperature, which implies that the β–CuMnSb polymorph can indeed form during epitaxy. We also stress that stoichiometry of the α and β phases is the same, which facilitates formation of β–CuMnSb. Finally, the observed β–CuMnSb inclusions are coherent, i.e., lattice matched, with the host structure. This agrees with the fact that the calculated excess elastic energy of matching the lattice parameters of the β phase to the host α phase is very low and ranges from 3 meV per f.u. (when the tetragonal a parameter constrained to the cubic a = 6.105 ˚A) to 20 meV per f.u. (the tetragonal c parameter constrained to the cubic a).
The second considered possibility, Cu3Mn2Sb<sup>2</sup> shown in Fig. [2](#page-3-0) (c), is higher in energy by 0.37 eV per f.u. in the Cu–rich conditions than the ideal CuMnSb, i.e., by 0.27 eV per f.u. than β–CuMnSb, its stoichiometry is markedly different, and thus we can eliminate this structure from considerations.
# D. Energy band structures of α–CuMnSb and β–CuMnSb
Figure [7](#page-8-1) (a) shows the energy bands and DOS of the AFM001 α–CuMnSb. We see that this phase has a metallic character, however DOS at the Fermi level is low. The states close to E<sup>F</sup> are built from s, p and d states of all ions with similar weights. The low DOS(EF) makes CuMnSb almost semimetallic with a low electrical conductivity. Compatible with the small DOS(EF) is the high resistivity measured in Ref. [41](#page-12-25) and [55.](#page-13-10)
Since the system is antiferromagnetically ordered, the total DOSs of spin-up and spin-down states are the same. In Fig. [7](#page-8-1) only contributions of the 3d(Mn) and 3d(Cu) orbitals are presented to reveal magnetic properties. We see that the exchange spin splitting of the d(Mn) shell is large, about 5 eV. The closely spaced levels contributing to the DOS maxima centered at 4 eV below the Fermi energy are composed mainly of the d states of both Cu and Mn. Spin-up and spin-down 3d(Cu) orbitals are almost
completely occupied, and thus Cu ions are non-magnetic. In turn, the majority spin states of the 3d(Mn) orbitals are completely occupied, while the minority spin states at 1 eV above the Fermi energy are partially filled thanks to a small overlap with spin up states. As a result, a single Mn ion is in between the d <sup>5</sup> and d 6 configuration, with the saturation magnetic moment of 4.6µ<sup>B</sup> consistent with Tab. [II.](#page-6-1) Our results for α–CuMnSb are close to those of Ref. [31.](#page-12-14) A similar electronic configuration takes place in CuMnAs, where the spin-down Mn states are partially filled.[56](#page-13-11)
The overall band structure of the FM β–CuMnSb displayed in Fig. [7](#page-8-1) (b) is close to that of α–CuMnSb, which is particularly clear when comparing partial DOS of both phases. In particular, msat(Mn) is about 4.5µ<sup>B</sup> in both phases, and energies of both d(Mn)- and d(Cu)-related bands are largely independent of the actual crystal structure. This similarity can be due to the fact that the MnSb (001) planes play a dominant role, and the exact locations of the Cu ions are less important.
On the other hand, the calculated DOS(EF) for the α phase is 0.35 states per spin and f.u., while for the β phase we find 1.26 states per spin and f.u., which is 3.6 times higher. As a consequence, α–CuMnSb is semimetallic, and the AFM order is dominant, while β phase is more metallic in character, which in turn favors the RKKY-type coupling and the FM order. This feature can explain the different magnetic phases of the α and β polymorphs.
Analysis of the calculated electronic structure of Heusler and half-Heusler CuMnZ led Sasioglu et al.[17](#page-12-0) to the conclusion that when the spin polarization of conduction electrons is large, and the d(Mn) spin down states are far above EF, then the RKKY coupling is dominant, and one should expect the FM order, otherwise the short range AFM coupling is dominant. Our results do not confirm this conclusion, and indicate that the important
## <span id="page-8-0"></span>E. Point native defects in α–CuMnSb
where E(CuMnSb) and E(CuMnSb : D) are the total energies of a supercell without and with a defect, and n<sup>i</sup> = +1(−1) corresponds to the removal (addition) of one ith atom. µis are the variable chemical potentials of atoms in the solid, which in general are different from the chemical potentials µi(bulk) of the standard state of elements, i.e., Cu, Mn and Sb bulk. Details of calculations of chemical potentials are given in Appendix [A.](#page-10-0)
The point native defects considered here are vacancies VX, interstitials X<sup>i</sup> , and antisites X<sup>Y</sup> (where X and Y are Cu, Mn, or Sb) for all three sublattices. As it was mentioned above, the Cu sublattice is "half- empty" compared to the MnSb sublattice. Consequently, we consider here formation of interstitials at the empty sites of the Cu sublattice only, and neglect other possibilities, expected to have higher formation energies Eform. Thus, the set of defects considered here only partially overlaps with that of Ref. [35.](#page-12-18) Of particular interest to the present study are defects involving Mn ions, since they can influence magnetic properties of α–CuMnSb .[35](#page-12-18) This is why we consider them more extensively, after briefly analyzing the non-magnetic defects. The calculated formation energies are summarized in Tab. [III.](#page-9-0) Because of the magnetic coupling, formation energies of the Mn-related defects depend on the spin direction relative to the spins of the host Mn neighbors. We consider possible spin configurations shown in Fig. [8](#page-9-1) (b).
<span id="page-9-0"></span>TABLE III. Formation energies (in eV) of isolated point defects in the Mn-rich conditions. In parentheses are Mn-related values corrected for ∆H<sup>f</sup> (MnSb) = 0.48 eV, which correspond to the Mn-poor case.
where k<sup>B</sup> is the Boltzmann constant and N<sup>0</sup> is the density of the relevant lattice sites. Details of the calculations of Eform are provided in Supporting Information. To put the calculated formation energies into a proper context, we note that if the growth temperatrure Tgrowth = 2500C and Eform = 0.1 eV, then exp(−Eform/kBTgrowth) = 0.1, which corresponds to a high 10 atomic per cent concentration of this defect on the considered sublattice. On the other hand, if Eform = 1 eV, then exp(−Eform/kBTgrowth) = 9 × 10<sup>−</sup><sup>11</sup>, which implies a negligible defect concentration.
Sb sublattice. The prohibitively high values of Eform demonstrate that VSb and Sb<sup>i</sup> should not form. Similarly, formation energies of SbCu, SbMn, CuSb and MnSb antisites exceed 1 eV, and those defects are not expected to be present at high concentrations. Consequently, the Sb sublattice is thermodynamically stable, robust, and constitutes a defect-free back-bone of CuMnSb.
(ii) Formation energy of Cu interstitials at the Cu sublattice, Eform(Cui) = 1 eV, is relatively high, and their concentrations are negligible. Additionally, the high formation energy of Cu<sup>i</sup> interstitials is consistent with the sparse character of the Cu sublattice in α–CuMnSb.
(iii) Formation of Mn<sup>i</sup> interstitials at the Cu sublattice is characterized by Eform = 0.7-1.4 eV, depending on the spin direction and conditions of growth, and therefore they are not expected to be present at high concentrations, especially in the Mn-poor conditions.
In brief, low formation energies are found for three defects, namely the VCu and VMn vacancies and the MnCu antisite, particularly at the Mn-rich growth conditions. This indicates that a Cu deficit on the Cu sublattice is possible, affecting stoichiometry. Significantly, MnCu antisites make the Cu sublattice magnetic, and also they can participate in the magnetic coupling between the adjacent MnSb (001) planes, thus influencing magnetic properties, as it will be discussed in more detail below. In contrast, SbCu antisites are present in negligible concentrations. Our results are in a reasonable agreement with those of Ref. [35,](#page-12-18) especially given their neglect of spin effects and a somewhat different theoretical approach. Interestingly, formation energies of native defects in CuMnAs calculated in Ref. [56](#page-13-11) are close to the present results in spite of the different anion.
## F. Defect-induced magnetic coupling
There are two Mn-related point defects, Mn<sup>i</sup> and MnCu, both situated on the Cu sublattice. When present at high concentrations, they affect magnetism of α– CuMnSb. Their coupling with host Mn ions is different than the Mn-Mn coupling between the host Mn because of the different local coordination. Energetics of both defects is complex and rich, since the total energy of the system (and thus formation energies) depends on their spin orientations relative to the neighborhood. At both substitutional and interstitial sites in the Cu layer, a Mn ion has 4 Mn nearest neighbors arranged in a tetrahedral configuration, 2 in the upper and 2 in the lower MnSb layer. The Mni–MnMn distance is shorter than that of
MnMn–MnMn, and equal to (<sup>√</sup> 3/4)a.
The possible local spin configurations are reduced to small clusters of 5 Mn ions, shown in Fig. [8.](#page-9-1) The Mn spin-up and spin-down (001) MnSb layers are denoted by in pink and blue, respectively, reflecting the calculated (001) AFM magnetic ground state. The central MnCu (or Mni) ion of such a cluster provides an additional channel of magnetic coupling between two adjacent MnSb layers. The corresponding formation energies are given in Fig. [8.](#page-9-1)
As it was pointed out, in ideal α–CuMnSb, the Mn ions are second neighbors only, separated either by Sb (i.e., the Mn-Sb-Mn "bridge" in the MnSb(001) plane), or by Cu (forming a Mn-Cu-Mn "bridge" linking 3 consecutive (001) planes.) Thus, the short range magnetic coupling in ideal α–CuMnSb is successfully modelled in Sec. [III B](#page-5-2) by the interaction between two Mn second neighbors, situated either in the same MnSb layer, or in two adjacent ones. In contrast, the 4 host Mn ions in the cluster are the first neighbors of a Mn<sup>i</sup> or a MnCu defect. Thus, one can expect that this coupling is stronger than the intrinsic one in the ideal host, and indeed, the differences in energy between various configurations in Fig. [8](#page-9-1) are about 100 meV, which is too high to be explained by the estimated Jsr = 0.4 meV.
As it follows from Fig. [8,](#page-9-1) 5-atom clusters are magnetically frustrated. In particular, the lowest energy case denoted as 4AFM favors the local FM orientation of spins in two adjacent (001) planes, which is opposite to the global host magnetic order. Our results do not confirm the conclusion of Ref. [56](#page-13-11) who find that the 3AFM configuration has the lowest energy, and thus it promotes the global AFM111 order. Instead, we rather expect that Mn-related point defects induce disorder of the host AFM phase, possibly leading to formation of a spin glass.[57](#page-13-12)
#### IV. SUMMARY
CuMnSb films were epitaxially grown on GaSb substrates. Magnetic measurements reveal the presence of two magnetic subsystems. The dominant magnetic order is AFM with the N´eel temperature of 62 K, which is the same as in bulk CuMnSb. It co-exists with a FM phase, characterized by the Curie temperature of about 100 K.
These findings go in hand with transmission electron microscopy and selective area diffraction measurements, which demonstrate coexistence of two structural polymorphs of the same stoichiometry. The dominant one is the cubic half-Heusler α–CuMnSb, which is the equilibrium structure of bulk samples. The second component is a tetragonal β–CuMnSb polymorph, which forms 10-100 nm long elongated inclusions.
(i) The β–CuMnSb phase is metastable, and its total energy is higher by 0.1 eV per f.u. only than that of the equilibrium α–CuMnSb. Lattice parameters of the β phase differ from those of α–CuMnSb by about 4 per cent. This lattice misfit between the two structures does not prevent the pseudomorphic coexistence of both phases, since the calculated misfit strain energy is below 20 meV per f.u.
(ii) In agreement with experiment, α–CuMnSb is AFM, and the FM order is 19 meV per f.u. higher in energy. In contrast, the magnetic ground state of β– CuMnSb is FM, which is more stable than AFM by 11 meV per f.u. This indicates that indeed the β–CuMnSb inclusions are responsible for the FM signal.
(iii) The different magnetic orders of the α and β phases originate in their somewhat different band structures. In particular, critical for magnetic order is the DOS at the Fermi level, which is about 4 times higher in β–CuMnSb than in the α phase. This shows that the β phase is more metallic in character, which in turn favors the FM order driven by the Ruderman-Kittel-Kasuya-Yoshida interaction.
(iv) Our calculations predict the saturated magnetic moment of Mn msat = 4.6µ<sup>B</sup> and 4.5µ<sup>B</sup> for the α and the β phase, respectively. This corresponds to the effective moment of 5.6µB, in good agreement with the measured 5.5µB.
(v) The calculated formation energies of point native defects indicate that the most probable are the MnCu antisites with low formation energies of 0–0.2 eV. However, their presence is expected to disorder the host magnetic AFM phase rather than to induce a transition to the FM configuration.
(vi) Regarding the properties of the CuMnX series we see that their structural stability is relatively weak, as they crystallize in a variety of structures. In particular, unlike the bulk orthorhombic CuMnAs, epitaxial films of CuMnAs are tetragonal, but both structures are AFM. In the case of CuMnSb, polymorphism comprises also the equilibrium magnetic structure, AFM in the bulk specimens, and FM in epitaxial films.
#### ACKNOWLEDGMENTS
LS, CG, JK and LWM thank M. Zipf for technical assistance. Our work was funded by the Deutsche Forschungsgemeinschaft (DFG,German Research Foundation) No. 397861849, by the Free State of Bavaria (Institute for Topological Insulators) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC2147 ct.qmat (Project-Id 390858490).
#### <span id="page-10-0"></span>Appendix A:
The highest possible value of µ<sup>i</sup> is µi(bulk), which implies that the studied system is in equilibrium with the given bulk source of atoms and δµ<sup>i</sup> = 0, otherwise δµ<sup>i</sup> < 0.
Chemical potentials of the components in the standard state are given by the total energies per atom of elemental solids. The calculated cohesive energies Ecoh of the face centered cubic Cu, the face centered cubic Mn with the AFM magnetic order, and the triclinic Sb are, respectively, 3.40 (3.49), 2.65 (2.92) and 2.68 (2.75) eV/atom. They compare reasonably well with the experimental values given in parentheses.[58](#page-13-13)
Chemical potentials of the involved atomic species depend on possible formation of compounds. The ranges of variations of chemical potentials are determined by conditions of equilibrium between various phases, i.e., Cu2Sb, MnSb and CuMnSb. Thermodynamic equilibrium requires that
$$\begin{aligned} \delta\mu(\text{Cu}) + 2\delta\mu(\text{Sb}) &= \Delta H\_f(\text{Cu}\_2\text{Sb}), \\ \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{MnSb}), \\ \delta\mu(\text{Cu}) + \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{CuMnSb}), \end{aligned} \quad \text{(A2)}$$
The calculated values ∆H<sup>f</sup> (Cu2Sb) = −0.03 eV per f.u., ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u., and ∆H<sup>f</sup> (CuMnSb) = −0.42 eV per f.u. The very low ∆H<sup>f</sup> (Cu2Sb) is somewhat unexpected, since Cu2Sb is a stable compound which crystallizes in the tetragonal phase.[43](#page-12-26) Next, our result ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u. agrees well with both the previous value -0.52 eV per f.u. calculated in Ref. [59,](#page-13-14) and the experimental - 0.52 eV per f.u.[60](#page-13-15) Assuming that the accuracy of the calculated values is 0.03 eV per f.u., the set of Equation [A2](#page-11-15) is consistent if we assume ∆H<sup>f</sup> (Cu2Sb) = 0, and ∆H<sup>f</sup> (MnSb) = ∆H<sup>f</sup> (CuMnSb) = −0.45 eV per f.u. This in turn implies that δµ(Cu) = δµ(Sb) = 0, and δµ(Mn) = −0.45 eV. Consequently, the allowed window of the Mn chemical potential is
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| |
FIG. 6. Volume dependence of the total energy relative to the ground state E⁰ = EAFM001(V₀) of α–CuMnSb in the AFM001, AFM002, AFM111 and FM phases. Both volume and energy are per formula unit. Lines are fitted to the calculated values (symbols).
|
# Coexistence of Antiferromagnetic Cubic and Ferromagnetic Tetragonal Polymorphs in Epitaxial CuMnSb
High-resolution transmission electron microscopy and superconducting quantum interference device magnetometry shows that epitaxial CuMnSb films exhibit a coexistence of two magnetic phases, coherently intertwined in nanometric scales. The dominant α phase is half-Heusler cubic antiferromagnet with the N´eel temperature of 62 K, the equilibrium structure of bulk CuMnSb. The secondary phase is its ferromagnetic tetragonal β polymorph with the Curie temperature of about 100 K. First principles calculations provide a consistent interpretation of experiment, since (i) total energy of β–CuMnSb is higher than that of α–CuMnSb only by 0.12 eV per formula unit, which allows for epitaxial stabilization of this phase, (ii) the metallic character of β–CuMnSb favors the Ruderman-Kittel-Kasuya-Yoshida ferromagnetic coupling, and (iii) the calculated effective Curie-Weiss magnetic moment of Mn ions in both phases is about 5.5 µB, favorably close to the measured value. Calculated properties of all point native defects indicate that the most likely to occur are MnCu antisites. They affect magnetic properties of epilayers, but they cannot induce the ferromagnetic order in CuMnSb. Combined, the findings highlight a practical route towards fabrication of functional materials in which coexisting polymorphs provide complementing functionalities in one host.
#### I. INTRODUCTION
One of the most challenging and long-standing problems in fundamental magnetism is a competition between ferromagnetic and antiferromagnetic phases. Their interplay at the interface results in a well known effect of the exchange bias,[1](#page-11-1)[,2](#page-11-2) which fuels now a rapid development of spintronics[3](#page-11-3) and unconventional computing.[4](#page-11-4) The material class of Heusler alloys was previously used to study the origin of the transition between magnetic phases because it offers a wide spectrum of functionalities.[5](#page-11-5) Indeed, Heusler alloys exhibit ferromagnetic (FM), antiferromagnetic (AFM), and canted ferromagnetic order. This indicates that different types of magnetic coupling are competing in this family. Moreover, some of its members display structural polymorphism, which allows studying relationships between the crystalline phase, the magnetic phase, and the corresponding electronic structure.
Heusler alloys incorporate full-Heusler (X2YZ) and half-Heusler (XYZ) variants, where X and Y stand for transition metals, whereas Z denotes anions from the main group. In this class, qualitative changes in material characteristics can be achieved by chemical substitution on either the transition metal cation or on the anion sublattice. Typically, the change of the cation does not change the crystal structure, but it can induce a crossover between the AFM and the FM magnetic phases. A rarely met complete solubility with only marginally affected crystallinity of the otherwise chemically homogenous systems allowed to study the FM-AFM phase competition in detail. The prominent examples are quaternary solid solutions such as Ru2Mn1−xFexSn[6–](#page-11-6)[8](#page-11-7)
Heuslers, and Co1−xNixMnSb,[9](#page-11-8)[,10](#page-11-9) Cu1−xNixMnSb,[11–](#page-11-10)[13](#page-11-11) Co1−xCuxMnSb,[14](#page-11-12) and Cu1−xPdxMnSb[15](#page-11-13) half-Heuslers. In the latter case, the crossover between AFM to FM phases is related to a change in the electronic structure from semimetallic to half-metallic.[16](#page-11-14)[,17](#page-12-0)
Cu–based CuMnZ compounds are antiferromagnets. This feature attracts attention given the recent progress achieved in the AFM spintronics.[18](#page-12-1) Of particular interest is CuMnAs, with a high N´eel temperature T<sup>N</sup> = 480 K.[19](#page-12-2) In this case, features essential for applications, such as anisotropic magnetoresistance,[20,](#page-12-3)[21](#page-12-4) current-induced electrical switching of the N´eel vector[22](#page-12-5) and of the magnetic domains,[23](#page-12-6) have been demonstrated.
The AFM order of CuMnZ is independent of the actual crystalline structure. The equilibrium structure of bulk CuMnP and CuMnAs is orthorhombic, while that of CuMnSb is half-Heusler cubic, referred to below as the α phase. On the other hand, epitaxial growth can stabilizes metastable phases. This is the case of epitaxial layers of CuMnAs, grown on both GaP[19](#page-12-2)[–21](#page-12-4)[,24](#page-12-7)[,25](#page-12-8) and GaAs[23](#page-12-6) substrates, which crystalize in the tetragonal structure, referred to below as the β phase. Theoretical investigations of the crystalline properties of CuMnZ series show that the total energy difference between the cubic and orthorhombic phase is about 1 eV per f.u. (formula unit) for CuMnP, and about 0.5 eV per f.u. for CuMnAs.[26](#page-12-9) This suggests that the orthorhombic phase of CuMnSb, the last member of the CuMnZ series, may not be stable, and indeed the stable structure is the α phase. However, as we show here, epitaxial stabilization of CuMnSb in the β phase is in principle possible, because the calculated energy difference between
Concerning the magnetic properties, the N´eel temperature of both orthorhombic CuMnAs and β–CuMnAs is well above the room temperature,[19](#page-12-2) whereas that of α– CuMnSb is lower, about 60 K.[28,](#page-12-11)[29](#page-12-12) Theory agrees with experiment, since according to Ref. [30,](#page-12-13) in the orthorhombic CuMnP and CuMnAs, the AFM order is more stable than the FM by about 250 meV/Mn. This energy difference is smaller in the cubic phase of CuMnZ compounds, for which the AFM order is lower in energy than FM one by about 50 meV per f.u.[30](#page-12-13)[,31](#page-12-14) Finally, the AFM order of α–CuMnSb is stable under applied magnetic field, as T<sup>N</sup> does not change up to 50 Tesla.[32](#page-12-15)
Turning to the electronic structure of the CuMnP-CuMnAs-CuMnSb series we observe that the character of the energy band gap depends on the anion. Similar to the case of e.g. zinc blende semiconductors, the band gap decreases with the increasing atomic number of the anion.[30](#page-12-13) Indeed, CuMnP is a semiconductor, CuMnAs has a practically vanishing band gap, and CuMnSb is a semimetal.[33](#page-12-16)
Here we experimentally confirm a puzzling coexistence of AFM and FM phases in epitaxial stoichiometric CuMnSb films, observed by us previously,[34](#page-12-17) and explain the underlying mechanism responsible for this effect. A fine analysis of transmission electron microscopy (TEM) images, Sec. [II B,](#page-2-0) points to the formation of tetragonal β–CuMnSb inclusions embedded coherently within the cubic α–CuMnSb host. The tetragonal structure of these inclusions is the same as that of the tetragonal β– CuMnAs. Magnetic properties of our films, Sec. [II C,](#page-4-0) demonstrate coexistence of two magnetic phases: apart from the dominant AFM one, expected for CuMnSb, the measurements reveal the presence of a FM contribution. This is an unexpected feature within the CuMnZ series, exhibiting the AFM order.
In Sec. [III,](#page-5-0) we employ calculations based on the density functional theory to assess properties of CuMnSb films. In agreement with the experiment, β–CuMnSb is weakly metastable, but its magnetic ground state is FM. Band structures of α and β polymorphs are close, but changes in the density of states at the Fermi level account for the change of the dominant mechanism of the magnetic coupling from AFM superexchange to FM Ruderman-Kittel- Kasuya-Yoshida (RKKY). Finally, in Sec. [III E](#page-8-0) native point defects in CuMnSb are examined to assess their possible influence on the magnetic properties.[35](#page-12-18) Our results indicate that the dominant native defects in α–CuMnSb are Mn antisites, and their presence in the films can possibly account for small differences between the measured and the calculated magnetic characteristics, but they do not stabilize the FM order of α–CuMnSb.
# II. EXPERIMENTAL RESULTS
## A. Experimental Methods
# Growth conditions.
CuMnSb layers about 200 nm thick are grown by molecular beam epitaxy. Separate growth chambers connected by an ultra-high vacuum transfer system are used for the growth of the individual layers. Low telluriumdoped epi-ready GaSb (001) wafers are used as substrates. Prior to the growth, the natural oxide layer is desorbed in an Sb atmosphere. Then, 150 nm thick GaSb buffer layers are grown on the substrates to ensure a high-quality interface for the growth of CuMnSb. The GaSb buffer layers are grown at a substrate temperature of 530◦C and a beam equivalent pressure of 4.0 × 10−<sup>6</sup> mbar and 5.3 × 10−<sup>7</sup> mbar for Sb and Ga, respectively. Sb supply is facilitated by a single-filament effusion cell, while Ga is provided by a double-filament effusion cell.
A substrate temperature of 250◦C is used for the growth of CuMnSb films. The corresponding beam equivalent pressures are as follows: BEPCu = 5.80 × 10<sup>−</sup><sup>9</sup> mbar, BEPMn = 9.03 × 10<sup>−</sup><sup>9</sup> mbar, and BEPSb = 4.23 × 10<sup>−</sup><sup>8</sup> mbar. Cu is supplied by a double filament effusion cell, while Mn and Sb are supplied by single filament effusion cells. Following the growth of CuMnSb, a 2.5 nm thick layer of Al2O<sup>3</sup> is deposited on the samples through a sequential process of aluminum DC magnetron sputtering and oxidation. Please, refer to Ref. [29](#page-12-12) for a comprehensive analysis of the growth process and physical properties of the CuMnSb layers produced using the methodology outlined above.
Transmission Electron Microscopy. Specimens for the transmission electron microscopy (TEM) investigations are prepared by the focused ion beam method in the form of lamellas cut along the [100] and [110] directions, i.e., perpendicularly to the surface (001) plane. Titan Cubed 80-300 electron transmission microscope operating with accelerating voltage 300 kV and equipped with energy-dispersive X-ray spectrometer (EDXS) is used for the study. Most of the investigations are done on Cu grids, but for EDXS elemental analysis a Mo grid is used to avoid interference of Cu fluorescence signal from the grid. This analysis yields percentage atomic concentration at 37(3) : 32(5) : 31(7) for Cu, Mn, and Sb, respectively, which, within the experimental errors (given in the parentheses), correspond to the expected stoichiometric ratio of 33 : 33 : 33.
SQUID Magnetometry. Magnetic characterization is performed in a commercial superconducting quantum interference device (SQUID) magnetometer MPMS XL7. The magnetic moment of antiferromagnetic layers is generally very weak and by far dominated by the magnetic response of the bulky semiconductor substrates. Therefore, to counter act the typical shortcomings of commercial magnetometers built around superconducting magnets[36](#page-12-19) and to minimize subtraction errors during
![<span id="page-2-1"></span>FIG. 1. (a) High-angle annular dark-field scanning transmission electron microscopy image of a CuMnSb layer in the [100] zone axis. The inset in the top-right corner brings up a part of the image in atomic resolution, where bright dots represent columns of Mn and Sb atoms. (b) Electron diffraction pattern of the layer. (c) Schematics of the positions of Bragg's spots from (b). Big bullets represent the main reflections from the cubic CuMnSb structure, whereas the open triangles mark the positions of the weak extra reflections. The orientation of the triangles follows from the analysis of the data in panels (d-g). (d-e) Blown up two regions from (a), in which either vertical or horizontal strips dominate. The corresponding Fourier transforms are showed in the top right corners of both panels. (f) Selected area electron diffraction pattern taken at the regions dominated by the vertically oriented strips. (g) Diffraction intensity profiles taken along the horizontal [010]\* and the vertical [001]\* lines passing through the center the diffraction pattern. The solid line corresponds to the horizontal [010]\* direction and the dashed one to the vertical [001]\* one in panel (f). Stars denote directions in the reciprocal space. The arrows α and β indicate the length of α–2g(002) and β–2g(002) diffraction vectors, respectively.](path)
data reduction we actively employ the in situ compensation.[37](#page-12-20) It allows us to reduce the coupling of the signal of the substrates to about 10% of their original strength. The actual effectiveness of the compensation depends on the mass of the sample and its orientation with respect to the SQUID pick-up coils.[36,](#page-12-19)[38](#page-12-21) We also strongly underline the importance of a thorough mechanical removal of the metallic MBE glue from the backside of the samples for any magnetic studies. Its strongly nonlinear magnetic contribution can be of the same magnitude as that of the layer of interest.[39](#page-12-22) To accurately establish the magnitude of magnetic moment specific to CuMnSb we measure a reference sample grown without the CuMnSb layer[29](#page-12-12) using the same sample holder and following exactly the
#### <span id="page-2-0"></span>B. Structural characterization
An exemplary atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF/STEM) image obtained for the [100] zone axis (the direction of the projection) is in Fig. [1](#page-2-1) (a). It confirms a high quality cubic constitution of the material, as it is underlined in the inset. However, at the contrast chosen here, the image in this field of view reveals the presence of stripe-like features, which are the main subject of this analysis. In this image, the apparent lengths and widths of the strips are about 40 nm and about 4 nm, respectively, running predominantly either vertically or horizontally in this particular projection. On other images, the strips exhibit a relatively wide distribution of lengths in the 10-100 nm window. Since similarly distributed shadowy stripes are observed also in the [110] zone axis, we conclude that they form along all three principal crystallographic directions without any particular preferences. The expected F43m cubic structure of α–CuMnSb is clearly confirmed by the fourfold symmetry of the dominant (bright) spots seen on electron diffraction pattern presented in Fig. [1](#page-2-1) (b).
Importantly, the diffraction pattern in Fig. [1](#page-2-1) (b) contains also a second set of much fainter reflections, situated halfway between two adjacent reflections of the main pattern. This indicates the presence of a second crystallographic β phase, which periodicity in the corresponding direction is doubled relative to that of α–CuMnSb, but otherwise coherent with this host structure. We bring all the Bragg's spots up in Fig. [1](#page-2-1) (c), in which the bullets represent the main reflections from α–CuMnSb, whereas the open triangles mark the positions of the weak ones, which are forbidden for this structure.
The presence of β–CuMnSb is further substantiated by the inspection of the two close-ups from Fig. [1](#page-2-1) (a), shown in Fig. [1](#page-2-1) (d) and (e). At this magnification they reveal that, on top of the otherwise cubic arrangement of atomic columns, the strips' brightness alternates every second {002} plane along the direction perpendicular to strip's long axis. The modulation is vertical in Fig. [1](#page-2-1) (d), whereas it goes horizontally in Fig. [1](#page-2-1) (e). The top right corners of these figures contain the corresponding Fourier transform of the parent image, and, similarly to Fig. [1](#page-2-1) (b), both patterns are dominated by the main reflections of α–CuMnSb. The additional spots are embedded either along vertical [Fig. [1](#page-2-1) (d)] or horizontal [Fig. [1](#page-2-1) (e)] lines, i.e., the presence of vertical and horizontal orientations is mutually exclusive. This feature is reflected in Fig. [1](#page-2-1) (c), where the additional spots are marked by differently oriented triangles. The triangles with apexes directed vertically correspond to the vertical orientation of the brightness modulation in Fig. [1](#page-2-1) (d), whereas the horizontal direction of apexes corresponds to the horizontal modulation.
Based on the data shown above we propose that the second phase of CuMnSb, present in our films in the form of strips, is a tetragonal structure, which also is the structure of epitaxial CuMnAs,[19–](#page-12-2)[21](#page-12-4)[,23](#page-12-6)[–25](#page-12-8) and of CuMnSb at high pressures.[27](#page-12-10) This β–CuMnSb polymorph is shown in the panel (b) of Fig. [2.](#page-3-0) The difference between α and β phases consists in the location of Cu ions: in the α phase every (001) plane between two consecutive MnSb planes is half-occupied by Cu, whereas in the β phase Cu ions completely fill up every second (001) plane, and the overall stoichiometry of the material is preserved.
![<span id="page-3-0"></span>FIG. 2. Crystal structures of (a) α–CuMnSb with the cubic lattice constant a, (b) tetragonal β–CuMnSb with the lattice constants a in the (x, y) plane and c in the [001] direction, and (c) Cu3Mn2Sb2.](path)
regions with different orientations of the strips. Diffraction pattern of an area dominated by the vertically oriented strips is shown in more detail in Fig. [1](#page-2-1) (f). In agreement with the Fourier transforms, SAED shows the occurrence of specific reflections corresponding to this particular orientation. The reflections common to both the cubic α and the tetragonal β polymorphs are split along the [010]\* direction, i.e., orthogonal to the strip's axis, whereas the weak spots of the β phase are not split and are commensurate with the cubic phase. (A star denotes a direction in the reciprocal space.)
We quantify the effect analyzing intensity profiles taken along lines passing through the center of diffraction. The profiles are superimposed, and presented in Fig. [1](#page-2-1) (g). The profile along the [001]\* direction reflects the periodicity of α–CuMnSb, while that along [010]\* is additionally split. From the Figure it follows that in our specimens the c lattice parameter of the β–CuMnSb strips is equal to that of the host α–CuMnSb, 6.2(1) ˚A, whereas the a and b parameters of the β phase, 5.8(1) ˚A, are smaller by about 7%. Analogous features are observed for the [010]-oriented strips.
The existence of such a significant strain is confirmed by the calculation of strain maps. We apply the geometrical phase analysis method[40](#page-12-23) for the main image presented in Fig. [1](#page-2-1) (a), and the results are presented in Fig. [3](#page-4-1) (a) and (b) for the horizontal, ϵxx, and the vertical, ϵzz, components of strain, respectively. It is seen that stripes' strain is negative (dark shade) perpendicular to strips and almost zero along the strips. For example, on the horizontal strain map [Fig. [3](#page-4-1) (a)] only vertical strips are visible because they are compressed horizontally, whereas the horizontal strips are invisible because they are not deformed in the horizontal direction.
 (a). (a) The horizontal component of strain ϵxx, and (b) the vertical one, ϵzz. Geometrical phase analysis method has been applied.[40](#page-12-23)](path)
The calculated properties of β–CuMnSb, such as its lattice parameters, stability, and magnetic properties, are discussed in detail in Sec. [III C.](#page-7-0) Anticipating, we mention that they are consistent with experiment. We have also considered a second possible structure which is (almost) compatible with the TEM data, Cu3Mn2Sb2, depicted in Fig. [2](#page-3-0) (c). However, this compound is higher in energy than the β phase, and was dropped from further considerations.
#### <span id="page-4-0"></span>C. Magnetic properties
The temperature T dependence of magnetization, M(T), of the 200 nm thick layer of CuMnSb, is depicted in Fig. [4](#page-4-2) (a). The clear kink on M(T) at T<sup>N</sup> = 62 K marks the position of the paramagnetic to antiferromagnetic N´eel transition in the layer. This value corresponds precisely to the values of T<sup>N</sup> established previously for CuMnSb/GaSb layers of the thickness t ≥ 200 nm, what, indirectly, indicates stoichiometric material composition of this layer.[29](#page-12-12)
More specific information about the magnetic state of that sample is obtained from the examination of the temperature dependence of the inverse magnetic susceptibility, χ −1 (T), shown in Fig. [4](#page-4-2) (b). We take here χ(T) = M(T)/H, where H = 10 kOe is the external magnetic field applied during the measurements. χ −1 (T) can be approximated by two straight lines. The abscissa of the first one, which approximates χ −1 (T) above 200 K (the solid orange line in Fig. [4\)](#page-4-2), yields exactly the same magnitude of the Curie-Weiss temperature TCW = −100(5) K as that established previously for a thicker 510 nm layer, for which χ −1 (T) formed a single straight line above T<sup>N</sup> at the same experimental conditions.[29](#page-12-12) Also the slope of this line yields the value of the effective magnetic moment meff = 5.4(1)µ<sup>B</sup> per f.u., which is very close to that found previously, meff = 5.6µ<sup>B</sup> per f.u.[29](#page-12-12) This correspondence indicates that the high temperature part of χ −1 (T) is determined predominantly by AFM excitations in the paramagnetic matrix of CuMnSb.
The abscissa of the second straight line, which approximates the experimental data between T<sup>N</sup> and about 200 K (marked as the dashed orange line in Fig. [4\)](#page-4-2), yields a more positive value of the Curie-Weiss temperature, T ′ CW = −10(10) K. This clear positive shift of TCW indicates the existence of a ferromagnetic contribution to the overall antiferromagnetic phase of the material, and that these FM excitations gain in importance below about 200 K. Interestingly, a somewhat stronger effect, characterized by a change of sign of TCW to T ′ CW = +60(10) K, was noted in 40 nm CuMnSb layer grown on InAs.[34](#page-12-17) In accordance with the findings of structural characterization we propose that the by far stronger AFM component originates from the dominant α phase, whereas the FM one is brought about by β–CuMnSb polymorph.
<span id="page-5-1"></span>TABLE I. Experimental N´eel temperature TN, effective Curie-Weiss magnetic moment of Mn ions meff (Mn), and Curie-Weiss temperature TCW of α–CuMnSb. Measured orientation of the AFM axis is also given (n.e. = not established). Refs. [42](#page-12-24) and [41](#page-12-25) report the saturation Mn moment.
Turning now to the magnetic characteristics established here for α–CuMnSb we note that they are close to those reported previously, as shown in Tab. [I.](#page-5-1) The published data exhibit a certain distribution, which may indicate that other factors, such as a weak crystalline disorder, may be at work. In particular, either additional Mn interstitial ions or CuMn-MnCu antisite pairs are likely to form.[35](#page-12-18) The presence of such defects was suggested to stabilize the experimentally observed AFM {111}-oriented phase of α–CuMnSb.[35](#page-12-18) Finally, we do not observe a canted AFM order at low temperatures[41](#page-12-25) in any of our samples.
#### <span id="page-5-0"></span>III. THEORY
## A. Theoretical Methods
Calculations are performed within the density functional theory[46,](#page-13-2)[47](#page-13-3) in the generalized gradient approximation of the exchange-correlation potential proposed by Perdew, Burke and Ernzerhof.[48](#page-13-4) To improve description of 3d electrons, the Hubbard-type +U correction on Mn is added.[49–](#page-13-5)[51](#page-13-6) The parameter U(Mn) = 1 eV reproduces the known formation energy of the intermetallic CuMn alloy and gives a reasonable value of the Mn cohesive energy. We use the pseudopotential method implemented in the Quantum ESPRESSO code,[52](#page-13-7) with the valence atomic configuration 4s <sup>1</sup>.<sup>5</sup>p <sup>0</sup>3d 9.5 for Cu,
3s 2p <sup>6</sup>4s 2p <sup>0</sup>3d 5 for Mn and 5s 2p 3 for Sb ions. The planewaves kinetic energy cutoffs of 50 Ry for wave functions and 250 Ry for charge density are employed. Finally, geometry relaxations are performed with a 0.05 GPa convergence criterion for pressure. In defected crystals ionic positions are optimized until the forces acting on ions become smaller than 0.02 eV/˚A.
The properties of defected α–CuMnSb are examined using cubic 2a×2a×2a supercells with 96 atoms (i.e., 32 f.u.), while magnetic order of ideal crystals are checked using the smallest possible supercells. Here a is the equilibrium lattice parameter. The k-space summations are performed with a 6 × 6 × 6 k-point grid for the largest supercell, and correspondingly denser grids are used for smaller cells.
Magnetic interactions and magnetic order depend on several factors, such as the exchange spin splitting of the d(TM) shells, charge states of TM ions, concentration of free carriers and their spin polarization, and the density of states (DOS) at the Fermi energy EF. These factors are interrelated, and are calculated self-consistently within ab initio approach.
Considering first the localized magnetic moments we note that spin polarization of Co, Ni, and Cu ions in XMnZ compounds practically vanishes, while that of the d(Mn) shell is substantial.[16,](#page-11-14)[17](#page-12-0)[,31](#page-12-14) The robustness of the Mn magnetic moment results from the large, 3 – 5 eV, spin splitting of the 3d(Mn) states. In fact, in XMnZ the d(Mn) spin up channel is occupied, while most of the spin down d(Mn) states lay above the Fermi level. Here, one can observe that spin polarization of the d(TM) electrons in free atoms depends on the difference in the number of spin up and spin down electrons, which is the highest in the case of Mn. Consequently, the Mn spin polarization persists in XMnZ. On the other hand, spin splitting of d electrons of Co and Ni atoms is smaller, and thus it vanishes in XMnSb hosts, see the analysis for TM dopants in ZnO.[53](#page-13-8)
In CuMnSb, the magnetic sublattice consists of Mn ions, which are second neighbors distant by 4.3 ˚A. Therefore, the direct exchange coupling between two Mn ions, given by overlaps of their d(Mn) orbitals, is negligibly small. The remaining indirect exchange coupling is the sum of two contributions, and the exchange constant Jindirect = Jsr + JRKKY . [16](#page-11-14)[,17](#page-12-0)[,54](#page-13-9) The first term Jsr has a short-range AFM character, and it is inversely proportional to the energy distance between the unoccupied d(Mn) states and EF. The second coupling channel is of RKKY type mediated by free carriers. This channel depends on the detailed electronic structure in the vicinity of EF, and JRKKY is proportional to DOS(EF). In particular, CoMnSb and NiMnSb half-metals are FM, while CuMnP and CuMnAs insulators are AFM. As we show here, CuMnSb is the border case.
#### <span id="page-5-2"></span>B. Crystal and magnetic properties of α–CuMnSb
A rhombohedral primitive cell of α–CuMnSb contains one formula unit. This structure consist in four interpenetrating fcc sublattices, one of them being empty. The consecutive (001) MnSb planes are followed by the "halfempty" Cu planes, in which the planar atomic density is twice lower. The cubic unit cell is presented in Fig. [2](#page-3-0) (a). Local coordination of Mn ions can be relevant from the point of view of magnetic interactions. With this respect we notice that the magnetic coordination of an Mn ion consists in 12 equidistant Mn atoms at a/<sup>√</sup> 2. More-
We consider four magnetic phases of α–CuMnSb. The corresponding supercells are shown in Fig. [5.](#page-6-0) Antiferromagnetic order with parallel Mn spins in the (001) planes, AFM001, is calculated using the cubic a×a×a cell with 4 f.u. (12 atoms), and shown in Fig. [5](#page-6-0) (a). The AFM order with a period doubled in the [001] direction with parallel Mn spins in each (001) plane, denoted as AFM002, is shown in Fig. [5](#page-6-0) (b). The corresponding a×a×2a cell contains 8 f.u., and is one of the possible supercells in which this phase can be realized. In the AFM111 phase, the Mn spins are parallel in each (111) plane, but the consecutive (111) planes are AFM, as shown in Fig. [5](#page-6-0) (c), and the corresponding rhombohedral unit cell a √ 2 × a √ 2 × a √ 2 contains 8 primitive cells with 24 atoms. Finally, the FM phase requires a primitive cell a/<sup>√</sup> 2×a/<sup>√</sup> 2×a/<sup>√</sup> 2 with 1 f.u., presented in Fig. [5](#page-6-0) (d).
<span id="page-6-1"></span>TABLE II. The calculated lattice parameter a, the saturation Mn magnetic moment, msat, and the energy of the given magnetic order relative to α–CuMnSb in the AFM001 ground state, ∆Etot. All energies are per one formula unit. Our measured TEM values are also given.
higher in energy. The least stable is the FM order, higher in energy than AFM001 by about 20 meV per f.u. The equilibrium lattice parameters a ≈ 6.1 ˚A are practically independent of the magnetic order, and close to the experimental value 6.088 ˚A.[42](#page-12-24) Some phases are characterized by a small distortion of the cubic symmetry caused by different bond lengths between ferromagnetically and antiferromagnetically oriented Mn ions. Differences in the lattice parameters between various magnetic phases are below 0.01 ˚A, and are not reported in the Table. Similar results for the AFM001 order were obtained in Ref. [35,](#page-12-18) while in Refs [16](#page-11-14) and [31](#page-12-14) the AFM order is more stable than FM by 50 and 90 meV per Mn, respectively.
The last property reported in Tab. [II](#page-6-1) is the saturation magnetic moment of Mn, which also is similar in all phases, and equal to about 4.6µB. This value corresponds to the Curie-Weiss moment of 5.5(1)µB, and compares favorably with the experimental values given in Tab. [I.](#page-5-1)
The obtained results allow estimating the relative roles of the short- and long-range contributions to the magnetic coupling. To this end, we assume the hamiltonian in the form Hex = −J/2 P i,j ⃗si⃗s<sup>j</sup> , where the short range interaction is limited to the Mn NNs neighbors, and the long-range term is neglected. The spin value, s<sup>i</sup> ≈ 2.3, is one half of the calculated magnetic moment of Mn.
The exchange constant J is positive (negative) for the FM (AFM) coupling, and is obtained by comparing energies of various magnetic orders. In the AFM001 phase, each Mn ion has 4 ferromagnetically oriented Mn NNs in the (001) plane and 8 antiferromagnetically oriented Mn NNs in the two adjacent planes. For the remaining magnetic phases, the energies calculated relative to the ground state E<sup>0</sup> ≡ EAFM001 depend on the magnetic order as shown in Tab. [II.](#page-6-1) These results give the coupling constant in the range −0.6 ≥ Jsr ≥ −0.2 meV. This spread is quite large and cannot be explained by (negligible) changes in atomic distances in cells with different magnetic ordering. Therefore, we conclude that the Heisenberg nearest neighbor model does not describe magnetic properties of bulk phases. Indeed, such a model is not appropriate for metallic or semimetallic systems such as α–CuMnSb, where the long-range RKKY coupling is present.
An opposite conclusion comes from the analysis of single spin excitations from the AFM001 ground state. We use a 2a×2a×2a supercell to calculate the energy differences ∆E for the following cases, in which we change (i) spin of one Mn ion, 1Mn ↑→ 1Mn ↓, called a single spin-flip, (ii) 2Mn↑→ 2Mn↓ for spins of two nearest Mn ions belonging to one layer and (iii) 2Mn ↑→ 2Mn ↓ for two distant Mn ions. In these processes the long-range coupling is not important, and indeed the calculated exchange constant consistently is Jsr ≈ −0.4 meV.
#### <span id="page-7-0"></span>C. Crystal and magnetic properties of β–CuMnSb
We now consider two possible structures of the secondary phase proposed based on the experimental results. They are characterized by doubling the periodicity in the [001] direction. The unit cell of β–CuMnSb, shown in Fig. [2,](#page-3-0) is tetragonally deformed relative to that of α–CuMnSb, with the corresponding lattice parameters a = 5.88 ˚A and c = 6.275 ˚A. They differ by about 3 per cent from our calculated cubic a(α– CuMnSb) = 6.105 ˚A. The two interlayer spacings between the consecutive MnSb planes in the [001] direction in the unit cell, shown in Fig. [2](#page-3-0) (b), are quite different, namely dinter<sup>1</sup> = 2.80 ˚A (no Cu), and dinter<sup>2</sup> = 3.48 ˚A (with Cu). Turing to the magnetic order of β–CuMnSb, we find that the FM phase constitutes the ground state with msat = 4.6µ<sup>B</sup> and is lower than the AFM phase by 11 meV per f.u., as indicated in Tab. [II.](#page-6-1) Thus, the
The experimental[27](#page-12-10) lattice parameters of β–CuMnSb reasonably agree with our values, i.e., the calculated a = 6.28 ˚A and c/a = 1.87 are about 2% larger than those measured for the compressed crystal at the critical pressure of 7 GPa. On the other hand, the calculations of Ref. [27](#page-12-10) predict that the magnetic order of the β phase is AFM, in striking contrast with our results. Also their calculated msat(Mn) = 3.8µ<sup>B</sup> is substantially smaller than our 4.6µB. The origin of these discrepancies is not clear, but it may be due to the different exchange-correlation functionals used, and/or to application of the +U(Mn) correction in our calculations (which can affect the results.[31](#page-12-14))
The calculated total energy of the FM β–CuMnSb relative to the AFM α–CuMnSb is higher by 102 meV per f.u. This energy difference is not large, being comparable to the growth temperature, which implies that the β–CuMnSb polymorph can indeed form during epitaxy. We also stress that stoichiometry of the α and β phases is the same, which facilitates formation of β–CuMnSb. Finally, the observed β–CuMnSb inclusions are coherent, i.e., lattice matched, with the host structure. This agrees with the fact that the calculated excess elastic energy of matching the lattice parameters of the β phase to the host α phase is very low and ranges from 3 meV per f.u. (when the tetragonal a parameter constrained to the cubic a = 6.105 ˚A) to 20 meV per f.u. (the tetragonal c parameter constrained to the cubic a).
The second considered possibility, Cu3Mn2Sb<sup>2</sup> shown in Fig. [2](#page-3-0) (c), is higher in energy by 0.37 eV per f.u. in the Cu–rich conditions than the ideal CuMnSb, i.e., by 0.27 eV per f.u. than β–CuMnSb, its stoichiometry is markedly different, and thus we can eliminate this structure from considerations.
# D. Energy band structures of α–CuMnSb and β–CuMnSb
Figure [7](#page-8-1) (a) shows the energy bands and DOS of the AFM001 α–CuMnSb. We see that this phase has a metallic character, however DOS at the Fermi level is low. The states close to E<sup>F</sup> are built from s, p and d states of all ions with similar weights. The low DOS(EF) makes CuMnSb almost semimetallic with a low electrical conductivity. Compatible with the small DOS(EF) is the high resistivity measured in Ref. [41](#page-12-25) and [55.](#page-13-10)
Since the system is antiferromagnetically ordered, the total DOSs of spin-up and spin-down states are the same. In Fig. [7](#page-8-1) only contributions of the 3d(Mn) and 3d(Cu) orbitals are presented to reveal magnetic properties. We see that the exchange spin splitting of the d(Mn) shell is large, about 5 eV. The closely spaced levels contributing to the DOS maxima centered at 4 eV below the Fermi energy are composed mainly of the d states of both Cu and Mn. Spin-up and spin-down 3d(Cu) orbitals are almost
completely occupied, and thus Cu ions are non-magnetic. In turn, the majority spin states of the 3d(Mn) orbitals are completely occupied, while the minority spin states at 1 eV above the Fermi energy are partially filled thanks to a small overlap with spin up states. As a result, a single Mn ion is in between the d <sup>5</sup> and d 6 configuration, with the saturation magnetic moment of 4.6µ<sup>B</sup> consistent with Tab. [II.](#page-6-1) Our results for α–CuMnSb are close to those of Ref. [31.](#page-12-14) A similar electronic configuration takes place in CuMnAs, where the spin-down Mn states are partially filled.[56](#page-13-11)
The overall band structure of the FM β–CuMnSb displayed in Fig. [7](#page-8-1) (b) is close to that of α–CuMnSb, which is particularly clear when comparing partial DOS of both phases. In particular, msat(Mn) is about 4.5µ<sup>B</sup> in both phases, and energies of both d(Mn)- and d(Cu)-related bands are largely independent of the actual crystal structure. This similarity can be due to the fact that the MnSb (001) planes play a dominant role, and the exact locations of the Cu ions are less important.
On the other hand, the calculated DOS(EF) for the α phase is 0.35 states per spin and f.u., while for the β phase we find 1.26 states per spin and f.u., which is 3.6 times higher. As a consequence, α–CuMnSb is semimetallic, and the AFM order is dominant, while β phase is more metallic in character, which in turn favors the RKKY-type coupling and the FM order. This feature can explain the different magnetic phases of the α and β polymorphs.
Analysis of the calculated electronic structure of Heusler and half-Heusler CuMnZ led Sasioglu et al.[17](#page-12-0) to the conclusion that when the spin polarization of conduction electrons is large, and the d(Mn) spin down states are far above EF, then the RKKY coupling is dominant, and one should expect the FM order, otherwise the short range AFM coupling is dominant. Our results do not confirm this conclusion, and indicate that the important
## <span id="page-8-0"></span>E. Point native defects in α–CuMnSb
where E(CuMnSb) and E(CuMnSb : D) are the total energies of a supercell without and with a defect, and n<sup>i</sup> = +1(−1) corresponds to the removal (addition) of one ith atom. µis are the variable chemical potentials of atoms in the solid, which in general are different from the chemical potentials µi(bulk) of the standard state of elements, i.e., Cu, Mn and Sb bulk. Details of calculations of chemical potentials are given in Appendix [A.](#page-10-0)
The point native defects considered here are vacancies VX, interstitials X<sup>i</sup> , and antisites X<sup>Y</sup> (where X and Y are Cu, Mn, or Sb) for all three sublattices. As it was mentioned above, the Cu sublattice is "half- empty" compared to the MnSb sublattice. Consequently, we consider here formation of interstitials at the empty sites of the Cu sublattice only, and neglect other possibilities, expected to have higher formation energies Eform. Thus, the set of defects considered here only partially overlaps with that of Ref. [35.](#page-12-18) Of particular interest to the present study are defects involving Mn ions, since they can influence magnetic properties of α–CuMnSb .[35](#page-12-18) This is why we consider them more extensively, after briefly analyzing the non-magnetic defects. The calculated formation energies are summarized in Tab. [III.](#page-9-0) Because of the magnetic coupling, formation energies of the Mn-related defects depend on the spin direction relative to the spins of the host Mn neighbors. We consider possible spin configurations shown in Fig. [8](#page-9-1) (b).
<span id="page-9-0"></span>TABLE III. Formation energies (in eV) of isolated point defects in the Mn-rich conditions. In parentheses are Mn-related values corrected for ∆H<sup>f</sup> (MnSb) = 0.48 eV, which correspond to the Mn-poor case.
where k<sup>B</sup> is the Boltzmann constant and N<sup>0</sup> is the density of the relevant lattice sites. Details of the calculations of Eform are provided in Supporting Information. To put the calculated formation energies into a proper context, we note that if the growth temperatrure Tgrowth = 2500C and Eform = 0.1 eV, then exp(−Eform/kBTgrowth) = 0.1, which corresponds to a high 10 atomic per cent concentration of this defect on the considered sublattice. On the other hand, if Eform = 1 eV, then exp(−Eform/kBTgrowth) = 9 × 10<sup>−</sup><sup>11</sup>, which implies a negligible defect concentration.
Sb sublattice. The prohibitively high values of Eform demonstrate that VSb and Sb<sup>i</sup> should not form. Similarly, formation energies of SbCu, SbMn, CuSb and MnSb antisites exceed 1 eV, and those defects are not expected to be present at high concentrations. Consequently, the Sb sublattice is thermodynamically stable, robust, and constitutes a defect-free back-bone of CuMnSb.
(ii) Formation energy of Cu interstitials at the Cu sublattice, Eform(Cui) = 1 eV, is relatively high, and their concentrations are negligible. Additionally, the high formation energy of Cu<sup>i</sup> interstitials is consistent with the sparse character of the Cu sublattice in α–CuMnSb.
(iii) Formation of Mn<sup>i</sup> interstitials at the Cu sublattice is characterized by Eform = 0.7-1.4 eV, depending on the spin direction and conditions of growth, and therefore they are not expected to be present at high concentrations, especially in the Mn-poor conditions.
In brief, low formation energies are found for three defects, namely the VCu and VMn vacancies and the MnCu antisite, particularly at the Mn-rich growth conditions. This indicates that a Cu deficit on the Cu sublattice is possible, affecting stoichiometry. Significantly, MnCu antisites make the Cu sublattice magnetic, and also they can participate in the magnetic coupling between the adjacent MnSb (001) planes, thus influencing magnetic properties, as it will be discussed in more detail below. In contrast, SbCu antisites are present in negligible concentrations. Our results are in a reasonable agreement with those of Ref. [35,](#page-12-18) especially given their neglect of spin effects and a somewhat different theoretical approach. Interestingly, formation energies of native defects in CuMnAs calculated in Ref. [56](#page-13-11) are close to the present results in spite of the different anion.
## F. Defect-induced magnetic coupling
There are two Mn-related point defects, Mn<sup>i</sup> and MnCu, both situated on the Cu sublattice. When present at high concentrations, they affect magnetism of α– CuMnSb. Their coupling with host Mn ions is different than the Mn-Mn coupling between the host Mn because of the different local coordination. Energetics of both defects is complex and rich, since the total energy of the system (and thus formation energies) depends on their spin orientations relative to the neighborhood. At both substitutional and interstitial sites in the Cu layer, a Mn ion has 4 Mn nearest neighbors arranged in a tetrahedral configuration, 2 in the upper and 2 in the lower MnSb layer. The Mni–MnMn distance is shorter than that of
MnMn–MnMn, and equal to (<sup>√</sup> 3/4)a.
The possible local spin configurations are reduced to small clusters of 5 Mn ions, shown in Fig. [8.](#page-9-1) The Mn spin-up and spin-down (001) MnSb layers are denoted by in pink and blue, respectively, reflecting the calculated (001) AFM magnetic ground state. The central MnCu (or Mni) ion of such a cluster provides an additional channel of magnetic coupling between two adjacent MnSb layers. The corresponding formation energies are given in Fig. [8.](#page-9-1)
As it was pointed out, in ideal α–CuMnSb, the Mn ions are second neighbors only, separated either by Sb (i.e., the Mn-Sb-Mn "bridge" in the MnSb(001) plane), or by Cu (forming a Mn-Cu-Mn "bridge" linking 3 consecutive (001) planes.) Thus, the short range magnetic coupling in ideal α–CuMnSb is successfully modelled in Sec. [III B](#page-5-2) by the interaction between two Mn second neighbors, situated either in the same MnSb layer, or in two adjacent ones. In contrast, the 4 host Mn ions in the cluster are the first neighbors of a Mn<sup>i</sup> or a MnCu defect. Thus, one can expect that this coupling is stronger than the intrinsic one in the ideal host, and indeed, the differences in energy between various configurations in Fig. [8](#page-9-1) are about 100 meV, which is too high to be explained by the estimated Jsr = 0.4 meV.
As it follows from Fig. [8,](#page-9-1) 5-atom clusters are magnetically frustrated. In particular, the lowest energy case denoted as 4AFM favors the local FM orientation of spins in two adjacent (001) planes, which is opposite to the global host magnetic order. Our results do not confirm the conclusion of Ref. [56](#page-13-11) who find that the 3AFM configuration has the lowest energy, and thus it promotes the global AFM111 order. Instead, we rather expect that Mn-related point defects induce disorder of the host AFM phase, possibly leading to formation of a spin glass.[57](#page-13-12)
#### IV. SUMMARY
CuMnSb films were epitaxially grown on GaSb substrates. Magnetic measurements reveal the presence of two magnetic subsystems. The dominant magnetic order is AFM with the N´eel temperature of 62 K, which is the same as in bulk CuMnSb. It co-exists with a FM phase, characterized by the Curie temperature of about 100 K.
These findings go in hand with transmission electron microscopy and selective area diffraction measurements, which demonstrate coexistence of two structural polymorphs of the same stoichiometry. The dominant one is the cubic half-Heusler α–CuMnSb, which is the equilibrium structure of bulk samples. The second component is a tetragonal β–CuMnSb polymorph, which forms 10-100 nm long elongated inclusions.
(i) The β–CuMnSb phase is metastable, and its total energy is higher by 0.1 eV per f.u. only than that of the equilibrium α–CuMnSb. Lattice parameters of the β phase differ from those of α–CuMnSb by about 4 per cent. This lattice misfit between the two structures does not prevent the pseudomorphic coexistence of both phases, since the calculated misfit strain energy is below 20 meV per f.u.
(ii) In agreement with experiment, α–CuMnSb is AFM, and the FM order is 19 meV per f.u. higher in energy. In contrast, the magnetic ground state of β– CuMnSb is FM, which is more stable than AFM by 11 meV per f.u. This indicates that indeed the β–CuMnSb inclusions are responsible for the FM signal.
(iii) The different magnetic orders of the α and β phases originate in their somewhat different band structures. In particular, critical for magnetic order is the DOS at the Fermi level, which is about 4 times higher in β–CuMnSb than in the α phase. This shows that the β phase is more metallic in character, which in turn favors the FM order driven by the Ruderman-Kittel-Kasuya-Yoshida interaction.
(iv) Our calculations predict the saturated magnetic moment of Mn msat = 4.6µ<sup>B</sup> and 4.5µ<sup>B</sup> for the α and the β phase, respectively. This corresponds to the effective moment of 5.6µB, in good agreement with the measured 5.5µB.
(v) The calculated formation energies of point native defects indicate that the most probable are the MnCu antisites with low formation energies of 0–0.2 eV. However, their presence is expected to disorder the host magnetic AFM phase rather than to induce a transition to the FM configuration.
(vi) Regarding the properties of the CuMnX series we see that their structural stability is relatively weak, as they crystallize in a variety of structures. In particular, unlike the bulk orthorhombic CuMnAs, epitaxial films of CuMnAs are tetragonal, but both structures are AFM. In the case of CuMnSb, polymorphism comprises also the equilibrium magnetic structure, AFM in the bulk specimens, and FM in epitaxial films.
#### ACKNOWLEDGMENTS
LS, CG, JK and LWM thank M. Zipf for technical assistance. Our work was funded by the Deutsche Forschungsgemeinschaft (DFG,German Research Foundation) No. 397861849, by the Free State of Bavaria (Institute for Topological Insulators) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC2147 ct.qmat (Project-Id 390858490).
#### <span id="page-10-0"></span>Appendix A:
The highest possible value of µ<sup>i</sup> is µi(bulk), which implies that the studied system is in equilibrium with the given bulk source of atoms and δµ<sup>i</sup> = 0, otherwise δµ<sup>i</sup> < 0.
Chemical potentials of the components in the standard state are given by the total energies per atom of elemental solids. The calculated cohesive energies Ecoh of the face centered cubic Cu, the face centered cubic Mn with the AFM magnetic order, and the triclinic Sb are, respectively, 3.40 (3.49), 2.65 (2.92) and 2.68 (2.75) eV/atom. They compare reasonably well with the experimental values given in parentheses.[58](#page-13-13)
Chemical potentials of the involved atomic species depend on possible formation of compounds. The ranges of variations of chemical potentials are determined by conditions of equilibrium between various phases, i.e., Cu2Sb, MnSb and CuMnSb. Thermodynamic equilibrium requires that
$$\begin{aligned} \delta\mu(\text{Cu}) + 2\delta\mu(\text{Sb}) &= \Delta H\_f(\text{Cu}\_2\text{Sb}), \\ \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{MnSb}), \\ \delta\mu(\text{Cu}) + \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{CuMnSb}), \end{aligned} \quad \text{(A2)}$$
The calculated values ∆H<sup>f</sup> (Cu2Sb) = −0.03 eV per f.u., ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u., and ∆H<sup>f</sup> (CuMnSb) = −0.42 eV per f.u. The very low ∆H<sup>f</sup> (Cu2Sb) is somewhat unexpected, since Cu2Sb is a stable compound which crystallizes in the tetragonal phase.[43](#page-12-26) Next, our result ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u. agrees well with both the previous value -0.52 eV per f.u. calculated in Ref. [59,](#page-13-14) and the experimental - 0.52 eV per f.u.[60](#page-13-15) Assuming that the accuracy of the calculated values is 0.03 eV per f.u., the set of Equation [A2](#page-11-15) is consistent if we assume ∆H<sup>f</sup> (Cu2Sb) = 0, and ∆H<sup>f</sup> (MnSb) = ∆H<sup>f</sup> (CuMnSb) = −0.45 eV per f.u. This in turn implies that δµ(Cu) = δµ(Sb) = 0, and δµ(Mn) = −0.45 eV. Consequently, the allowed window of the Mn chemical potential is
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- <span id="page-13-14"></span><sup>59</sup> R. Podloucky and J. Redinger, "Density functional theory study of structural and thermodynamical stabilities of ferromagnetic MnX (X = P, As, Sb, Bi) compounds," [J.](http://dx.doi.org/ 10.1088/1361-648x/aaf2db) [Phys. Condens. Matter](http://dx.doi.org/ 10.1088/1361-648x/aaf2db) 31, 054001 (2018).
- <span id="page-13-16"></span><sup>61</sup> P. G. van Engen, K. H. J. Buschow, R. Jongebreur, and M. Erman, "PtMnSb, a material with very high magnetooptical Kerr effect," [Appl. Phys. Lett.](http://dx.doi.org/ 10.1063/1.93849) 42, 202–204 (1983).
| |
FIG. 3. Strain maps of image shown in Fig. [1](#page-2-1) (a). (a) The horizontal component of strain ϵxx, and (b) the vertical one, ϵzz. Geometrical phase analysis method has been applied.[40](#page-12-23)
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# Coexistence of Antiferromagnetic Cubic and Ferromagnetic Tetragonal Polymorphs in Epitaxial CuMnSb
High-resolution transmission electron microscopy and superconducting quantum interference device magnetometry shows that epitaxial CuMnSb films exhibit a coexistence of two magnetic phases, coherently intertwined in nanometric scales. The dominant α phase is half-Heusler cubic antiferromagnet with the N´eel temperature of 62 K, the equilibrium structure of bulk CuMnSb. The secondary phase is its ferromagnetic tetragonal β polymorph with the Curie temperature of about 100 K. First principles calculations provide a consistent interpretation of experiment, since (i) total energy of β–CuMnSb is higher than that of α–CuMnSb only by 0.12 eV per formula unit, which allows for epitaxial stabilization of this phase, (ii) the metallic character of β–CuMnSb favors the Ruderman-Kittel-Kasuya-Yoshida ferromagnetic coupling, and (iii) the calculated effective Curie-Weiss magnetic moment of Mn ions in both phases is about 5.5 µB, favorably close to the measured value. Calculated properties of all point native defects indicate that the most likely to occur are MnCu antisites. They affect magnetic properties of epilayers, but they cannot induce the ferromagnetic order in CuMnSb. Combined, the findings highlight a practical route towards fabrication of functional materials in which coexisting polymorphs provide complementing functionalities in one host.
#### I. INTRODUCTION
One of the most challenging and long-standing problems in fundamental magnetism is a competition between ferromagnetic and antiferromagnetic phases. Their interplay at the interface results in a well known effect of the exchange bias,[1](#page-11-1)[,2](#page-11-2) which fuels now a rapid development of spintronics[3](#page-11-3) and unconventional computing.[4](#page-11-4) The material class of Heusler alloys was previously used to study the origin of the transition between magnetic phases because it offers a wide spectrum of functionalities.[5](#page-11-5) Indeed, Heusler alloys exhibit ferromagnetic (FM), antiferromagnetic (AFM), and canted ferromagnetic order. This indicates that different types of magnetic coupling are competing in this family. Moreover, some of its members display structural polymorphism, which allows studying relationships between the crystalline phase, the magnetic phase, and the corresponding electronic structure.
Heusler alloys incorporate full-Heusler (X2YZ) and half-Heusler (XYZ) variants, where X and Y stand for transition metals, whereas Z denotes anions from the main group. In this class, qualitative changes in material characteristics can be achieved by chemical substitution on either the transition metal cation or on the anion sublattice. Typically, the change of the cation does not change the crystal structure, but it can induce a crossover between the AFM and the FM magnetic phases. A rarely met complete solubility with only marginally affected crystallinity of the otherwise chemically homogenous systems allowed to study the FM-AFM phase competition in detail. The prominent examples are quaternary solid solutions such as Ru2Mn1−xFexSn[6–](#page-11-6)[8](#page-11-7)
Heuslers, and Co1−xNixMnSb,[9](#page-11-8)[,10](#page-11-9) Cu1−xNixMnSb,[11–](#page-11-10)[13](#page-11-11) Co1−xCuxMnSb,[14](#page-11-12) and Cu1−xPdxMnSb[15](#page-11-13) half-Heuslers. In the latter case, the crossover between AFM to FM phases is related to a change in the electronic structure from semimetallic to half-metallic.[16](#page-11-14)[,17](#page-12-0)
Cu–based CuMnZ compounds are antiferromagnets. This feature attracts attention given the recent progress achieved in the AFM spintronics.[18](#page-12-1) Of particular interest is CuMnAs, with a high N´eel temperature T<sup>N</sup> = 480 K.[19](#page-12-2) In this case, features essential for applications, such as anisotropic magnetoresistance,[20,](#page-12-3)[21](#page-12-4) current-induced electrical switching of the N´eel vector[22](#page-12-5) and of the magnetic domains,[23](#page-12-6) have been demonstrated.
The AFM order of CuMnZ is independent of the actual crystalline structure. The equilibrium structure of bulk CuMnP and CuMnAs is orthorhombic, while that of CuMnSb is half-Heusler cubic, referred to below as the α phase. On the other hand, epitaxial growth can stabilizes metastable phases. This is the case of epitaxial layers of CuMnAs, grown on both GaP[19](#page-12-2)[–21](#page-12-4)[,24](#page-12-7)[,25](#page-12-8) and GaAs[23](#page-12-6) substrates, which crystalize in the tetragonal structure, referred to below as the β phase. Theoretical investigations of the crystalline properties of CuMnZ series show that the total energy difference between the cubic and orthorhombic phase is about 1 eV per f.u. (formula unit) for CuMnP, and about 0.5 eV per f.u. for CuMnAs.[26](#page-12-9) This suggests that the orthorhombic phase of CuMnSb, the last member of the CuMnZ series, may not be stable, and indeed the stable structure is the α phase. However, as we show here, epitaxial stabilization of CuMnSb in the β phase is in principle possible, because the calculated energy difference between
Concerning the magnetic properties, the N´eel temperature of both orthorhombic CuMnAs and β–CuMnAs is well above the room temperature,[19](#page-12-2) whereas that of α– CuMnSb is lower, about 60 K.[28,](#page-12-11)[29](#page-12-12) Theory agrees with experiment, since according to Ref. [30,](#page-12-13) in the orthorhombic CuMnP and CuMnAs, the AFM order is more stable than the FM by about 250 meV/Mn. This energy difference is smaller in the cubic phase of CuMnZ compounds, for which the AFM order is lower in energy than FM one by about 50 meV per f.u.[30](#page-12-13)[,31](#page-12-14) Finally, the AFM order of α–CuMnSb is stable under applied magnetic field, as T<sup>N</sup> does not change up to 50 Tesla.[32](#page-12-15)
Turning to the electronic structure of the CuMnP-CuMnAs-CuMnSb series we observe that the character of the energy band gap depends on the anion. Similar to the case of e.g. zinc blende semiconductors, the band gap decreases with the increasing atomic number of the anion.[30](#page-12-13) Indeed, CuMnP is a semiconductor, CuMnAs has a practically vanishing band gap, and CuMnSb is a semimetal.[33](#page-12-16)
Here we experimentally confirm a puzzling coexistence of AFM and FM phases in epitaxial stoichiometric CuMnSb films, observed by us previously,[34](#page-12-17) and explain the underlying mechanism responsible for this effect. A fine analysis of transmission electron microscopy (TEM) images, Sec. [II B,](#page-2-0) points to the formation of tetragonal β–CuMnSb inclusions embedded coherently within the cubic α–CuMnSb host. The tetragonal structure of these inclusions is the same as that of the tetragonal β– CuMnAs. Magnetic properties of our films, Sec. [II C,](#page-4-0) demonstrate coexistence of two magnetic phases: apart from the dominant AFM one, expected for CuMnSb, the measurements reveal the presence of a FM contribution. This is an unexpected feature within the CuMnZ series, exhibiting the AFM order.
In Sec. [III,](#page-5-0) we employ calculations based on the density functional theory to assess properties of CuMnSb films. In agreement with the experiment, β–CuMnSb is weakly metastable, but its magnetic ground state is FM. Band structures of α and β polymorphs are close, but changes in the density of states at the Fermi level account for the change of the dominant mechanism of the magnetic coupling from AFM superexchange to FM Ruderman-Kittel- Kasuya-Yoshida (RKKY). Finally, in Sec. [III E](#page-8-0) native point defects in CuMnSb are examined to assess their possible influence on the magnetic properties.[35](#page-12-18) Our results indicate that the dominant native defects in α–CuMnSb are Mn antisites, and their presence in the films can possibly account for small differences between the measured and the calculated magnetic characteristics, but they do not stabilize the FM order of α–CuMnSb.
# II. EXPERIMENTAL RESULTS
## A. Experimental Methods
# Growth conditions.
CuMnSb layers about 200 nm thick are grown by molecular beam epitaxy. Separate growth chambers connected by an ultra-high vacuum transfer system are used for the growth of the individual layers. Low telluriumdoped epi-ready GaSb (001) wafers are used as substrates. Prior to the growth, the natural oxide layer is desorbed in an Sb atmosphere. Then, 150 nm thick GaSb buffer layers are grown on the substrates to ensure a high-quality interface for the growth of CuMnSb. The GaSb buffer layers are grown at a substrate temperature of 530◦C and a beam equivalent pressure of 4.0 × 10−<sup>6</sup> mbar and 5.3 × 10−<sup>7</sup> mbar for Sb and Ga, respectively. Sb supply is facilitated by a single-filament effusion cell, while Ga is provided by a double-filament effusion cell.
A substrate temperature of 250◦C is used for the growth of CuMnSb films. The corresponding beam equivalent pressures are as follows: BEPCu = 5.80 × 10<sup>−</sup><sup>9</sup> mbar, BEPMn = 9.03 × 10<sup>−</sup><sup>9</sup> mbar, and BEPSb = 4.23 × 10<sup>−</sup><sup>8</sup> mbar. Cu is supplied by a double filament effusion cell, while Mn and Sb are supplied by single filament effusion cells. Following the growth of CuMnSb, a 2.5 nm thick layer of Al2O<sup>3</sup> is deposited on the samples through a sequential process of aluminum DC magnetron sputtering and oxidation. Please, refer to Ref. [29](#page-12-12) for a comprehensive analysis of the growth process and physical properties of the CuMnSb layers produced using the methodology outlined above.
Transmission Electron Microscopy. Specimens for the transmission electron microscopy (TEM) investigations are prepared by the focused ion beam method in the form of lamellas cut along the [100] and [110] directions, i.e., perpendicularly to the surface (001) plane. Titan Cubed 80-300 electron transmission microscope operating with accelerating voltage 300 kV and equipped with energy-dispersive X-ray spectrometer (EDXS) is used for the study. Most of the investigations are done on Cu grids, but for EDXS elemental analysis a Mo grid is used to avoid interference of Cu fluorescence signal from the grid. This analysis yields percentage atomic concentration at 37(3) : 32(5) : 31(7) for Cu, Mn, and Sb, respectively, which, within the experimental errors (given in the parentheses), correspond to the expected stoichiometric ratio of 33 : 33 : 33.
SQUID Magnetometry. Magnetic characterization is performed in a commercial superconducting quantum interference device (SQUID) magnetometer MPMS XL7. The magnetic moment of antiferromagnetic layers is generally very weak and by far dominated by the magnetic response of the bulky semiconductor substrates. Therefore, to counter act the typical shortcomings of commercial magnetometers built around superconducting magnets[36](#page-12-19) and to minimize subtraction errors during
![<span id="page-2-1"></span>FIG. 1. (a) High-angle annular dark-field scanning transmission electron microscopy image of a CuMnSb layer in the [100] zone axis. The inset in the top-right corner brings up a part of the image in atomic resolution, where bright dots represent columns of Mn and Sb atoms. (b) Electron diffraction pattern of the layer. (c) Schematics of the positions of Bragg's spots from (b). Big bullets represent the main reflections from the cubic CuMnSb structure, whereas the open triangles mark the positions of the weak extra reflections. The orientation of the triangles follows from the analysis of the data in panels (d-g). (d-e) Blown up two regions from (a), in which either vertical or horizontal strips dominate. The corresponding Fourier transforms are showed in the top right corners of both panels. (f) Selected area electron diffraction pattern taken at the regions dominated by the vertically oriented strips. (g) Diffraction intensity profiles taken along the horizontal [010]\* and the vertical [001]\* lines passing through the center the diffraction pattern. The solid line corresponds to the horizontal [010]\* direction and the dashed one to the vertical [001]\* one in panel (f). Stars denote directions in the reciprocal space. The arrows α and β indicate the length of α–2g(002) and β–2g(002) diffraction vectors, respectively.](path)
data reduction we actively employ the in situ compensation.[37](#page-12-20) It allows us to reduce the coupling of the signal of the substrates to about 10% of their original strength. The actual effectiveness of the compensation depends on the mass of the sample and its orientation with respect to the SQUID pick-up coils.[36,](#page-12-19)[38](#page-12-21) We also strongly underline the importance of a thorough mechanical removal of the metallic MBE glue from the backside of the samples for any magnetic studies. Its strongly nonlinear magnetic contribution can be of the same magnitude as that of the layer of interest.[39](#page-12-22) To accurately establish the magnitude of magnetic moment specific to CuMnSb we measure a reference sample grown without the CuMnSb layer[29](#page-12-12) using the same sample holder and following exactly the
#### <span id="page-2-0"></span>B. Structural characterization
An exemplary atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF/STEM) image obtained for the [100] zone axis (the direction of the projection) is in Fig. [1](#page-2-1) (a). It confirms a high quality cubic constitution of the material, as it is underlined in the inset. However, at the contrast chosen here, the image in this field of view reveals the presence of stripe-like features, which are the main subject of this analysis. In this image, the apparent lengths and widths of the strips are about 40 nm and about 4 nm, respectively, running predominantly either vertically or horizontally in this particular projection. On other images, the strips exhibit a relatively wide distribution of lengths in the 10-100 nm window. Since similarly distributed shadowy stripes are observed also in the [110] zone axis, we conclude that they form along all three principal crystallographic directions without any particular preferences. The expected F43m cubic structure of α–CuMnSb is clearly confirmed by the fourfold symmetry of the dominant (bright) spots seen on electron diffraction pattern presented in Fig. [1](#page-2-1) (b).
Importantly, the diffraction pattern in Fig. [1](#page-2-1) (b) contains also a second set of much fainter reflections, situated halfway between two adjacent reflections of the main pattern. This indicates the presence of a second crystallographic β phase, which periodicity in the corresponding direction is doubled relative to that of α–CuMnSb, but otherwise coherent with this host structure. We bring all the Bragg's spots up in Fig. [1](#page-2-1) (c), in which the bullets represent the main reflections from α–CuMnSb, whereas the open triangles mark the positions of the weak ones, which are forbidden for this structure.
The presence of β–CuMnSb is further substantiated by the inspection of the two close-ups from Fig. [1](#page-2-1) (a), shown in Fig. [1](#page-2-1) (d) and (e). At this magnification they reveal that, on top of the otherwise cubic arrangement of atomic columns, the strips' brightness alternates every second {002} plane along the direction perpendicular to strip's long axis. The modulation is vertical in Fig. [1](#page-2-1) (d), whereas it goes horizontally in Fig. [1](#page-2-1) (e). The top right corners of these figures contain the corresponding Fourier transform of the parent image, and, similarly to Fig. [1](#page-2-1) (b), both patterns are dominated by the main reflections of α–CuMnSb. The additional spots are embedded either along vertical [Fig. [1](#page-2-1) (d)] or horizontal [Fig. [1](#page-2-1) (e)] lines, i.e., the presence of vertical and horizontal orientations is mutually exclusive. This feature is reflected in Fig. [1](#page-2-1) (c), where the additional spots are marked by differently oriented triangles. The triangles with apexes directed vertically correspond to the vertical orientation of the brightness modulation in Fig. [1](#page-2-1) (d), whereas the horizontal direction of apexes corresponds to the horizontal modulation.
Based on the data shown above we propose that the second phase of CuMnSb, present in our films in the form of strips, is a tetragonal structure, which also is the structure of epitaxial CuMnAs,[19–](#page-12-2)[21](#page-12-4)[,23](#page-12-6)[–25](#page-12-8) and of CuMnSb at high pressures.[27](#page-12-10) This β–CuMnSb polymorph is shown in the panel (b) of Fig. [2.](#page-3-0) The difference between α and β phases consists in the location of Cu ions: in the α phase every (001) plane between two consecutive MnSb planes is half-occupied by Cu, whereas in the β phase Cu ions completely fill up every second (001) plane, and the overall stoichiometry of the material is preserved.
![<span id="page-3-0"></span>FIG. 2. Crystal structures of (a) α–CuMnSb with the cubic lattice constant a, (b) tetragonal β–CuMnSb with the lattice constants a in the (x, y) plane and c in the [001] direction, and (c) Cu3Mn2Sb2.](path)
regions with different orientations of the strips. Diffraction pattern of an area dominated by the vertically oriented strips is shown in more detail in Fig. [1](#page-2-1) (f). In agreement with the Fourier transforms, SAED shows the occurrence of specific reflections corresponding to this particular orientation. The reflections common to both the cubic α and the tetragonal β polymorphs are split along the [010]\* direction, i.e., orthogonal to the strip's axis, whereas the weak spots of the β phase are not split and are commensurate with the cubic phase. (A star denotes a direction in the reciprocal space.)
We quantify the effect analyzing intensity profiles taken along lines passing through the center of diffraction. The profiles are superimposed, and presented in Fig. [1](#page-2-1) (g). The profile along the [001]\* direction reflects the periodicity of α–CuMnSb, while that along [010]\* is additionally split. From the Figure it follows that in our specimens the c lattice parameter of the β–CuMnSb strips is equal to that of the host α–CuMnSb, 6.2(1) ˚A, whereas the a and b parameters of the β phase, 5.8(1) ˚A, are smaller by about 7%. Analogous features are observed for the [010]-oriented strips.
The existence of such a significant strain is confirmed by the calculation of strain maps. We apply the geometrical phase analysis method[40](#page-12-23) for the main image presented in Fig. [1](#page-2-1) (a), and the results are presented in Fig. [3](#page-4-1) (a) and (b) for the horizontal, ϵxx, and the vertical, ϵzz, components of strain, respectively. It is seen that stripes' strain is negative (dark shade) perpendicular to strips and almost zero along the strips. For example, on the horizontal strain map [Fig. [3](#page-4-1) (a)] only vertical strips are visible because they are compressed horizontally, whereas the horizontal strips are invisible because they are not deformed in the horizontal direction.
 (a). (a) The horizontal component of strain ϵxx, and (b) the vertical one, ϵzz. Geometrical phase analysis method has been applied.[40](#page-12-23)](path)
The calculated properties of β–CuMnSb, such as its lattice parameters, stability, and magnetic properties, are discussed in detail in Sec. [III C.](#page-7-0) Anticipating, we mention that they are consistent with experiment. We have also considered a second possible structure which is (almost) compatible with the TEM data, Cu3Mn2Sb2, depicted in Fig. [2](#page-3-0) (c). However, this compound is higher in energy than the β phase, and was dropped from further considerations.
#### <span id="page-4-0"></span>C. Magnetic properties
The temperature T dependence of magnetization, M(T), of the 200 nm thick layer of CuMnSb, is depicted in Fig. [4](#page-4-2) (a). The clear kink on M(T) at T<sup>N</sup> = 62 K marks the position of the paramagnetic to antiferromagnetic N´eel transition in the layer. This value corresponds precisely to the values of T<sup>N</sup> established previously for CuMnSb/GaSb layers of the thickness t ≥ 200 nm, what, indirectly, indicates stoichiometric material composition of this layer.[29](#page-12-12)
More specific information about the magnetic state of that sample is obtained from the examination of the temperature dependence of the inverse magnetic susceptibility, χ −1 (T), shown in Fig. [4](#page-4-2) (b). We take here χ(T) = M(T)/H, where H = 10 kOe is the external magnetic field applied during the measurements. χ −1 (T) can be approximated by two straight lines. The abscissa of the first one, which approximates χ −1 (T) above 200 K (the solid orange line in Fig. [4\)](#page-4-2), yields exactly the same magnitude of the Curie-Weiss temperature TCW = −100(5) K as that established previously for a thicker 510 nm layer, for which χ −1 (T) formed a single straight line above T<sup>N</sup> at the same experimental conditions.[29](#page-12-12) Also the slope of this line yields the value of the effective magnetic moment meff = 5.4(1)µ<sup>B</sup> per f.u., which is very close to that found previously, meff = 5.6µ<sup>B</sup> per f.u.[29](#page-12-12) This correspondence indicates that the high temperature part of χ −1 (T) is determined predominantly by AFM excitations in the paramagnetic matrix of CuMnSb.
The abscissa of the second straight line, which approximates the experimental data between T<sup>N</sup> and about 200 K (marked as the dashed orange line in Fig. [4\)](#page-4-2), yields a more positive value of the Curie-Weiss temperature, T ′ CW = −10(10) K. This clear positive shift of TCW indicates the existence of a ferromagnetic contribution to the overall antiferromagnetic phase of the material, and that these FM excitations gain in importance below about 200 K. Interestingly, a somewhat stronger effect, characterized by a change of sign of TCW to T ′ CW = +60(10) K, was noted in 40 nm CuMnSb layer grown on InAs.[34](#page-12-17) In accordance with the findings of structural characterization we propose that the by far stronger AFM component originates from the dominant α phase, whereas the FM one is brought about by β–CuMnSb polymorph.
<span id="page-5-1"></span>TABLE I. Experimental N´eel temperature TN, effective Curie-Weiss magnetic moment of Mn ions meff (Mn), and Curie-Weiss temperature TCW of α–CuMnSb. Measured orientation of the AFM axis is also given (n.e. = not established). Refs. [42](#page-12-24) and [41](#page-12-25) report the saturation Mn moment.
Turning now to the magnetic characteristics established here for α–CuMnSb we note that they are close to those reported previously, as shown in Tab. [I.](#page-5-1) The published data exhibit a certain distribution, which may indicate that other factors, such as a weak crystalline disorder, may be at work. In particular, either additional Mn interstitial ions or CuMn-MnCu antisite pairs are likely to form.[35](#page-12-18) The presence of such defects was suggested to stabilize the experimentally observed AFM {111}-oriented phase of α–CuMnSb.[35](#page-12-18) Finally, we do not observe a canted AFM order at low temperatures[41](#page-12-25) in any of our samples.
#### <span id="page-5-0"></span>III. THEORY
## A. Theoretical Methods
Calculations are performed within the density functional theory[46,](#page-13-2)[47](#page-13-3) in the generalized gradient approximation of the exchange-correlation potential proposed by Perdew, Burke and Ernzerhof.[48](#page-13-4) To improve description of 3d electrons, the Hubbard-type +U correction on Mn is added.[49–](#page-13-5)[51](#page-13-6) The parameter U(Mn) = 1 eV reproduces the known formation energy of the intermetallic CuMn alloy and gives a reasonable value of the Mn cohesive energy. We use the pseudopotential method implemented in the Quantum ESPRESSO code,[52](#page-13-7) with the valence atomic configuration 4s <sup>1</sup>.<sup>5</sup>p <sup>0</sup>3d 9.5 for Cu,
3s 2p <sup>6</sup>4s 2p <sup>0</sup>3d 5 for Mn and 5s 2p 3 for Sb ions. The planewaves kinetic energy cutoffs of 50 Ry for wave functions and 250 Ry for charge density are employed. Finally, geometry relaxations are performed with a 0.05 GPa convergence criterion for pressure. In defected crystals ionic positions are optimized until the forces acting on ions become smaller than 0.02 eV/˚A.
The properties of defected α–CuMnSb are examined using cubic 2a×2a×2a supercells with 96 atoms (i.e., 32 f.u.), while magnetic order of ideal crystals are checked using the smallest possible supercells. Here a is the equilibrium lattice parameter. The k-space summations are performed with a 6 × 6 × 6 k-point grid for the largest supercell, and correspondingly denser grids are used for smaller cells.
Magnetic interactions and magnetic order depend on several factors, such as the exchange spin splitting of the d(TM) shells, charge states of TM ions, concentration of free carriers and their spin polarization, and the density of states (DOS) at the Fermi energy EF. These factors are interrelated, and are calculated self-consistently within ab initio approach.
Considering first the localized magnetic moments we note that spin polarization of Co, Ni, and Cu ions in XMnZ compounds practically vanishes, while that of the d(Mn) shell is substantial.[16,](#page-11-14)[17](#page-12-0)[,31](#page-12-14) The robustness of the Mn magnetic moment results from the large, 3 – 5 eV, spin splitting of the 3d(Mn) states. In fact, in XMnZ the d(Mn) spin up channel is occupied, while most of the spin down d(Mn) states lay above the Fermi level. Here, one can observe that spin polarization of the d(TM) electrons in free atoms depends on the difference in the number of spin up and spin down electrons, which is the highest in the case of Mn. Consequently, the Mn spin polarization persists in XMnZ. On the other hand, spin splitting of d electrons of Co and Ni atoms is smaller, and thus it vanishes in XMnSb hosts, see the analysis for TM dopants in ZnO.[53](#page-13-8)
In CuMnSb, the magnetic sublattice consists of Mn ions, which are second neighbors distant by 4.3 ˚A. Therefore, the direct exchange coupling between two Mn ions, given by overlaps of their d(Mn) orbitals, is negligibly small. The remaining indirect exchange coupling is the sum of two contributions, and the exchange constant Jindirect = Jsr + JRKKY . [16](#page-11-14)[,17](#page-12-0)[,54](#page-13-9) The first term Jsr has a short-range AFM character, and it is inversely proportional to the energy distance between the unoccupied d(Mn) states and EF. The second coupling channel is of RKKY type mediated by free carriers. This channel depends on the detailed electronic structure in the vicinity of EF, and JRKKY is proportional to DOS(EF). In particular, CoMnSb and NiMnSb half-metals are FM, while CuMnP and CuMnAs insulators are AFM. As we show here, CuMnSb is the border case.
#### <span id="page-5-2"></span>B. Crystal and magnetic properties of α–CuMnSb
A rhombohedral primitive cell of α–CuMnSb contains one formula unit. This structure consist in four interpenetrating fcc sublattices, one of them being empty. The consecutive (001) MnSb planes are followed by the "halfempty" Cu planes, in which the planar atomic density is twice lower. The cubic unit cell is presented in Fig. [2](#page-3-0) (a). Local coordination of Mn ions can be relevant from the point of view of magnetic interactions. With this respect we notice that the magnetic coordination of an Mn ion consists in 12 equidistant Mn atoms at a/<sup>√</sup> 2. More-
We consider four magnetic phases of α–CuMnSb. The corresponding supercells are shown in Fig. [5.](#page-6-0) Antiferromagnetic order with parallel Mn spins in the (001) planes, AFM001, is calculated using the cubic a×a×a cell with 4 f.u. (12 atoms), and shown in Fig. [5](#page-6-0) (a). The AFM order with a period doubled in the [001] direction with parallel Mn spins in each (001) plane, denoted as AFM002, is shown in Fig. [5](#page-6-0) (b). The corresponding a×a×2a cell contains 8 f.u., and is one of the possible supercells in which this phase can be realized. In the AFM111 phase, the Mn spins are parallel in each (111) plane, but the consecutive (111) planes are AFM, as shown in Fig. [5](#page-6-0) (c), and the corresponding rhombohedral unit cell a √ 2 × a √ 2 × a √ 2 contains 8 primitive cells with 24 atoms. Finally, the FM phase requires a primitive cell a/<sup>√</sup> 2×a/<sup>√</sup> 2×a/<sup>√</sup> 2 with 1 f.u., presented in Fig. [5](#page-6-0) (d).
<span id="page-6-1"></span>TABLE II. The calculated lattice parameter a, the saturation Mn magnetic moment, msat, and the energy of the given magnetic order relative to α–CuMnSb in the AFM001 ground state, ∆Etot. All energies are per one formula unit. Our measured TEM values are also given.
higher in energy. The least stable is the FM order, higher in energy than AFM001 by about 20 meV per f.u. The equilibrium lattice parameters a ≈ 6.1 ˚A are practically independent of the magnetic order, and close to the experimental value 6.088 ˚A.[42](#page-12-24) Some phases are characterized by a small distortion of the cubic symmetry caused by different bond lengths between ferromagnetically and antiferromagnetically oriented Mn ions. Differences in the lattice parameters between various magnetic phases are below 0.01 ˚A, and are not reported in the Table. Similar results for the AFM001 order were obtained in Ref. [35,](#page-12-18) while in Refs [16](#page-11-14) and [31](#page-12-14) the AFM order is more stable than FM by 50 and 90 meV per Mn, respectively.
The last property reported in Tab. [II](#page-6-1) is the saturation magnetic moment of Mn, which also is similar in all phases, and equal to about 4.6µB. This value corresponds to the Curie-Weiss moment of 5.5(1)µB, and compares favorably with the experimental values given in Tab. [I.](#page-5-1)
The obtained results allow estimating the relative roles of the short- and long-range contributions to the magnetic coupling. To this end, we assume the hamiltonian in the form Hex = −J/2 P i,j ⃗si⃗s<sup>j</sup> , where the short range interaction is limited to the Mn NNs neighbors, and the long-range term is neglected. The spin value, s<sup>i</sup> ≈ 2.3, is one half of the calculated magnetic moment of Mn.
The exchange constant J is positive (negative) for the FM (AFM) coupling, and is obtained by comparing energies of various magnetic orders. In the AFM001 phase, each Mn ion has 4 ferromagnetically oriented Mn NNs in the (001) plane and 8 antiferromagnetically oriented Mn NNs in the two adjacent planes. For the remaining magnetic phases, the energies calculated relative to the ground state E<sup>0</sup> ≡ EAFM001 depend on the magnetic order as shown in Tab. [II.](#page-6-1) These results give the coupling constant in the range −0.6 ≥ Jsr ≥ −0.2 meV. This spread is quite large and cannot be explained by (negligible) changes in atomic distances in cells with different magnetic ordering. Therefore, we conclude that the Heisenberg nearest neighbor model does not describe magnetic properties of bulk phases. Indeed, such a model is not appropriate for metallic or semimetallic systems such as α–CuMnSb, where the long-range RKKY coupling is present.
An opposite conclusion comes from the analysis of single spin excitations from the AFM001 ground state. We use a 2a×2a×2a supercell to calculate the energy differences ∆E for the following cases, in which we change (i) spin of one Mn ion, 1Mn ↑→ 1Mn ↓, called a single spin-flip, (ii) 2Mn↑→ 2Mn↓ for spins of two nearest Mn ions belonging to one layer and (iii) 2Mn ↑→ 2Mn ↓ for two distant Mn ions. In these processes the long-range coupling is not important, and indeed the calculated exchange constant consistently is Jsr ≈ −0.4 meV.
#### <span id="page-7-0"></span>C. Crystal and magnetic properties of β–CuMnSb
We now consider two possible structures of the secondary phase proposed based on the experimental results. They are characterized by doubling the periodicity in the [001] direction. The unit cell of β–CuMnSb, shown in Fig. [2,](#page-3-0) is tetragonally deformed relative to that of α–CuMnSb, with the corresponding lattice parameters a = 5.88 ˚A and c = 6.275 ˚A. They differ by about 3 per cent from our calculated cubic a(α– CuMnSb) = 6.105 ˚A. The two interlayer spacings between the consecutive MnSb planes in the [001] direction in the unit cell, shown in Fig. [2](#page-3-0) (b), are quite different, namely dinter<sup>1</sup> = 2.80 ˚A (no Cu), and dinter<sup>2</sup> = 3.48 ˚A (with Cu). Turing to the magnetic order of β–CuMnSb, we find that the FM phase constitutes the ground state with msat = 4.6µ<sup>B</sup> and is lower than the AFM phase by 11 meV per f.u., as indicated in Tab. [II.](#page-6-1) Thus, the
The experimental[27](#page-12-10) lattice parameters of β–CuMnSb reasonably agree with our values, i.e., the calculated a = 6.28 ˚A and c/a = 1.87 are about 2% larger than those measured for the compressed crystal at the critical pressure of 7 GPa. On the other hand, the calculations of Ref. [27](#page-12-10) predict that the magnetic order of the β phase is AFM, in striking contrast with our results. Also their calculated msat(Mn) = 3.8µ<sup>B</sup> is substantially smaller than our 4.6µB. The origin of these discrepancies is not clear, but it may be due to the different exchange-correlation functionals used, and/or to application of the +U(Mn) correction in our calculations (which can affect the results.[31](#page-12-14))
The calculated total energy of the FM β–CuMnSb relative to the AFM α–CuMnSb is higher by 102 meV per f.u. This energy difference is not large, being comparable to the growth temperature, which implies that the β–CuMnSb polymorph can indeed form during epitaxy. We also stress that stoichiometry of the α and β phases is the same, which facilitates formation of β–CuMnSb. Finally, the observed β–CuMnSb inclusions are coherent, i.e., lattice matched, with the host structure. This agrees with the fact that the calculated excess elastic energy of matching the lattice parameters of the β phase to the host α phase is very low and ranges from 3 meV per f.u. (when the tetragonal a parameter constrained to the cubic a = 6.105 ˚A) to 20 meV per f.u. (the tetragonal c parameter constrained to the cubic a).
The second considered possibility, Cu3Mn2Sb<sup>2</sup> shown in Fig. [2](#page-3-0) (c), is higher in energy by 0.37 eV per f.u. in the Cu–rich conditions than the ideal CuMnSb, i.e., by 0.27 eV per f.u. than β–CuMnSb, its stoichiometry is markedly different, and thus we can eliminate this structure from considerations.
# D. Energy band structures of α–CuMnSb and β–CuMnSb
Figure [7](#page-8-1) (a) shows the energy bands and DOS of the AFM001 α–CuMnSb. We see that this phase has a metallic character, however DOS at the Fermi level is low. The states close to E<sup>F</sup> are built from s, p and d states of all ions with similar weights. The low DOS(EF) makes CuMnSb almost semimetallic with a low electrical conductivity. Compatible with the small DOS(EF) is the high resistivity measured in Ref. [41](#page-12-25) and [55.](#page-13-10)
Since the system is antiferromagnetically ordered, the total DOSs of spin-up and spin-down states are the same. In Fig. [7](#page-8-1) only contributions of the 3d(Mn) and 3d(Cu) orbitals are presented to reveal magnetic properties. We see that the exchange spin splitting of the d(Mn) shell is large, about 5 eV. The closely spaced levels contributing to the DOS maxima centered at 4 eV below the Fermi energy are composed mainly of the d states of both Cu and Mn. Spin-up and spin-down 3d(Cu) orbitals are almost
completely occupied, and thus Cu ions are non-magnetic. In turn, the majority spin states of the 3d(Mn) orbitals are completely occupied, while the minority spin states at 1 eV above the Fermi energy are partially filled thanks to a small overlap with spin up states. As a result, a single Mn ion is in between the d <sup>5</sup> and d 6 configuration, with the saturation magnetic moment of 4.6µ<sup>B</sup> consistent with Tab. [II.](#page-6-1) Our results for α–CuMnSb are close to those of Ref. [31.](#page-12-14) A similar electronic configuration takes place in CuMnAs, where the spin-down Mn states are partially filled.[56](#page-13-11)
The overall band structure of the FM β–CuMnSb displayed in Fig. [7](#page-8-1) (b) is close to that of α–CuMnSb, which is particularly clear when comparing partial DOS of both phases. In particular, msat(Mn) is about 4.5µ<sup>B</sup> in both phases, and energies of both d(Mn)- and d(Cu)-related bands are largely independent of the actual crystal structure. This similarity can be due to the fact that the MnSb (001) planes play a dominant role, and the exact locations of the Cu ions are less important.
On the other hand, the calculated DOS(EF) for the α phase is 0.35 states per spin and f.u., while for the β phase we find 1.26 states per spin and f.u., which is 3.6 times higher. As a consequence, α–CuMnSb is semimetallic, and the AFM order is dominant, while β phase is more metallic in character, which in turn favors the RKKY-type coupling and the FM order. This feature can explain the different magnetic phases of the α and β polymorphs.
Analysis of the calculated electronic structure of Heusler and half-Heusler CuMnZ led Sasioglu et al.[17](#page-12-0) to the conclusion that when the spin polarization of conduction electrons is large, and the d(Mn) spin down states are far above EF, then the RKKY coupling is dominant, and one should expect the FM order, otherwise the short range AFM coupling is dominant. Our results do not confirm this conclusion, and indicate that the important
## <span id="page-8-0"></span>E. Point native defects in α–CuMnSb
where E(CuMnSb) and E(CuMnSb : D) are the total energies of a supercell without and with a defect, and n<sup>i</sup> = +1(−1) corresponds to the removal (addition) of one ith atom. µis are the variable chemical potentials of atoms in the solid, which in general are different from the chemical potentials µi(bulk) of the standard state of elements, i.e., Cu, Mn and Sb bulk. Details of calculations of chemical potentials are given in Appendix [A.](#page-10-0)
The point native defects considered here are vacancies VX, interstitials X<sup>i</sup> , and antisites X<sup>Y</sup> (where X and Y are Cu, Mn, or Sb) for all three sublattices. As it was mentioned above, the Cu sublattice is "half- empty" compared to the MnSb sublattice. Consequently, we consider here formation of interstitials at the empty sites of the Cu sublattice only, and neglect other possibilities, expected to have higher formation energies Eform. Thus, the set of defects considered here only partially overlaps with that of Ref. [35.](#page-12-18) Of particular interest to the present study are defects involving Mn ions, since they can influence magnetic properties of α–CuMnSb .[35](#page-12-18) This is why we consider them more extensively, after briefly analyzing the non-magnetic defects. The calculated formation energies are summarized in Tab. [III.](#page-9-0) Because of the magnetic coupling, formation energies of the Mn-related defects depend on the spin direction relative to the spins of the host Mn neighbors. We consider possible spin configurations shown in Fig. [8](#page-9-1) (b).
<span id="page-9-0"></span>TABLE III. Formation energies (in eV) of isolated point defects in the Mn-rich conditions. In parentheses are Mn-related values corrected for ∆H<sup>f</sup> (MnSb) = 0.48 eV, which correspond to the Mn-poor case.
where k<sup>B</sup> is the Boltzmann constant and N<sup>0</sup> is the density of the relevant lattice sites. Details of the calculations of Eform are provided in Supporting Information. To put the calculated formation energies into a proper context, we note that if the growth temperatrure Tgrowth = 2500C and Eform = 0.1 eV, then exp(−Eform/kBTgrowth) = 0.1, which corresponds to a high 10 atomic per cent concentration of this defect on the considered sublattice. On the other hand, if Eform = 1 eV, then exp(−Eform/kBTgrowth) = 9 × 10<sup>−</sup><sup>11</sup>, which implies a negligible defect concentration.
Sb sublattice. The prohibitively high values of Eform demonstrate that VSb and Sb<sup>i</sup> should not form. Similarly, formation energies of SbCu, SbMn, CuSb and MnSb antisites exceed 1 eV, and those defects are not expected to be present at high concentrations. Consequently, the Sb sublattice is thermodynamically stable, robust, and constitutes a defect-free back-bone of CuMnSb.
(ii) Formation energy of Cu interstitials at the Cu sublattice, Eform(Cui) = 1 eV, is relatively high, and their concentrations are negligible. Additionally, the high formation energy of Cu<sup>i</sup> interstitials is consistent with the sparse character of the Cu sublattice in α–CuMnSb.
(iii) Formation of Mn<sup>i</sup> interstitials at the Cu sublattice is characterized by Eform = 0.7-1.4 eV, depending on the spin direction and conditions of growth, and therefore they are not expected to be present at high concentrations, especially in the Mn-poor conditions.
In brief, low formation energies are found for three defects, namely the VCu and VMn vacancies and the MnCu antisite, particularly at the Mn-rich growth conditions. This indicates that a Cu deficit on the Cu sublattice is possible, affecting stoichiometry. Significantly, MnCu antisites make the Cu sublattice magnetic, and also they can participate in the magnetic coupling between the adjacent MnSb (001) planes, thus influencing magnetic properties, as it will be discussed in more detail below. In contrast, SbCu antisites are present in negligible concentrations. Our results are in a reasonable agreement with those of Ref. [35,](#page-12-18) especially given their neglect of spin effects and a somewhat different theoretical approach. Interestingly, formation energies of native defects in CuMnAs calculated in Ref. [56](#page-13-11) are close to the present results in spite of the different anion.
## F. Defect-induced magnetic coupling
There are two Mn-related point defects, Mn<sup>i</sup> and MnCu, both situated on the Cu sublattice. When present at high concentrations, they affect magnetism of α– CuMnSb. Their coupling with host Mn ions is different than the Mn-Mn coupling between the host Mn because of the different local coordination. Energetics of both defects is complex and rich, since the total energy of the system (and thus formation energies) depends on their spin orientations relative to the neighborhood. At both substitutional and interstitial sites in the Cu layer, a Mn ion has 4 Mn nearest neighbors arranged in a tetrahedral configuration, 2 in the upper and 2 in the lower MnSb layer. The Mni–MnMn distance is shorter than that of
MnMn–MnMn, and equal to (<sup>√</sup> 3/4)a.
The possible local spin configurations are reduced to small clusters of 5 Mn ions, shown in Fig. [8.](#page-9-1) The Mn spin-up and spin-down (001) MnSb layers are denoted by in pink and blue, respectively, reflecting the calculated (001) AFM magnetic ground state. The central MnCu (or Mni) ion of such a cluster provides an additional channel of magnetic coupling between two adjacent MnSb layers. The corresponding formation energies are given in Fig. [8.](#page-9-1)
As it was pointed out, in ideal α–CuMnSb, the Mn ions are second neighbors only, separated either by Sb (i.e., the Mn-Sb-Mn "bridge" in the MnSb(001) plane), or by Cu (forming a Mn-Cu-Mn "bridge" linking 3 consecutive (001) planes.) Thus, the short range magnetic coupling in ideal α–CuMnSb is successfully modelled in Sec. [III B](#page-5-2) by the interaction between two Mn second neighbors, situated either in the same MnSb layer, or in two adjacent ones. In contrast, the 4 host Mn ions in the cluster are the first neighbors of a Mn<sup>i</sup> or a MnCu defect. Thus, one can expect that this coupling is stronger than the intrinsic one in the ideal host, and indeed, the differences in energy between various configurations in Fig. [8](#page-9-1) are about 100 meV, which is too high to be explained by the estimated Jsr = 0.4 meV.
As it follows from Fig. [8,](#page-9-1) 5-atom clusters are magnetically frustrated. In particular, the lowest energy case denoted as 4AFM favors the local FM orientation of spins in two adjacent (001) planes, which is opposite to the global host magnetic order. Our results do not confirm the conclusion of Ref. [56](#page-13-11) who find that the 3AFM configuration has the lowest energy, and thus it promotes the global AFM111 order. Instead, we rather expect that Mn-related point defects induce disorder of the host AFM phase, possibly leading to formation of a spin glass.[57](#page-13-12)
#### IV. SUMMARY
CuMnSb films were epitaxially grown on GaSb substrates. Magnetic measurements reveal the presence of two magnetic subsystems. The dominant magnetic order is AFM with the N´eel temperature of 62 K, which is the same as in bulk CuMnSb. It co-exists with a FM phase, characterized by the Curie temperature of about 100 K.
These findings go in hand with transmission electron microscopy and selective area diffraction measurements, which demonstrate coexistence of two structural polymorphs of the same stoichiometry. The dominant one is the cubic half-Heusler α–CuMnSb, which is the equilibrium structure of bulk samples. The second component is a tetragonal β–CuMnSb polymorph, which forms 10-100 nm long elongated inclusions.
(i) The β–CuMnSb phase is metastable, and its total energy is higher by 0.1 eV per f.u. only than that of the equilibrium α–CuMnSb. Lattice parameters of the β phase differ from those of α–CuMnSb by about 4 per cent. This lattice misfit between the two structures does not prevent the pseudomorphic coexistence of both phases, since the calculated misfit strain energy is below 20 meV per f.u.
(ii) In agreement with experiment, α–CuMnSb is AFM, and the FM order is 19 meV per f.u. higher in energy. In contrast, the magnetic ground state of β– CuMnSb is FM, which is more stable than AFM by 11 meV per f.u. This indicates that indeed the β–CuMnSb inclusions are responsible for the FM signal.
(iii) The different magnetic orders of the α and β phases originate in their somewhat different band structures. In particular, critical for magnetic order is the DOS at the Fermi level, which is about 4 times higher in β–CuMnSb than in the α phase. This shows that the β phase is more metallic in character, which in turn favors the FM order driven by the Ruderman-Kittel-Kasuya-Yoshida interaction.
(iv) Our calculations predict the saturated magnetic moment of Mn msat = 4.6µ<sup>B</sup> and 4.5µ<sup>B</sup> for the α and the β phase, respectively. This corresponds to the effective moment of 5.6µB, in good agreement with the measured 5.5µB.
(v) The calculated formation energies of point native defects indicate that the most probable are the MnCu antisites with low formation energies of 0–0.2 eV. However, their presence is expected to disorder the host magnetic AFM phase rather than to induce a transition to the FM configuration.
(vi) Regarding the properties of the CuMnX series we see that their structural stability is relatively weak, as they crystallize in a variety of structures. In particular, unlike the bulk orthorhombic CuMnAs, epitaxial films of CuMnAs are tetragonal, but both structures are AFM. In the case of CuMnSb, polymorphism comprises also the equilibrium magnetic structure, AFM in the bulk specimens, and FM in epitaxial films.
#### ACKNOWLEDGMENTS
LS, CG, JK and LWM thank M. Zipf for technical assistance. Our work was funded by the Deutsche Forschungsgemeinschaft (DFG,German Research Foundation) No. 397861849, by the Free State of Bavaria (Institute for Topological Insulators) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC2147 ct.qmat (Project-Id 390858490).
#### <span id="page-10-0"></span>Appendix A:
The highest possible value of µ<sup>i</sup> is µi(bulk), which implies that the studied system is in equilibrium with the given bulk source of atoms and δµ<sup>i</sup> = 0, otherwise δµ<sup>i</sup> < 0.
Chemical potentials of the components in the standard state are given by the total energies per atom of elemental solids. The calculated cohesive energies Ecoh of the face centered cubic Cu, the face centered cubic Mn with the AFM magnetic order, and the triclinic Sb are, respectively, 3.40 (3.49), 2.65 (2.92) and 2.68 (2.75) eV/atom. They compare reasonably well with the experimental values given in parentheses.[58](#page-13-13)
Chemical potentials of the involved atomic species depend on possible formation of compounds. The ranges of variations of chemical potentials are determined by conditions of equilibrium between various phases, i.e., Cu2Sb, MnSb and CuMnSb. Thermodynamic equilibrium requires that
$$\begin{aligned} \delta\mu(\text{Cu}) + 2\delta\mu(\text{Sb}) &= \Delta H\_f(\text{Cu}\_2\text{Sb}), \\ \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{MnSb}), \\ \delta\mu(\text{Cu}) + \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{CuMnSb}), \end{aligned} \quad \text{(A2)}$$
The calculated values ∆H<sup>f</sup> (Cu2Sb) = −0.03 eV per f.u., ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u., and ∆H<sup>f</sup> (CuMnSb) = −0.42 eV per f.u. The very low ∆H<sup>f</sup> (Cu2Sb) is somewhat unexpected, since Cu2Sb is a stable compound which crystallizes in the tetragonal phase.[43](#page-12-26) Next, our result ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u. agrees well with both the previous value -0.52 eV per f.u. calculated in Ref. [59,](#page-13-14) and the experimental - 0.52 eV per f.u.[60](#page-13-15) Assuming that the accuracy of the calculated values is 0.03 eV per f.u., the set of Equation [A2](#page-11-15) is consistent if we assume ∆H<sup>f</sup> (Cu2Sb) = 0, and ∆H<sup>f</sup> (MnSb) = ∆H<sup>f</sup> (CuMnSb) = −0.45 eV per f.u. This in turn implies that δµ(Cu) = δµ(Sb) = 0, and δµ(Mn) = −0.45 eV. Consequently, the allowed window of the Mn chemical potential is
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| |
FIG. 2. Crystal structures of (a) α–CuMnSb with the cubic lattice constant a, (b) tetragonal β–CuMnSb with the lattice constants a in the (x, y) plane and c in the [001] direction, and (c) Cu3Mn2Sb2.
|
# Coexistence of Antiferromagnetic Cubic and Ferromagnetic Tetragonal Polymorphs in Epitaxial CuMnSb
High-resolution transmission electron microscopy and superconducting quantum interference device magnetometry shows that epitaxial CuMnSb films exhibit a coexistence of two magnetic phases, coherently intertwined in nanometric scales. The dominant α phase is half-Heusler cubic antiferromagnet with the N´eel temperature of 62 K, the equilibrium structure of bulk CuMnSb. The secondary phase is its ferromagnetic tetragonal β polymorph with the Curie temperature of about 100 K. First principles calculations provide a consistent interpretation of experiment, since (i) total energy of β–CuMnSb is higher than that of α–CuMnSb only by 0.12 eV per formula unit, which allows for epitaxial stabilization of this phase, (ii) the metallic character of β–CuMnSb favors the Ruderman-Kittel-Kasuya-Yoshida ferromagnetic coupling, and (iii) the calculated effective Curie-Weiss magnetic moment of Mn ions in both phases is about 5.5 µB, favorably close to the measured value. Calculated properties of all point native defects indicate that the most likely to occur are MnCu antisites. They affect magnetic properties of epilayers, but they cannot induce the ferromagnetic order in CuMnSb. Combined, the findings highlight a practical route towards fabrication of functional materials in which coexisting polymorphs provide complementing functionalities in one host.
#### I. INTRODUCTION
One of the most challenging and long-standing problems in fundamental magnetism is a competition between ferromagnetic and antiferromagnetic phases. Their interplay at the interface results in a well known effect of the exchange bias,[1](#page-11-1)[,2](#page-11-2) which fuels now a rapid development of spintronics[3](#page-11-3) and unconventional computing.[4](#page-11-4) The material class of Heusler alloys was previously used to study the origin of the transition between magnetic phases because it offers a wide spectrum of functionalities.[5](#page-11-5) Indeed, Heusler alloys exhibit ferromagnetic (FM), antiferromagnetic (AFM), and canted ferromagnetic order. This indicates that different types of magnetic coupling are competing in this family. Moreover, some of its members display structural polymorphism, which allows studying relationships between the crystalline phase, the magnetic phase, and the corresponding electronic structure.
Heusler alloys incorporate full-Heusler (X2YZ) and half-Heusler (XYZ) variants, where X and Y stand for transition metals, whereas Z denotes anions from the main group. In this class, qualitative changes in material characteristics can be achieved by chemical substitution on either the transition metal cation or on the anion sublattice. Typically, the change of the cation does not change the crystal structure, but it can induce a crossover between the AFM and the FM magnetic phases. A rarely met complete solubility with only marginally affected crystallinity of the otherwise chemically homogenous systems allowed to study the FM-AFM phase competition in detail. The prominent examples are quaternary solid solutions such as Ru2Mn1−xFexSn[6–](#page-11-6)[8](#page-11-7)
Heuslers, and Co1−xNixMnSb,[9](#page-11-8)[,10](#page-11-9) Cu1−xNixMnSb,[11–](#page-11-10)[13](#page-11-11) Co1−xCuxMnSb,[14](#page-11-12) and Cu1−xPdxMnSb[15](#page-11-13) half-Heuslers. In the latter case, the crossover between AFM to FM phases is related to a change in the electronic structure from semimetallic to half-metallic.[16](#page-11-14)[,17](#page-12-0)
Cu–based CuMnZ compounds are antiferromagnets. This feature attracts attention given the recent progress achieved in the AFM spintronics.[18](#page-12-1) Of particular interest is CuMnAs, with a high N´eel temperature T<sup>N</sup> = 480 K.[19](#page-12-2) In this case, features essential for applications, such as anisotropic magnetoresistance,[20,](#page-12-3)[21](#page-12-4) current-induced electrical switching of the N´eel vector[22](#page-12-5) and of the magnetic domains,[23](#page-12-6) have been demonstrated.
The AFM order of CuMnZ is independent of the actual crystalline structure. The equilibrium structure of bulk CuMnP and CuMnAs is orthorhombic, while that of CuMnSb is half-Heusler cubic, referred to below as the α phase. On the other hand, epitaxial growth can stabilizes metastable phases. This is the case of epitaxial layers of CuMnAs, grown on both GaP[19](#page-12-2)[–21](#page-12-4)[,24](#page-12-7)[,25](#page-12-8) and GaAs[23](#page-12-6) substrates, which crystalize in the tetragonal structure, referred to below as the β phase. Theoretical investigations of the crystalline properties of CuMnZ series show that the total energy difference between the cubic and orthorhombic phase is about 1 eV per f.u. (formula unit) for CuMnP, and about 0.5 eV per f.u. for CuMnAs.[26](#page-12-9) This suggests that the orthorhombic phase of CuMnSb, the last member of the CuMnZ series, may not be stable, and indeed the stable structure is the α phase. However, as we show here, epitaxial stabilization of CuMnSb in the β phase is in principle possible, because the calculated energy difference between
Concerning the magnetic properties, the N´eel temperature of both orthorhombic CuMnAs and β–CuMnAs is well above the room temperature,[19](#page-12-2) whereas that of α– CuMnSb is lower, about 60 K.[28,](#page-12-11)[29](#page-12-12) Theory agrees with experiment, since according to Ref. [30,](#page-12-13) in the orthorhombic CuMnP and CuMnAs, the AFM order is more stable than the FM by about 250 meV/Mn. This energy difference is smaller in the cubic phase of CuMnZ compounds, for which the AFM order is lower in energy than FM one by about 50 meV per f.u.[30](#page-12-13)[,31](#page-12-14) Finally, the AFM order of α–CuMnSb is stable under applied magnetic field, as T<sup>N</sup> does not change up to 50 Tesla.[32](#page-12-15)
Turning to the electronic structure of the CuMnP-CuMnAs-CuMnSb series we observe that the character of the energy band gap depends on the anion. Similar to the case of e.g. zinc blende semiconductors, the band gap decreases with the increasing atomic number of the anion.[30](#page-12-13) Indeed, CuMnP is a semiconductor, CuMnAs has a practically vanishing band gap, and CuMnSb is a semimetal.[33](#page-12-16)
Here we experimentally confirm a puzzling coexistence of AFM and FM phases in epitaxial stoichiometric CuMnSb films, observed by us previously,[34](#page-12-17) and explain the underlying mechanism responsible for this effect. A fine analysis of transmission electron microscopy (TEM) images, Sec. [II B,](#page-2-0) points to the formation of tetragonal β–CuMnSb inclusions embedded coherently within the cubic α–CuMnSb host. The tetragonal structure of these inclusions is the same as that of the tetragonal β– CuMnAs. Magnetic properties of our films, Sec. [II C,](#page-4-0) demonstrate coexistence of two magnetic phases: apart from the dominant AFM one, expected for CuMnSb, the measurements reveal the presence of a FM contribution. This is an unexpected feature within the CuMnZ series, exhibiting the AFM order.
In Sec. [III,](#page-5-0) we employ calculations based on the density functional theory to assess properties of CuMnSb films. In agreement with the experiment, β–CuMnSb is weakly metastable, but its magnetic ground state is FM. Band structures of α and β polymorphs are close, but changes in the density of states at the Fermi level account for the change of the dominant mechanism of the magnetic coupling from AFM superexchange to FM Ruderman-Kittel- Kasuya-Yoshida (RKKY). Finally, in Sec. [III E](#page-8-0) native point defects in CuMnSb are examined to assess their possible influence on the magnetic properties.[35](#page-12-18) Our results indicate that the dominant native defects in α–CuMnSb are Mn antisites, and their presence in the films can possibly account for small differences between the measured and the calculated magnetic characteristics, but they do not stabilize the FM order of α–CuMnSb.
# II. EXPERIMENTAL RESULTS
## A. Experimental Methods
# Growth conditions.
CuMnSb layers about 200 nm thick are grown by molecular beam epitaxy. Separate growth chambers connected by an ultra-high vacuum transfer system are used for the growth of the individual layers. Low telluriumdoped epi-ready GaSb (001) wafers are used as substrates. Prior to the growth, the natural oxide layer is desorbed in an Sb atmosphere. Then, 150 nm thick GaSb buffer layers are grown on the substrates to ensure a high-quality interface for the growth of CuMnSb. The GaSb buffer layers are grown at a substrate temperature of 530◦C and a beam equivalent pressure of 4.0 × 10−<sup>6</sup> mbar and 5.3 × 10−<sup>7</sup> mbar for Sb and Ga, respectively. Sb supply is facilitated by a single-filament effusion cell, while Ga is provided by a double-filament effusion cell.
A substrate temperature of 250◦C is used for the growth of CuMnSb films. The corresponding beam equivalent pressures are as follows: BEPCu = 5.80 × 10<sup>−</sup><sup>9</sup> mbar, BEPMn = 9.03 × 10<sup>−</sup><sup>9</sup> mbar, and BEPSb = 4.23 × 10<sup>−</sup><sup>8</sup> mbar. Cu is supplied by a double filament effusion cell, while Mn and Sb are supplied by single filament effusion cells. Following the growth of CuMnSb, a 2.5 nm thick layer of Al2O<sup>3</sup> is deposited on the samples through a sequential process of aluminum DC magnetron sputtering and oxidation. Please, refer to Ref. [29](#page-12-12) for a comprehensive analysis of the growth process and physical properties of the CuMnSb layers produced using the methodology outlined above.
Transmission Electron Microscopy. Specimens for the transmission electron microscopy (TEM) investigations are prepared by the focused ion beam method in the form of lamellas cut along the [100] and [110] directions, i.e., perpendicularly to the surface (001) plane. Titan Cubed 80-300 electron transmission microscope operating with accelerating voltage 300 kV and equipped with energy-dispersive X-ray spectrometer (EDXS) is used for the study. Most of the investigations are done on Cu grids, but for EDXS elemental analysis a Mo grid is used to avoid interference of Cu fluorescence signal from the grid. This analysis yields percentage atomic concentration at 37(3) : 32(5) : 31(7) for Cu, Mn, and Sb, respectively, which, within the experimental errors (given in the parentheses), correspond to the expected stoichiometric ratio of 33 : 33 : 33.
SQUID Magnetometry. Magnetic characterization is performed in a commercial superconducting quantum interference device (SQUID) magnetometer MPMS XL7. The magnetic moment of antiferromagnetic layers is generally very weak and by far dominated by the magnetic response of the bulky semiconductor substrates. Therefore, to counter act the typical shortcomings of commercial magnetometers built around superconducting magnets[36](#page-12-19) and to minimize subtraction errors during
![<span id="page-2-1"></span>FIG. 1. (a) High-angle annular dark-field scanning transmission electron microscopy image of a CuMnSb layer in the [100] zone axis. The inset in the top-right corner brings up a part of the image in atomic resolution, where bright dots represent columns of Mn and Sb atoms. (b) Electron diffraction pattern of the layer. (c) Schematics of the positions of Bragg's spots from (b). Big bullets represent the main reflections from the cubic CuMnSb structure, whereas the open triangles mark the positions of the weak extra reflections. The orientation of the triangles follows from the analysis of the data in panels (d-g). (d-e) Blown up two regions from (a), in which either vertical or horizontal strips dominate. The corresponding Fourier transforms are showed in the top right corners of both panels. (f) Selected area electron diffraction pattern taken at the regions dominated by the vertically oriented strips. (g) Diffraction intensity profiles taken along the horizontal [010]\* and the vertical [001]\* lines passing through the center the diffraction pattern. The solid line corresponds to the horizontal [010]\* direction and the dashed one to the vertical [001]\* one in panel (f). Stars denote directions in the reciprocal space. The arrows α and β indicate the length of α–2g(002) and β–2g(002) diffraction vectors, respectively.](path)
data reduction we actively employ the in situ compensation.[37](#page-12-20) It allows us to reduce the coupling of the signal of the substrates to about 10% of their original strength. The actual effectiveness of the compensation depends on the mass of the sample and its orientation with respect to the SQUID pick-up coils.[36,](#page-12-19)[38](#page-12-21) We also strongly underline the importance of a thorough mechanical removal of the metallic MBE glue from the backside of the samples for any magnetic studies. Its strongly nonlinear magnetic contribution can be of the same magnitude as that of the layer of interest.[39](#page-12-22) To accurately establish the magnitude of magnetic moment specific to CuMnSb we measure a reference sample grown without the CuMnSb layer[29](#page-12-12) using the same sample holder and following exactly the
#### <span id="page-2-0"></span>B. Structural characterization
An exemplary atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF/STEM) image obtained for the [100] zone axis (the direction of the projection) is in Fig. [1](#page-2-1) (a). It confirms a high quality cubic constitution of the material, as it is underlined in the inset. However, at the contrast chosen here, the image in this field of view reveals the presence of stripe-like features, which are the main subject of this analysis. In this image, the apparent lengths and widths of the strips are about 40 nm and about 4 nm, respectively, running predominantly either vertically or horizontally in this particular projection. On other images, the strips exhibit a relatively wide distribution of lengths in the 10-100 nm window. Since similarly distributed shadowy stripes are observed also in the [110] zone axis, we conclude that they form along all three principal crystallographic directions without any particular preferences. The expected F43m cubic structure of α–CuMnSb is clearly confirmed by the fourfold symmetry of the dominant (bright) spots seen on electron diffraction pattern presented in Fig. [1](#page-2-1) (b).
Importantly, the diffraction pattern in Fig. [1](#page-2-1) (b) contains also a second set of much fainter reflections, situated halfway between two adjacent reflections of the main pattern. This indicates the presence of a second crystallographic β phase, which periodicity in the corresponding direction is doubled relative to that of α–CuMnSb, but otherwise coherent with this host structure. We bring all the Bragg's spots up in Fig. [1](#page-2-1) (c), in which the bullets represent the main reflections from α–CuMnSb, whereas the open triangles mark the positions of the weak ones, which are forbidden for this structure.
The presence of β–CuMnSb is further substantiated by the inspection of the two close-ups from Fig. [1](#page-2-1) (a), shown in Fig. [1](#page-2-1) (d) and (e). At this magnification they reveal that, on top of the otherwise cubic arrangement of atomic columns, the strips' brightness alternates every second {002} plane along the direction perpendicular to strip's long axis. The modulation is vertical in Fig. [1](#page-2-1) (d), whereas it goes horizontally in Fig. [1](#page-2-1) (e). The top right corners of these figures contain the corresponding Fourier transform of the parent image, and, similarly to Fig. [1](#page-2-1) (b), both patterns are dominated by the main reflections of α–CuMnSb. The additional spots are embedded either along vertical [Fig. [1](#page-2-1) (d)] or horizontal [Fig. [1](#page-2-1) (e)] lines, i.e., the presence of vertical and horizontal orientations is mutually exclusive. This feature is reflected in Fig. [1](#page-2-1) (c), where the additional spots are marked by differently oriented triangles. The triangles with apexes directed vertically correspond to the vertical orientation of the brightness modulation in Fig. [1](#page-2-1) (d), whereas the horizontal direction of apexes corresponds to the horizontal modulation.
Based on the data shown above we propose that the second phase of CuMnSb, present in our films in the form of strips, is a tetragonal structure, which also is the structure of epitaxial CuMnAs,[19–](#page-12-2)[21](#page-12-4)[,23](#page-12-6)[–25](#page-12-8) and of CuMnSb at high pressures.[27](#page-12-10) This β–CuMnSb polymorph is shown in the panel (b) of Fig. [2.](#page-3-0) The difference between α and β phases consists in the location of Cu ions: in the α phase every (001) plane between two consecutive MnSb planes is half-occupied by Cu, whereas in the β phase Cu ions completely fill up every second (001) plane, and the overall stoichiometry of the material is preserved.
![<span id="page-3-0"></span>FIG. 2. Crystal structures of (a) α–CuMnSb with the cubic lattice constant a, (b) tetragonal β–CuMnSb with the lattice constants a in the (x, y) plane and c in the [001] direction, and (c) Cu3Mn2Sb2.](path)
regions with different orientations of the strips. Diffraction pattern of an area dominated by the vertically oriented strips is shown in more detail in Fig. [1](#page-2-1) (f). In agreement with the Fourier transforms, SAED shows the occurrence of specific reflections corresponding to this particular orientation. The reflections common to both the cubic α and the tetragonal β polymorphs are split along the [010]\* direction, i.e., orthogonal to the strip's axis, whereas the weak spots of the β phase are not split and are commensurate with the cubic phase. (A star denotes a direction in the reciprocal space.)
We quantify the effect analyzing intensity profiles taken along lines passing through the center of diffraction. The profiles are superimposed, and presented in Fig. [1](#page-2-1) (g). The profile along the [001]\* direction reflects the periodicity of α–CuMnSb, while that along [010]\* is additionally split. From the Figure it follows that in our specimens the c lattice parameter of the β–CuMnSb strips is equal to that of the host α–CuMnSb, 6.2(1) ˚A, whereas the a and b parameters of the β phase, 5.8(1) ˚A, are smaller by about 7%. Analogous features are observed for the [010]-oriented strips.
The existence of such a significant strain is confirmed by the calculation of strain maps. We apply the geometrical phase analysis method[40](#page-12-23) for the main image presented in Fig. [1](#page-2-1) (a), and the results are presented in Fig. [3](#page-4-1) (a) and (b) for the horizontal, ϵxx, and the vertical, ϵzz, components of strain, respectively. It is seen that stripes' strain is negative (dark shade) perpendicular to strips and almost zero along the strips. For example, on the horizontal strain map [Fig. [3](#page-4-1) (a)] only vertical strips are visible because they are compressed horizontally, whereas the horizontal strips are invisible because they are not deformed in the horizontal direction.
 (a). (a) The horizontal component of strain ϵxx, and (b) the vertical one, ϵzz. Geometrical phase analysis method has been applied.[40](#page-12-23)](path)
The calculated properties of β–CuMnSb, such as its lattice parameters, stability, and magnetic properties, are discussed in detail in Sec. [III C.](#page-7-0) Anticipating, we mention that they are consistent with experiment. We have also considered a second possible structure which is (almost) compatible with the TEM data, Cu3Mn2Sb2, depicted in Fig. [2](#page-3-0) (c). However, this compound is higher in energy than the β phase, and was dropped from further considerations.
#### <span id="page-4-0"></span>C. Magnetic properties
The temperature T dependence of magnetization, M(T), of the 200 nm thick layer of CuMnSb, is depicted in Fig. [4](#page-4-2) (a). The clear kink on M(T) at T<sup>N</sup> = 62 K marks the position of the paramagnetic to antiferromagnetic N´eel transition in the layer. This value corresponds precisely to the values of T<sup>N</sup> established previously for CuMnSb/GaSb layers of the thickness t ≥ 200 nm, what, indirectly, indicates stoichiometric material composition of this layer.[29](#page-12-12)
More specific information about the magnetic state of that sample is obtained from the examination of the temperature dependence of the inverse magnetic susceptibility, χ −1 (T), shown in Fig. [4](#page-4-2) (b). We take here χ(T) = M(T)/H, where H = 10 kOe is the external magnetic field applied during the measurements. χ −1 (T) can be approximated by two straight lines. The abscissa of the first one, which approximates χ −1 (T) above 200 K (the solid orange line in Fig. [4\)](#page-4-2), yields exactly the same magnitude of the Curie-Weiss temperature TCW = −100(5) K as that established previously for a thicker 510 nm layer, for which χ −1 (T) formed a single straight line above T<sup>N</sup> at the same experimental conditions.[29](#page-12-12) Also the slope of this line yields the value of the effective magnetic moment meff = 5.4(1)µ<sup>B</sup> per f.u., which is very close to that found previously, meff = 5.6µ<sup>B</sup> per f.u.[29](#page-12-12) This correspondence indicates that the high temperature part of χ −1 (T) is determined predominantly by AFM excitations in the paramagnetic matrix of CuMnSb.
The abscissa of the second straight line, which approximates the experimental data between T<sup>N</sup> and about 200 K (marked as the dashed orange line in Fig. [4\)](#page-4-2), yields a more positive value of the Curie-Weiss temperature, T ′ CW = −10(10) K. This clear positive shift of TCW indicates the existence of a ferromagnetic contribution to the overall antiferromagnetic phase of the material, and that these FM excitations gain in importance below about 200 K. Interestingly, a somewhat stronger effect, characterized by a change of sign of TCW to T ′ CW = +60(10) K, was noted in 40 nm CuMnSb layer grown on InAs.[34](#page-12-17) In accordance with the findings of structural characterization we propose that the by far stronger AFM component originates from the dominant α phase, whereas the FM one is brought about by β–CuMnSb polymorph.
<span id="page-5-1"></span>TABLE I. Experimental N´eel temperature TN, effective Curie-Weiss magnetic moment of Mn ions meff (Mn), and Curie-Weiss temperature TCW of α–CuMnSb. Measured orientation of the AFM axis is also given (n.e. = not established). Refs. [42](#page-12-24) and [41](#page-12-25) report the saturation Mn moment.
Turning now to the magnetic characteristics established here for α–CuMnSb we note that they are close to those reported previously, as shown in Tab. [I.](#page-5-1) The published data exhibit a certain distribution, which may indicate that other factors, such as a weak crystalline disorder, may be at work. In particular, either additional Mn interstitial ions or CuMn-MnCu antisite pairs are likely to form.[35](#page-12-18) The presence of such defects was suggested to stabilize the experimentally observed AFM {111}-oriented phase of α–CuMnSb.[35](#page-12-18) Finally, we do not observe a canted AFM order at low temperatures[41](#page-12-25) in any of our samples.
#### <span id="page-5-0"></span>III. THEORY
## A. Theoretical Methods
Calculations are performed within the density functional theory[46,](#page-13-2)[47](#page-13-3) in the generalized gradient approximation of the exchange-correlation potential proposed by Perdew, Burke and Ernzerhof.[48](#page-13-4) To improve description of 3d electrons, the Hubbard-type +U correction on Mn is added.[49–](#page-13-5)[51](#page-13-6) The parameter U(Mn) = 1 eV reproduces the known formation energy of the intermetallic CuMn alloy and gives a reasonable value of the Mn cohesive energy. We use the pseudopotential method implemented in the Quantum ESPRESSO code,[52](#page-13-7) with the valence atomic configuration 4s <sup>1</sup>.<sup>5</sup>p <sup>0</sup>3d 9.5 for Cu,
3s 2p <sup>6</sup>4s 2p <sup>0</sup>3d 5 for Mn and 5s 2p 3 for Sb ions. The planewaves kinetic energy cutoffs of 50 Ry for wave functions and 250 Ry for charge density are employed. Finally, geometry relaxations are performed with a 0.05 GPa convergence criterion for pressure. In defected crystals ionic positions are optimized until the forces acting on ions become smaller than 0.02 eV/˚A.
The properties of defected α–CuMnSb are examined using cubic 2a×2a×2a supercells with 96 atoms (i.e., 32 f.u.), while magnetic order of ideal crystals are checked using the smallest possible supercells. Here a is the equilibrium lattice parameter. The k-space summations are performed with a 6 × 6 × 6 k-point grid for the largest supercell, and correspondingly denser grids are used for smaller cells.
Magnetic interactions and magnetic order depend on several factors, such as the exchange spin splitting of the d(TM) shells, charge states of TM ions, concentration of free carriers and their spin polarization, and the density of states (DOS) at the Fermi energy EF. These factors are interrelated, and are calculated self-consistently within ab initio approach.
Considering first the localized magnetic moments we note that spin polarization of Co, Ni, and Cu ions in XMnZ compounds practically vanishes, while that of the d(Mn) shell is substantial.[16,](#page-11-14)[17](#page-12-0)[,31](#page-12-14) The robustness of the Mn magnetic moment results from the large, 3 – 5 eV, spin splitting of the 3d(Mn) states. In fact, in XMnZ the d(Mn) spin up channel is occupied, while most of the spin down d(Mn) states lay above the Fermi level. Here, one can observe that spin polarization of the d(TM) electrons in free atoms depends on the difference in the number of spin up and spin down electrons, which is the highest in the case of Mn. Consequently, the Mn spin polarization persists in XMnZ. On the other hand, spin splitting of d electrons of Co and Ni atoms is smaller, and thus it vanishes in XMnSb hosts, see the analysis for TM dopants in ZnO.[53](#page-13-8)
In CuMnSb, the magnetic sublattice consists of Mn ions, which are second neighbors distant by 4.3 ˚A. Therefore, the direct exchange coupling between two Mn ions, given by overlaps of their d(Mn) orbitals, is negligibly small. The remaining indirect exchange coupling is the sum of two contributions, and the exchange constant Jindirect = Jsr + JRKKY . [16](#page-11-14)[,17](#page-12-0)[,54](#page-13-9) The first term Jsr has a short-range AFM character, and it is inversely proportional to the energy distance between the unoccupied d(Mn) states and EF. The second coupling channel is of RKKY type mediated by free carriers. This channel depends on the detailed electronic structure in the vicinity of EF, and JRKKY is proportional to DOS(EF). In particular, CoMnSb and NiMnSb half-metals are FM, while CuMnP and CuMnAs insulators are AFM. As we show here, CuMnSb is the border case.
#### <span id="page-5-2"></span>B. Crystal and magnetic properties of α–CuMnSb
A rhombohedral primitive cell of α–CuMnSb contains one formula unit. This structure consist in four interpenetrating fcc sublattices, one of them being empty. The consecutive (001) MnSb planes are followed by the "halfempty" Cu planes, in which the planar atomic density is twice lower. The cubic unit cell is presented in Fig. [2](#page-3-0) (a). Local coordination of Mn ions can be relevant from the point of view of magnetic interactions. With this respect we notice that the magnetic coordination of an Mn ion consists in 12 equidistant Mn atoms at a/<sup>√</sup> 2. More-
We consider four magnetic phases of α–CuMnSb. The corresponding supercells are shown in Fig. [5.](#page-6-0) Antiferromagnetic order with parallel Mn spins in the (001) planes, AFM001, is calculated using the cubic a×a×a cell with 4 f.u. (12 atoms), and shown in Fig. [5](#page-6-0) (a). The AFM order with a period doubled in the [001] direction with parallel Mn spins in each (001) plane, denoted as AFM002, is shown in Fig. [5](#page-6-0) (b). The corresponding a×a×2a cell contains 8 f.u., and is one of the possible supercells in which this phase can be realized. In the AFM111 phase, the Mn spins are parallel in each (111) plane, but the consecutive (111) planes are AFM, as shown in Fig. [5](#page-6-0) (c), and the corresponding rhombohedral unit cell a √ 2 × a √ 2 × a √ 2 contains 8 primitive cells with 24 atoms. Finally, the FM phase requires a primitive cell a/<sup>√</sup> 2×a/<sup>√</sup> 2×a/<sup>√</sup> 2 with 1 f.u., presented in Fig. [5](#page-6-0) (d).
<span id="page-6-1"></span>TABLE II. The calculated lattice parameter a, the saturation Mn magnetic moment, msat, and the energy of the given magnetic order relative to α–CuMnSb in the AFM001 ground state, ∆Etot. All energies are per one formula unit. Our measured TEM values are also given.
higher in energy. The least stable is the FM order, higher in energy than AFM001 by about 20 meV per f.u. The equilibrium lattice parameters a ≈ 6.1 ˚A are practically independent of the magnetic order, and close to the experimental value 6.088 ˚A.[42](#page-12-24) Some phases are characterized by a small distortion of the cubic symmetry caused by different bond lengths between ferromagnetically and antiferromagnetically oriented Mn ions. Differences in the lattice parameters between various magnetic phases are below 0.01 ˚A, and are not reported in the Table. Similar results for the AFM001 order were obtained in Ref. [35,](#page-12-18) while in Refs [16](#page-11-14) and [31](#page-12-14) the AFM order is more stable than FM by 50 and 90 meV per Mn, respectively.
The last property reported in Tab. [II](#page-6-1) is the saturation magnetic moment of Mn, which also is similar in all phases, and equal to about 4.6µB. This value corresponds to the Curie-Weiss moment of 5.5(1)µB, and compares favorably with the experimental values given in Tab. [I.](#page-5-1)
The obtained results allow estimating the relative roles of the short- and long-range contributions to the magnetic coupling. To this end, we assume the hamiltonian in the form Hex = −J/2 P i,j ⃗si⃗s<sup>j</sup> , where the short range interaction is limited to the Mn NNs neighbors, and the long-range term is neglected. The spin value, s<sup>i</sup> ≈ 2.3, is one half of the calculated magnetic moment of Mn.
The exchange constant J is positive (negative) for the FM (AFM) coupling, and is obtained by comparing energies of various magnetic orders. In the AFM001 phase, each Mn ion has 4 ferromagnetically oriented Mn NNs in the (001) plane and 8 antiferromagnetically oriented Mn NNs in the two adjacent planes. For the remaining magnetic phases, the energies calculated relative to the ground state E<sup>0</sup> ≡ EAFM001 depend on the magnetic order as shown in Tab. [II.](#page-6-1) These results give the coupling constant in the range −0.6 ≥ Jsr ≥ −0.2 meV. This spread is quite large and cannot be explained by (negligible) changes in atomic distances in cells with different magnetic ordering. Therefore, we conclude that the Heisenberg nearest neighbor model does not describe magnetic properties of bulk phases. Indeed, such a model is not appropriate for metallic or semimetallic systems such as α–CuMnSb, where the long-range RKKY coupling is present.
An opposite conclusion comes from the analysis of single spin excitations from the AFM001 ground state. We use a 2a×2a×2a supercell to calculate the energy differences ∆E for the following cases, in which we change (i) spin of one Mn ion, 1Mn ↑→ 1Mn ↓, called a single spin-flip, (ii) 2Mn↑→ 2Mn↓ for spins of two nearest Mn ions belonging to one layer and (iii) 2Mn ↑→ 2Mn ↓ for two distant Mn ions. In these processes the long-range coupling is not important, and indeed the calculated exchange constant consistently is Jsr ≈ −0.4 meV.
#### <span id="page-7-0"></span>C. Crystal and magnetic properties of β–CuMnSb
We now consider two possible structures of the secondary phase proposed based on the experimental results. They are characterized by doubling the periodicity in the [001] direction. The unit cell of β–CuMnSb, shown in Fig. [2,](#page-3-0) is tetragonally deformed relative to that of α–CuMnSb, with the corresponding lattice parameters a = 5.88 ˚A and c = 6.275 ˚A. They differ by about 3 per cent from our calculated cubic a(α– CuMnSb) = 6.105 ˚A. The two interlayer spacings between the consecutive MnSb planes in the [001] direction in the unit cell, shown in Fig. [2](#page-3-0) (b), are quite different, namely dinter<sup>1</sup> = 2.80 ˚A (no Cu), and dinter<sup>2</sup> = 3.48 ˚A (with Cu). Turing to the magnetic order of β–CuMnSb, we find that the FM phase constitutes the ground state with msat = 4.6µ<sup>B</sup> and is lower than the AFM phase by 11 meV per f.u., as indicated in Tab. [II.](#page-6-1) Thus, the
The experimental[27](#page-12-10) lattice parameters of β–CuMnSb reasonably agree with our values, i.e., the calculated a = 6.28 ˚A and c/a = 1.87 are about 2% larger than those measured for the compressed crystal at the critical pressure of 7 GPa. On the other hand, the calculations of Ref. [27](#page-12-10) predict that the magnetic order of the β phase is AFM, in striking contrast with our results. Also their calculated msat(Mn) = 3.8µ<sup>B</sup> is substantially smaller than our 4.6µB. The origin of these discrepancies is not clear, but it may be due to the different exchange-correlation functionals used, and/or to application of the +U(Mn) correction in our calculations (which can affect the results.[31](#page-12-14))
The calculated total energy of the FM β–CuMnSb relative to the AFM α–CuMnSb is higher by 102 meV per f.u. This energy difference is not large, being comparable to the growth temperature, which implies that the β–CuMnSb polymorph can indeed form during epitaxy. We also stress that stoichiometry of the α and β phases is the same, which facilitates formation of β–CuMnSb. Finally, the observed β–CuMnSb inclusions are coherent, i.e., lattice matched, with the host structure. This agrees with the fact that the calculated excess elastic energy of matching the lattice parameters of the β phase to the host α phase is very low and ranges from 3 meV per f.u. (when the tetragonal a parameter constrained to the cubic a = 6.105 ˚A) to 20 meV per f.u. (the tetragonal c parameter constrained to the cubic a).
The second considered possibility, Cu3Mn2Sb<sup>2</sup> shown in Fig. [2](#page-3-0) (c), is higher in energy by 0.37 eV per f.u. in the Cu–rich conditions than the ideal CuMnSb, i.e., by 0.27 eV per f.u. than β–CuMnSb, its stoichiometry is markedly different, and thus we can eliminate this structure from considerations.
# D. Energy band structures of α–CuMnSb and β–CuMnSb
Figure [7](#page-8-1) (a) shows the energy bands and DOS of the AFM001 α–CuMnSb. We see that this phase has a metallic character, however DOS at the Fermi level is low. The states close to E<sup>F</sup> are built from s, p and d states of all ions with similar weights. The low DOS(EF) makes CuMnSb almost semimetallic with a low electrical conductivity. Compatible with the small DOS(EF) is the high resistivity measured in Ref. [41](#page-12-25) and [55.](#page-13-10)
Since the system is antiferromagnetically ordered, the total DOSs of spin-up and spin-down states are the same. In Fig. [7](#page-8-1) only contributions of the 3d(Mn) and 3d(Cu) orbitals are presented to reveal magnetic properties. We see that the exchange spin splitting of the d(Mn) shell is large, about 5 eV. The closely spaced levels contributing to the DOS maxima centered at 4 eV below the Fermi energy are composed mainly of the d states of both Cu and Mn. Spin-up and spin-down 3d(Cu) orbitals are almost
completely occupied, and thus Cu ions are non-magnetic. In turn, the majority spin states of the 3d(Mn) orbitals are completely occupied, while the minority spin states at 1 eV above the Fermi energy are partially filled thanks to a small overlap with spin up states. As a result, a single Mn ion is in between the d <sup>5</sup> and d 6 configuration, with the saturation magnetic moment of 4.6µ<sup>B</sup> consistent with Tab. [II.](#page-6-1) Our results for α–CuMnSb are close to those of Ref. [31.](#page-12-14) A similar electronic configuration takes place in CuMnAs, where the spin-down Mn states are partially filled.[56](#page-13-11)
The overall band structure of the FM β–CuMnSb displayed in Fig. [7](#page-8-1) (b) is close to that of α–CuMnSb, which is particularly clear when comparing partial DOS of both phases. In particular, msat(Mn) is about 4.5µ<sup>B</sup> in both phases, and energies of both d(Mn)- and d(Cu)-related bands are largely independent of the actual crystal structure. This similarity can be due to the fact that the MnSb (001) planes play a dominant role, and the exact locations of the Cu ions are less important.
On the other hand, the calculated DOS(EF) for the α phase is 0.35 states per spin and f.u., while for the β phase we find 1.26 states per spin and f.u., which is 3.6 times higher. As a consequence, α–CuMnSb is semimetallic, and the AFM order is dominant, while β phase is more metallic in character, which in turn favors the RKKY-type coupling and the FM order. This feature can explain the different magnetic phases of the α and β polymorphs.
Analysis of the calculated electronic structure of Heusler and half-Heusler CuMnZ led Sasioglu et al.[17](#page-12-0) to the conclusion that when the spin polarization of conduction electrons is large, and the d(Mn) spin down states are far above EF, then the RKKY coupling is dominant, and one should expect the FM order, otherwise the short range AFM coupling is dominant. Our results do not confirm this conclusion, and indicate that the important
## <span id="page-8-0"></span>E. Point native defects in α–CuMnSb
where E(CuMnSb) and E(CuMnSb : D) are the total energies of a supercell without and with a defect, and n<sup>i</sup> = +1(−1) corresponds to the removal (addition) of one ith atom. µis are the variable chemical potentials of atoms in the solid, which in general are different from the chemical potentials µi(bulk) of the standard state of elements, i.e., Cu, Mn and Sb bulk. Details of calculations of chemical potentials are given in Appendix [A.](#page-10-0)
The point native defects considered here are vacancies VX, interstitials X<sup>i</sup> , and antisites X<sup>Y</sup> (where X and Y are Cu, Mn, or Sb) for all three sublattices. As it was mentioned above, the Cu sublattice is "half- empty" compared to the MnSb sublattice. Consequently, we consider here formation of interstitials at the empty sites of the Cu sublattice only, and neglect other possibilities, expected to have higher formation energies Eform. Thus, the set of defects considered here only partially overlaps with that of Ref. [35.](#page-12-18) Of particular interest to the present study are defects involving Mn ions, since they can influence magnetic properties of α–CuMnSb .[35](#page-12-18) This is why we consider them more extensively, after briefly analyzing the non-magnetic defects. The calculated formation energies are summarized in Tab. [III.](#page-9-0) Because of the magnetic coupling, formation energies of the Mn-related defects depend on the spin direction relative to the spins of the host Mn neighbors. We consider possible spin configurations shown in Fig. [8](#page-9-1) (b).
<span id="page-9-0"></span>TABLE III. Formation energies (in eV) of isolated point defects in the Mn-rich conditions. In parentheses are Mn-related values corrected for ∆H<sup>f</sup> (MnSb) = 0.48 eV, which correspond to the Mn-poor case.
where k<sup>B</sup> is the Boltzmann constant and N<sup>0</sup> is the density of the relevant lattice sites. Details of the calculations of Eform are provided in Supporting Information. To put the calculated formation energies into a proper context, we note that if the growth temperatrure Tgrowth = 2500C and Eform = 0.1 eV, then exp(−Eform/kBTgrowth) = 0.1, which corresponds to a high 10 atomic per cent concentration of this defect on the considered sublattice. On the other hand, if Eform = 1 eV, then exp(−Eform/kBTgrowth) = 9 × 10<sup>−</sup><sup>11</sup>, which implies a negligible defect concentration.
Sb sublattice. The prohibitively high values of Eform demonstrate that VSb and Sb<sup>i</sup> should not form. Similarly, formation energies of SbCu, SbMn, CuSb and MnSb antisites exceed 1 eV, and those defects are not expected to be present at high concentrations. Consequently, the Sb sublattice is thermodynamically stable, robust, and constitutes a defect-free back-bone of CuMnSb.
(ii) Formation energy of Cu interstitials at the Cu sublattice, Eform(Cui) = 1 eV, is relatively high, and their concentrations are negligible. Additionally, the high formation energy of Cu<sup>i</sup> interstitials is consistent with the sparse character of the Cu sublattice in α–CuMnSb.
(iii) Formation of Mn<sup>i</sup> interstitials at the Cu sublattice is characterized by Eform = 0.7-1.4 eV, depending on the spin direction and conditions of growth, and therefore they are not expected to be present at high concentrations, especially in the Mn-poor conditions.
In brief, low formation energies are found for three defects, namely the VCu and VMn vacancies and the MnCu antisite, particularly at the Mn-rich growth conditions. This indicates that a Cu deficit on the Cu sublattice is possible, affecting stoichiometry. Significantly, MnCu antisites make the Cu sublattice magnetic, and also they can participate in the magnetic coupling between the adjacent MnSb (001) planes, thus influencing magnetic properties, as it will be discussed in more detail below. In contrast, SbCu antisites are present in negligible concentrations. Our results are in a reasonable agreement with those of Ref. [35,](#page-12-18) especially given their neglect of spin effects and a somewhat different theoretical approach. Interestingly, formation energies of native defects in CuMnAs calculated in Ref. [56](#page-13-11) are close to the present results in spite of the different anion.
## F. Defect-induced magnetic coupling
There are two Mn-related point defects, Mn<sup>i</sup> and MnCu, both situated on the Cu sublattice. When present at high concentrations, they affect magnetism of α– CuMnSb. Their coupling with host Mn ions is different than the Mn-Mn coupling between the host Mn because of the different local coordination. Energetics of both defects is complex and rich, since the total energy of the system (and thus formation energies) depends on their spin orientations relative to the neighborhood. At both substitutional and interstitial sites in the Cu layer, a Mn ion has 4 Mn nearest neighbors arranged in a tetrahedral configuration, 2 in the upper and 2 in the lower MnSb layer. The Mni–MnMn distance is shorter than that of
MnMn–MnMn, and equal to (<sup>√</sup> 3/4)a.
The possible local spin configurations are reduced to small clusters of 5 Mn ions, shown in Fig. [8.](#page-9-1) The Mn spin-up and spin-down (001) MnSb layers are denoted by in pink and blue, respectively, reflecting the calculated (001) AFM magnetic ground state. The central MnCu (or Mni) ion of such a cluster provides an additional channel of magnetic coupling between two adjacent MnSb layers. The corresponding formation energies are given in Fig. [8.](#page-9-1)
As it was pointed out, in ideal α–CuMnSb, the Mn ions are second neighbors only, separated either by Sb (i.e., the Mn-Sb-Mn "bridge" in the MnSb(001) plane), or by Cu (forming a Mn-Cu-Mn "bridge" linking 3 consecutive (001) planes.) Thus, the short range magnetic coupling in ideal α–CuMnSb is successfully modelled in Sec. [III B](#page-5-2) by the interaction between two Mn second neighbors, situated either in the same MnSb layer, or in two adjacent ones. In contrast, the 4 host Mn ions in the cluster are the first neighbors of a Mn<sup>i</sup> or a MnCu defect. Thus, one can expect that this coupling is stronger than the intrinsic one in the ideal host, and indeed, the differences in energy between various configurations in Fig. [8](#page-9-1) are about 100 meV, which is too high to be explained by the estimated Jsr = 0.4 meV.
As it follows from Fig. [8,](#page-9-1) 5-atom clusters are magnetically frustrated. In particular, the lowest energy case denoted as 4AFM favors the local FM orientation of spins in two adjacent (001) planes, which is opposite to the global host magnetic order. Our results do not confirm the conclusion of Ref. [56](#page-13-11) who find that the 3AFM configuration has the lowest energy, and thus it promotes the global AFM111 order. Instead, we rather expect that Mn-related point defects induce disorder of the host AFM phase, possibly leading to formation of a spin glass.[57](#page-13-12)
#### IV. SUMMARY
CuMnSb films were epitaxially grown on GaSb substrates. Magnetic measurements reveal the presence of two magnetic subsystems. The dominant magnetic order is AFM with the N´eel temperature of 62 K, which is the same as in bulk CuMnSb. It co-exists with a FM phase, characterized by the Curie temperature of about 100 K.
These findings go in hand with transmission electron microscopy and selective area diffraction measurements, which demonstrate coexistence of two structural polymorphs of the same stoichiometry. The dominant one is the cubic half-Heusler α–CuMnSb, which is the equilibrium structure of bulk samples. The second component is a tetragonal β–CuMnSb polymorph, which forms 10-100 nm long elongated inclusions.
(i) The β–CuMnSb phase is metastable, and its total energy is higher by 0.1 eV per f.u. only than that of the equilibrium α–CuMnSb. Lattice parameters of the β phase differ from those of α–CuMnSb by about 4 per cent. This lattice misfit between the two structures does not prevent the pseudomorphic coexistence of both phases, since the calculated misfit strain energy is below 20 meV per f.u.
(ii) In agreement with experiment, α–CuMnSb is AFM, and the FM order is 19 meV per f.u. higher in energy. In contrast, the magnetic ground state of β– CuMnSb is FM, which is more stable than AFM by 11 meV per f.u. This indicates that indeed the β–CuMnSb inclusions are responsible for the FM signal.
(iii) The different magnetic orders of the α and β phases originate in their somewhat different band structures. In particular, critical for magnetic order is the DOS at the Fermi level, which is about 4 times higher in β–CuMnSb than in the α phase. This shows that the β phase is more metallic in character, which in turn favors the FM order driven by the Ruderman-Kittel-Kasuya-Yoshida interaction.
(iv) Our calculations predict the saturated magnetic moment of Mn msat = 4.6µ<sup>B</sup> and 4.5µ<sup>B</sup> for the α and the β phase, respectively. This corresponds to the effective moment of 5.6µB, in good agreement with the measured 5.5µB.
(v) The calculated formation energies of point native defects indicate that the most probable are the MnCu antisites with low formation energies of 0–0.2 eV. However, their presence is expected to disorder the host magnetic AFM phase rather than to induce a transition to the FM configuration.
(vi) Regarding the properties of the CuMnX series we see that their structural stability is relatively weak, as they crystallize in a variety of structures. In particular, unlike the bulk orthorhombic CuMnAs, epitaxial films of CuMnAs are tetragonal, but both structures are AFM. In the case of CuMnSb, polymorphism comprises also the equilibrium magnetic structure, AFM in the bulk specimens, and FM in epitaxial films.
#### ACKNOWLEDGMENTS
LS, CG, JK and LWM thank M. Zipf for technical assistance. Our work was funded by the Deutsche Forschungsgemeinschaft (DFG,German Research Foundation) No. 397861849, by the Free State of Bavaria (Institute for Topological Insulators) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC2147 ct.qmat (Project-Id 390858490).
#### <span id="page-10-0"></span>Appendix A:
The highest possible value of µ<sup>i</sup> is µi(bulk), which implies that the studied system is in equilibrium with the given bulk source of atoms and δµ<sup>i</sup> = 0, otherwise δµ<sup>i</sup> < 0.
Chemical potentials of the components in the standard state are given by the total energies per atom of elemental solids. The calculated cohesive energies Ecoh of the face centered cubic Cu, the face centered cubic Mn with the AFM magnetic order, and the triclinic Sb are, respectively, 3.40 (3.49), 2.65 (2.92) and 2.68 (2.75) eV/atom. They compare reasonably well with the experimental values given in parentheses.[58](#page-13-13)
Chemical potentials of the involved atomic species depend on possible formation of compounds. The ranges of variations of chemical potentials are determined by conditions of equilibrium between various phases, i.e., Cu2Sb, MnSb and CuMnSb. Thermodynamic equilibrium requires that
$$\begin{aligned} \delta\mu(\text{Cu}) + 2\delta\mu(\text{Sb}) &= \Delta H\_f(\text{Cu}\_2\text{Sb}), \\ \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{MnSb}), \\ \delta\mu(\text{Cu}) + \delta\mu(\text{Mn}) + \delta\mu(\text{Sb}) &= \Delta H\_f(\text{CuMnSb}), \end{aligned} \quad \text{(A2)}$$
The calculated values ∆H<sup>f</sup> (Cu2Sb) = −0.03 eV per f.u., ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u., and ∆H<sup>f</sup> (CuMnSb) = −0.42 eV per f.u. The very low ∆H<sup>f</sup> (Cu2Sb) is somewhat unexpected, since Cu2Sb is a stable compound which crystallizes in the tetragonal phase.[43](#page-12-26) Next, our result ∆H<sup>f</sup> (MnSb) = −0.48 eV per f.u. agrees well with both the previous value -0.52 eV per f.u. calculated in Ref. [59,](#page-13-14) and the experimental - 0.52 eV per f.u.[60](#page-13-15) Assuming that the accuracy of the calculated values is 0.03 eV per f.u., the set of Equation [A2](#page-11-15) is consistent if we assume ∆H<sup>f</sup> (Cu2Sb) = 0, and ∆H<sup>f</sup> (MnSb) = ∆H<sup>f</sup> (CuMnSb) = −0.45 eV per f.u. This in turn implies that δµ(Cu) = δµ(Sb) = 0, and δµ(Mn) = −0.45 eV. Consequently, the allowed window of the Mn chemical potential is
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| |
*Figure SI 8: Zero magnetic-field THz spectra for Co4Ta2-xNbxO<sup>9</sup> at various x values (x=0, 1, 1.7, 2). Offset is provided in the plot for clarity.*
|
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
### **2. Results and Discussions**
The susceptibility versus temperature data shows a Neel's temperature (TN) of 20.5 K and a complex magnetic transition at 10 K which corroborates well with the previous reports [8,15,16] [Figure 2(a) and Inset Figure 2(a)]. THz response in three different magnetic phases [Figure 2(b)], namely, 20.5 K in paramagnetic region, 13 K in AFM region, and 6 K in complex magnetic region displays distinct
features. The strength of periodic THz oscillation in higher time scale (64-74 ps) shows abrupt increase at the onset of these regions. The time scale of this periodicity is approximately 2 ps in AFM state. This feature is absent above TN.
The normalized THz peak amplitude defined as the ratio of THz electric field peak position with and without the sample, ()(,) ()(,) , displays a sudden drop of ~12 % at the T<sup>N</sup> [Figure 2(c)] depicting a sensitivity of THz electric field to the spin-order at the magnetic transition. This feature combined with a large magnetic field dependence of normalized THz electric-field peak at 6 K [Inset Figure 2(c)] are unambiguous evidence of THz ME effect in this system. Also, The THz data yields a real refractive index of ~ 4 [Inset Figure 2(d)], which agrees well with the literature. [8] The real dielectric constant [at *ω* = 0.71 THz] increases with decreasing temperature and exhibits anomalies at both the magnetic transitions at 20.5 and 10 K [Figure 2(d)], which is consistent with the behavior of magnetization data [Inset Figure 2(a)].
In Co4Ta2O9, the magnetic symmetry lowers from trigonal in the paramagnetic state to monoclinic symmetry in the AFM state. Due to a large in-plane anisotropy, spins lie in the basal plane with an in-plane canting angle of 14° between Co(I) and Co(II) ions. [7,15] Figure 3(a) depicts the temperaturedependent THz absorption spectra of Co4Ta2O<sup>9</sup> in the frequency range 0.1-2.1 THz. As is evident, a large number of resonance absorption peaks, expectedly spin wave excitations/magnons, manifest in two different regimes of the spectra. Below TN, THz absorption spectra reveals three excitations, namely, *s4*, *s5*, and *s6* (broad mode) at 0.42, 0.54, and 1.2-1.9 THz, respectively. Below 10 K, additional excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* emerge sharply at 0.17, 0.24, 0.32, 1.44, 1.57, 1.62 THz, respectively. It may be seen that these sharp excitations (*s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* ) are superimposed on *s6* mode. These additional modes in THz spectra are in accordance with the distinct wiggles in the THz electric field tail (64 to 74 ps) at 13 and 6 K corresponding to these resonances [Figure 2(b)]. Accounting all these sharp and broad modes, it may be noted that the zero-field ground state of Co4Ta2O<sup>9</sup> at 2.5 K exhibits **nine excitations** in a narrow frequency range of 0.1-2.2 THz which is significantly larger than three zero-field excitations in Co4Nb2O9. [17] This rare manifestation of closely spaced multitude magnetic excitations in the THz frequency is potentially relevant for fundamental and applied pursuits in the field of antiferromagnetic magnonics algebra. [32-33]
Now we shed light on the origin and detailed scrutiny of thus observed magnetic modes. Starting with broad mode *s6*, we observe that it continues to grow beyond magnetic ordering [Figure 3(b)]. In the paramagnetic region, the red shift in this peak position and a larger full-width half-maximum (FWHM) [Figure 3(d)] with increasing temperature are its attributes that point towards the pure phonon mode. This was confirmed in the paramagnetic state, [Figure 3(c)] where the applied field does not affect the structure and strength of this mode. In contrast, it shows profound field-induced changes in the magnetic ordered region below T<sup>N</sup> which points towards coupling of the lattice and spin waves, consequently, giving rise to magnon-phonon excitation. This is further evidenced by the deviation of FWHM from the cubic anharmonicity of phonon-linewidth [Figure 3(d)] (in accordance with phonon-phonon anharmonic model) defined as[18]
where, ω<sup>0</sup> and Г<sup>0</sup> are the mode frequency and linewidth at absolute zero temperature, respectively. This demonstration of low-lying phonon mode and its entanglement with spins via magnetic field is an important lead to unravel its ME character in a later section.
Now we turn our attention to multiple gapped excitations *s4* and *s5* which we assign to pure spinexcitation / magnon modes, for the following reasons. As the magnetic symmetry lowers, below TN, the gapped modes emerge with their origin expected in strong in-plane single-ion anisotropy. To verify this, we collected the THz spectra of Mn4Ta2O9, which is isostructural equivalent of Co4Ta2O9. Unlike Co4Ta2O9, Mn2+ spins lie along the trigonal axis in the AFM state. [19,20] Its THz spectra clearly shows the absence of '*s4* and *s5*' type gapped modes at 10 K [Figure SI 4; Supporting Information], elucidating that the origin of gapped mode to be associated with the basal in-plane single-ion anisotropy of Co4Ta2O9. Normalized force constant as a function of temperature unveils the softening of s4 mode as temperature is lowered [Inset Figure 3(a)].
The magnon and phonon lifetime is an important factor in contemplating various THz magnonics based devices. In the present case, this was calculated using energy-time uncertainty principle. [21] For the phonon excitation, its linewidth decreases with decreasing temperature below T<sup>N</sup> owing to reduced strength of thermal fluctuation, phonon-phonon scattering, and anharmonic effect [Figure 3(d)]. Phonon lifetime [Figure SI 5(a)] in magnetic ordered phase (1 ± 0.09 ps) is smaller than that in paramagnetic phase (1.83 ± 0.07 ps). This is because at T<sup>N</sup> the linewidth begins to deviate from the pure phonon vibration as this phonon couples with magnons and hence suffers additional scattering mechanism. For the gapped spin-excitation, the strength of relevant mode should strengthen as the temperature is lowered. Exact trend can be observed in Figure SI 5(b), where the spin-gapped mode (*s4*) lifetime increases as temperature is lowered implying a long coherent length in the low temperature regime with a lifetime of 17.21 ± 2.99 ps at 2.5 K.
Using the THz gapped mode, *s4*, we tried to estimate the magnetic exchange interaction and magnetic anisotropy for Co4Ta2O9. The gapped mode originates from single ion anisotropy, = 4√, where D, J, S are the single-ion anisotropy constant, nearest neighbor interaction, and spin moments, respectively. [22] We assume that the nearest neighbor interaction in isostructural Co4Nb2O9 and Co4Ta2O9 are same (JCo4Nb2O9 = -0.7 meV and DCo4Nb2O9 = 1.8 meV). [23] From THz experiments, (Egapped)Co4Nb2O9 = 3.15 meV [Supporting Information] and, (Egapped)Co4Ta2O9 = 1.72 meV. Using the above relation, the single-ion anisotropy constant (DCo4Ta2O9) was calculated to be 0.53 meV, which turns out to be less than the absolute value of nearest neighbor exchange interaction JCo4Ta2O9 = 0.7 meV. However, it is inadmissible for the following reasons: i) Co4B2O9 (B=Nb, Ta) possesses large in-plane anisotropy such that even large value of external magnetic field along c direction cannot flop the spin from basal plane, which implies that D>J [6,23,24] and, ii) as per Goodenough-Kanamori-Anderson (GKA) rules, the super exchange interaction J is proportional to t<sup>2</sup> /U, where t is effective orbital hopping and U is the Hubbard repulsion. [25,26] The first-principle studies[15] suggest that UCo4Nb2O9 < UCo4Ta2O9 and Co are more localized in Co4Ta2O9, which implies a small spatial extent of the electron wavefunction and a reduced overlap between adjacent atomic orbital; hence, JCo4Ta2O9 < JCo4Nb2O9. Therefore, our assumption in similarity of nearest neighbor interaction does not hold suggesting that these systems behave differently. It is required that DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9.
$$H = H\_c + H\_{p,b,pb} + \Sigma\_{Co(l)} D \left( S\_{l\text{z}}^{l} \right)^2 + \Sigma\_{Co(l\text{I})} D \left( S\_{l\text{z}}^{\text{II}} \right)^2 + \Sigma\_{\text{cf,j}>} D\_{l\text{j}}. \left( \text{S}\_{l} \times \text{S}\_{\text{j}} \right) \tag{2}$$
where H<sup>c</sup> is the Heisenberg term for the nearest and next nearest neighbor along c; Hp,b,pb are the Heisenberg terms for the planar, buckled, and planar-buckled networks. Third and fourth term represent single-ion in plane anisotropy where I and II denote two inequivalent sites of cobalt [Co(I) and Co(II) sites] and Dij represent the DM interaction.
Here, the magnetic exchange interaction, single-ion anisotropy strength and high-resolution observations of magnons at Г point by THz spectroscopy underpins the magnetic structure and the magnonic dynamics. To get insights of the Brillouin zone, beyond the Г point, spin-wave calculations were performed using the above spin Hamiltonian in SPINW. [27] In-plane magnetic structure was considered as revealed by neutron diffraction experiments [28] and using the THz Г point data, the magnetic exchange interactions were computed. The average powder spin-wave spectra for Co4Nb2O<sup>9</sup> [Figure 4(a)] shows gapped and gapless excitations which matches accurately with the Г point of THz data. The magnetic exchange interactions (JCo4Nb2O9=-0.6 meV and DCo4Nb2O9=1.6 meV) too agree well with those depicted by the inelastic neutron experimental results. [28] Using magnetic structure of temperature above 10 K for Co4Ta2O<sup>9</sup> [29] , the powder averaged spin-wave calculations yielded gapped excitations and magnetic exchange interactions JCo4Ta2O9=-0.4 meV and DCo4Ta2O9=1.1 meV. These are at lower energy and weaker, respectively, as compared to those of Co4Nb2O<sup>9</sup> and in perfect agreement with the condition DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9 [Figure 4(b)].
In contrast to above-mentioned low-energy spin-excitations, the higher energy modes (> 5 meV) obtained from spin-wave calculations and THz experimental data do not agree for either of Co4Ta2O<sup>9</sup> and Co4Nb2O9. This is because the spin Hamiltonian accounts only for spin-excitations while the phonon contribution as well as spin-lattice coupling terms are not incorporated. This deviation is further verification of broad mode s<sup>6</sup> being [Figure 3(a)] a spin-phonon coupled mode. As Nb is systematically replaced by Ta in Co4Ta2O9 [Figure 4(c)], the gapped mode (*s4*) gradually shifts to higher energies owing to gradual enhancement of the magnetic exchange interactions (J and D) [Figure 4(d)]. Thus, magnetic exchange interactions play a prominent role in driving the spinexcitations.
Now, to shed light on the origin of excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* (Figure 3a), it is imperative to invoke comparison of some relevant properties of Co4Ta2O<sup>9</sup> from Co4Nb2O9. As noted in previous section, weaker exchange interactions in Co4Ta2O<sup>9</sup> compared to that in Co4Nb2O<sup>9</sup> render it a softer magnet. In the latter, there has been no indication of structural transition even at 5 K, [6,7,16,24] though the possibility of local lattice distortion and magnetostriction was never ruled out. [15] In the case of Co4Ta2O9, however, the structural transitions, larger local lattice distortions and magnetostriction becomes more promising owing to its sensitivity to change in magnetic structure due to weaker magnetic interactions. This deviation of Co4Ta2O<sup>9</sup> from Co4Nb2O9, below 10 K, is the source of nonlinear ME response[30] and complex magnetic state[29,30] (in χ-T curve) in the former. However, its magnetic structure is reported only down to a minimum temperature of 15 K, [29] which is higher than the complexity-rich magnetism regime of below 10K. It is this low temperature regime, wherein the complex magnetic state, magnetostriction and local lattice distortion in Co4Ta2O<sup>9</sup> create entangled magnetic moments and lattice vibrations, which consequently give rise to six spin excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* in the THz spectra [Figure 3(a, b)]. No such excitations have been observed in Co4Nb2O9. The Co4Ta2O9, thus, hosts a ground for unique correlation between magnetic exchange interactions, local lattice distortion, and magnetostriction phenomena.
As Co4Ta2O<sup>9</sup> is a magnetic-field induced ME system, it is imperative to understand the magneticfield control of THz spin-wave excitation and the ME character. Magnetic field dependence of THz spectra is plotted in Figure 5 (a). Spin-excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* and *s6<sup>c</sup>* get suppressed with increasing magnetic field which reflects the expected magnetically malleable structure of Co4Ta2O9. At 2T, all these excitations annihilate while *s4* and *s5* shift to higher frequencies. Derived from the gapped mode (*s4*), the normalized force constant (kH/k0T; k<sup>H</sup> is the force constant at magnetic-field H and k0T is force constant at zero magnetic-field) indicates the hardening of the magnetic coupling between neighboring spins as a function of increasing magnetic-field [Inset Figure 5(a)]. As magnetic field exceeds 3 T, mode *s7* appears in the detectable range of our THz spectra. This excitation, identified as goldstone (/gapless) mode, appears in the microwave region due to spontaneous symmetry-breaking at T<sup>N</sup> and it shifts linearly towards higher THz frequency with increasing field [Figure 5(a) inset]. This gapless mode is shown in the spin-excitation simulations as well as in the THz spectra. The behaviour of peak frequency of this gapless excitation yields Landé g-factor g=3.09 for Co4Ta2O<sup>9</sup> and g=2.68 for Co4Nb2O<sup>9</sup> [Figure SI 3 and 7, Supporting Information]. Clearly the value of Landé g-factor suggests unquenched orbital moments both in Co4Ta2O<sup>9</sup> and Nb counterpart.
The mechanism of the field-induced polarization in this series has been of great interest to understand the induced ME character. Knowledge of spin-phonon mode and its magnetic-field dependence from THz spectroscopy can provide valuable insights into this process. At 6 K, the peak strength of spinphonon mode of Co4Ta2O<sup>9</sup> increases with an increase in magnetic field [Figure 5 (a, b)] which is associated with the field induced electric polarization. As lattice distortion, magnetostriction, and spin-phonon coupling are highly inter-related in these materials, the induced electric polarization can be explained as follows. At zero magnetic-field, below TN, the presence of spin-phonon coupling suggests the entanglement of spin and lattice. However, the Co ions hold two inequivalent sites Co(I) and Co(II) which are in centrosymmetric positions with respect to trigonal axis, hence, lacks any net polarization. However, on the application of magnetic-field the strength of spin-phonon coupling increases [Figure 5 (b)]. This expectedly displaces the magnetic ions from their centrosymmetric positions, resulting in the manifestation of magnetically induced polarization. This scenario of fieldinduced displacement of Co-ion is depicted in Figure 5 (c) As the mass of Ta is larger than Nb (ions to which Co-ions are bonded), the effective displacement in case of Co4Ta2O<sup>9</sup> is less than that in Co4Nb2O9. This also explains why magnetic field induced polarization in Co4Nb2O<sup>9</sup> is more as compared to Co4Ta2O9. The THz characteristic features of the magnetic resonances too possess this mass effect where with increasing concentration of Nb the resonances are shifting to higher THz frequency [Figure SI 8]. To surmise, this entire mechanism based on modulation of magnetic exchange interactions provides a pathway to control the energy of spin-gapped modes, spin-phonon coupled mode, and phonon mode whereas the effective lattice displacement of cobalt ions is responsible for magnetic-field induced polarization.
From the applied pursuit, the wave nature of magnons (spin-waves) offers a pathway to encode information in amplitude, phase, or the combination of both [Figure 6(a)] which is at core of nonBoolean algebra driven spin-wave computation.[31-33] The spin excitations in THz regime offer two novel characteristics, namely, the THz magnons propagate with ultra-low dissipation as it does not involve flow of electric charge, and with ultrafast speeds, both of which are much desired attributes for futuristic technologies. The existence of multiple magnon modes, as demonstrated in this work, is a pre-requisite for efficient data transfer spin-wave logic operations. In another facet, in the direction of spin-wave computation the multitude of spin waves in Co4Ta2O<sup>9</sup> present itself as a potential candidate for multifrequency channeling in a narrow bandwidth of 0.1 – 2.5 THz. Such multi-channels allow for simultaneous transmission of multiple signals at different frequencies, increasing the overall data capacity. A schematic serving as a proof-of-concept for terahertzmagnonics-electronics multifrequency channeling is shown in Figure 6(b). Here, the frequency of THz radiation drives the resonant condition corresponding to that magnon which carries the information and provides the output as electronic signal via a spin wave to charge converter. Experimental realization of this concept requires systems having multiple magnons or other hybrid modes in THz regime. In this work, the magnetoelectric systems with non-collinear magnetic order prone to strong spin-lattice interactions provide appropriate platform for THz magnonics.
### **3. Conclusions**
A myriad of low-energy excitations in Co4Ta2O9 probed using magneto-THz spectroscopy evidence a remarkable host magnetoelectric system with a rare multitude of ten excitations comprising of magnon, phonon, and hybridized magnon-phonon modes. The THz probes and non-collinear magnetism further combine to unravel a THz magnetoelectric effect; a novel functionality not known to manifest at such high frequencies so far. The origin of magnon in a strong basal-plane anisotropy emphasized the structural, magnetic and electronic controls to all excitation modes. These experimental data are supported by theoretical spin-wave computations along with quantifiable strength of magnetic exchange interactions. Furthermore, magnetic-field induced enhanced spinphonon coupling corroborates the proposition of magnetic-ion lattice displacement being the dominant factor for the ME behavior in this family of systems. Our results emphasize that the powderaveraged THz absorption spectrum acquired on a polycrystalline sample is not a limitation, rather an advantage over single crystals to facilitate faster screening of magnetic materials for spin-wave excitation mode, thus, expediting the search for potential materials for THz magnonic applications.
# **Supporting Information**
Supporting Information is available from the Wiley Online Library or from the author.
### **Acknowledgements**
D.S.R. thanks the Science and Engineering Research Board (SERB), Department of Science and Technology, New Delhi, for financial support under research Project No. CRG/2020/002338. K.S. thanks SERB for financial support under research Project No. CRG/2021/007075. B.S.M thanks Prime Minister Research Fellowship (PMRF; 0401968) funding agency, Ministry of Education, New Delhi, and Dr. Sunil Nair for providing Mn4Ta2O<sup>9</sup> sample.
### **Conflict of Interest**
Authors declare no conflict of interest.
# **Data Availability Statement**
The data that support the findings of this study are available from the corresponding author upon reasonable request.
## **References**
- [19] N. Narayanan, A. Senyshyn, D. Mikhailova, T. Faske, T. Lu, Z. Liu, B. Weise, H. Ehrenberg, R. A. Mole, W. D. Hutchison, H. Fuess, G. J. McIntyre, Y. Liu, D. Yu, *Phys. Rev. B* **2018**, *94*, 134438.
# **SUPPORTING INFORMATION**
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
# **S1: Experimental Details:**
# **A) Sample Preparation and Magnetic Characterization:**
Polycrystalline sample of Co4Ta2O<sup>9</sup> was prepared from solid state reaction route. The stoichiometric amount of Co3O<sup>4</sup> and Ta2O<sup>5</sup> (99.99% purities) powders were ground and calcined in air at 1000°C for 10 h. Sample was reground, pressed, and sintered at 1100°C for 10 h. The outcome was phasepure disc-shaped sample (diameter ~ 7 mm & thickness ~ 600 µm). Phase purity was confirmed at room temperature by PANalytical ''Empyrean' powder X-ray diffractometer (PXRD) with Cu K<sup>α</sup> radiation (1.54 Å). [Figure SI 1] Rietveld refinement analysis provided a good fit with χ<sup>2</sup> =1.8 and lattice parameters a=b=0.5173 nm, and c=1.415 nm.
Magnetic measurements were performed using a superconducting quantum interference device [SQUID-VSM (Quantum Design)] in the temperature range of 2-80 K.
# **B) Magneto-THz time-domain Spectroscopy:**
Fiber-coupled TeraK15 THz time-domain transmission spectrometer equipped with top-loading closed-cycle He cryostat and Oxford Spectramag split-coil magnet (magnetic field up to 7T) was implemented in Faraday geometry [Figure SI 2] to measure the absorption coefficient in the spectral range 0.1-2 THz with a spectral resolution of 0.0146 THz. The path of the THz radiation is purged with nitrogen gas ten minutes before and during measurement to circumvent the water absorption peaks. THz measurement generates raw data in the form of time-dependent picosecond pulses of electric fields, which are then transformed into complex-valued frequency functions via Fast Fourier transformation. Absorption Coefficient was calculated by,
where d is the thickness of the sample, Ssample and Sreference are the spectral amplitude with and without the sample, respectively. THz study on the polycrystalline sample provides an averaged-THz spectrum permitting us to observe excitations over all the spatial directions.
# **S2: Magneto-THz time-domain Experiment:**
# **A) Co4Ta2O<sup>9</sup>**
In Co4Ta2O9, there is one magnetic-field induced excitation termed as gapless/Goldstone mode in the absorption spectrum. At 0 T it is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 3.09 was obtained which suggests the presence of unquenched orbital moments in it.
## **Goldstone Mode:**
### **B) Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup>**
Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup> are isostructural members of A4B2O<sup>9</sup> family. In the magnetic-ordered state spins of Mn2+ in Mn4Ta2O<sup>9</sup> have uniaxial anisotropy spins along the c-direction whereas Co2+ in Co4Ta2O<sup>9</sup> possess strong basal plane anisotropy [Figure SI 3 inset (a)]. Figure SI3 shows THz spectra with and without the sample at 10 K which emphasizes the presence (/absence) of the gapped modes in Co4Ta2O9 (/Mn4Ta2O9).
![*Figure SI 4: THz spectra with (Mn4Ta2O9 and Co4Ta2O9) and without the samples at 10 K. Note: [Mn4Ta2O9 sample is taken from Ref (1)]*](path)
### **C) Spin gapped and Phonon lifetime in Co4Ta2O9:**
# **D) Co4Nb2O<sup>9</sup>**
# **Goldstone Mode:**
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
| |
Figure SI 4: THz spectra with (Mn4Ta2O9 and Co4Ta2O9) and without the samples at 10 K. Note: [Mn4Ta2O9 sample is taken from Ref (1)]
|
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
### **C) Spin gapped and Phonon lifetime in Co4Ta2O9:**
# **D) Co4Nb2O<sup>9</sup>**
# **Goldstone Mode:**
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
| |
**Figure 1:** Schematic depiction of experimental set up of magneto-THz time-domain spectroscopy and the observation of nine temperature-dependent magnons in the polycrystalline sample of Co4Ta2O9.
|
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
### **2. Results and Discussions**
The susceptibility versus temperature data shows a Neel's temperature (TN) of 20.5 K and a complex magnetic transition at 10 K which corroborates well with the previous reports [8,15,16] [Figure 2(a) and Inset Figure 2(a)]. THz response in three different magnetic phases [Figure 2(b)], namely, 20.5 K in paramagnetic region, 13 K in AFM region, and 6 K in complex magnetic region displays distinct
features. The strength of periodic THz oscillation in higher time scale (64-74 ps) shows abrupt increase at the onset of these regions. The time scale of this periodicity is approximately 2 ps in AFM state. This feature is absent above TN.
The normalized THz peak amplitude defined as the ratio of THz electric field peak position with and without the sample, ()(,) ()(,) , displays a sudden drop of ~12 % at the T<sup>N</sup> [Figure 2(c)] depicting a sensitivity of THz electric field to the spin-order at the magnetic transition. This feature combined with a large magnetic field dependence of normalized THz electric-field peak at 6 K [Inset Figure 2(c)] are unambiguous evidence of THz ME effect in this system. Also, The THz data yields a real refractive index of ~ 4 [Inset Figure 2(d)], which agrees well with the literature. [8] The real dielectric constant [at *ω* = 0.71 THz] increases with decreasing temperature and exhibits anomalies at both the magnetic transitions at 20.5 and 10 K [Figure 2(d)], which is consistent with the behavior of magnetization data [Inset Figure 2(a)].
In Co4Ta2O9, the magnetic symmetry lowers from trigonal in the paramagnetic state to monoclinic symmetry in the AFM state. Due to a large in-plane anisotropy, spins lie in the basal plane with an in-plane canting angle of 14° between Co(I) and Co(II) ions. [7,15] Figure 3(a) depicts the temperaturedependent THz absorption spectra of Co4Ta2O<sup>9</sup> in the frequency range 0.1-2.1 THz. As is evident, a large number of resonance absorption peaks, expectedly spin wave excitations/magnons, manifest in two different regimes of the spectra. Below TN, THz absorption spectra reveals three excitations, namely, *s4*, *s5*, and *s6* (broad mode) at 0.42, 0.54, and 1.2-1.9 THz, respectively. Below 10 K, additional excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* emerge sharply at 0.17, 0.24, 0.32, 1.44, 1.57, 1.62 THz, respectively. It may be seen that these sharp excitations (*s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* ) are superimposed on *s6* mode. These additional modes in THz spectra are in accordance with the distinct wiggles in the THz electric field tail (64 to 74 ps) at 13 and 6 K corresponding to these resonances [Figure 2(b)]. Accounting all these sharp and broad modes, it may be noted that the zero-field ground state of Co4Ta2O<sup>9</sup> at 2.5 K exhibits **nine excitations** in a narrow frequency range of 0.1-2.2 THz which is significantly larger than three zero-field excitations in Co4Nb2O9. [17] This rare manifestation of closely spaced multitude magnetic excitations in the THz frequency is potentially relevant for fundamental and applied pursuits in the field of antiferromagnetic magnonics algebra. [32-33]
Now we shed light on the origin and detailed scrutiny of thus observed magnetic modes. Starting with broad mode *s6*, we observe that it continues to grow beyond magnetic ordering [Figure 3(b)]. In the paramagnetic region, the red shift in this peak position and a larger full-width half-maximum (FWHM) [Figure 3(d)] with increasing temperature are its attributes that point towards the pure phonon mode. This was confirmed in the paramagnetic state, [Figure 3(c)] where the applied field does not affect the structure and strength of this mode. In contrast, it shows profound field-induced changes in the magnetic ordered region below T<sup>N</sup> which points towards coupling of the lattice and spin waves, consequently, giving rise to magnon-phonon excitation. This is further evidenced by the deviation of FWHM from the cubic anharmonicity of phonon-linewidth [Figure 3(d)] (in accordance with phonon-phonon anharmonic model) defined as[18]
where, ω<sup>0</sup> and Г<sup>0</sup> are the mode frequency and linewidth at absolute zero temperature, respectively. This demonstration of low-lying phonon mode and its entanglement with spins via magnetic field is an important lead to unravel its ME character in a later section.
Now we turn our attention to multiple gapped excitations *s4* and *s5* which we assign to pure spinexcitation / magnon modes, for the following reasons. As the magnetic symmetry lowers, below TN, the gapped modes emerge with their origin expected in strong in-plane single-ion anisotropy. To verify this, we collected the THz spectra of Mn4Ta2O9, which is isostructural equivalent of Co4Ta2O9. Unlike Co4Ta2O9, Mn2+ spins lie along the trigonal axis in the AFM state. [19,20] Its THz spectra clearly shows the absence of '*s4* and *s5*' type gapped modes at 10 K [Figure SI 4; Supporting Information], elucidating that the origin of gapped mode to be associated with the basal in-plane single-ion anisotropy of Co4Ta2O9. Normalized force constant as a function of temperature unveils the softening of s4 mode as temperature is lowered [Inset Figure 3(a)].
The magnon and phonon lifetime is an important factor in contemplating various THz magnonics based devices. In the present case, this was calculated using energy-time uncertainty principle. [21] For the phonon excitation, its linewidth decreases with decreasing temperature below T<sup>N</sup> owing to reduced strength of thermal fluctuation, phonon-phonon scattering, and anharmonic effect [Figure 3(d)]. Phonon lifetime [Figure SI 5(a)] in magnetic ordered phase (1 ± 0.09 ps) is smaller than that in paramagnetic phase (1.83 ± 0.07 ps). This is because at T<sup>N</sup> the linewidth begins to deviate from the pure phonon vibration as this phonon couples with magnons and hence suffers additional scattering mechanism. For the gapped spin-excitation, the strength of relevant mode should strengthen as the temperature is lowered. Exact trend can be observed in Figure SI 5(b), where the spin-gapped mode (*s4*) lifetime increases as temperature is lowered implying a long coherent length in the low temperature regime with a lifetime of 17.21 ± 2.99 ps at 2.5 K.
Using the THz gapped mode, *s4*, we tried to estimate the magnetic exchange interaction and magnetic anisotropy for Co4Ta2O9. The gapped mode originates from single ion anisotropy, = 4√, where D, J, S are the single-ion anisotropy constant, nearest neighbor interaction, and spin moments, respectively. [22] We assume that the nearest neighbor interaction in isostructural Co4Nb2O9 and Co4Ta2O9 are same (JCo4Nb2O9 = -0.7 meV and DCo4Nb2O9 = 1.8 meV). [23] From THz experiments, (Egapped)Co4Nb2O9 = 3.15 meV [Supporting Information] and, (Egapped)Co4Ta2O9 = 1.72 meV. Using the above relation, the single-ion anisotropy constant (DCo4Ta2O9) was calculated to be 0.53 meV, which turns out to be less than the absolute value of nearest neighbor exchange interaction JCo4Ta2O9 = 0.7 meV. However, it is inadmissible for the following reasons: i) Co4B2O9 (B=Nb, Ta) possesses large in-plane anisotropy such that even large value of external magnetic field along c direction cannot flop the spin from basal plane, which implies that D>J [6,23,24] and, ii) as per Goodenough-Kanamori-Anderson (GKA) rules, the super exchange interaction J is proportional to t<sup>2</sup> /U, where t is effective orbital hopping and U is the Hubbard repulsion. [25,26] The first-principle studies[15] suggest that UCo4Nb2O9 < UCo4Ta2O9 and Co are more localized in Co4Ta2O9, which implies a small spatial extent of the electron wavefunction and a reduced overlap between adjacent atomic orbital; hence, JCo4Ta2O9 < JCo4Nb2O9. Therefore, our assumption in similarity of nearest neighbor interaction does not hold suggesting that these systems behave differently. It is required that DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9.
$$H = H\_c + H\_{p,b,pb} + \Sigma\_{Co(l)} D \left( S\_{l\text{z}}^{l} \right)^2 + \Sigma\_{Co(l\text{I})} D \left( S\_{l\text{z}}^{\text{II}} \right)^2 + \Sigma\_{\text{cf,j}>} D\_{l\text{j}}. \left( \text{S}\_{l} \times \text{S}\_{\text{j}} \right) \tag{2}$$
where H<sup>c</sup> is the Heisenberg term for the nearest and next nearest neighbor along c; Hp,b,pb are the Heisenberg terms for the planar, buckled, and planar-buckled networks. Third and fourth term represent single-ion in plane anisotropy where I and II denote two inequivalent sites of cobalt [Co(I) and Co(II) sites] and Dij represent the DM interaction.
Here, the magnetic exchange interaction, single-ion anisotropy strength and high-resolution observations of magnons at Г point by THz spectroscopy underpins the magnetic structure and the magnonic dynamics. To get insights of the Brillouin zone, beyond the Г point, spin-wave calculations were performed using the above spin Hamiltonian in SPINW. [27] In-plane magnetic structure was considered as revealed by neutron diffraction experiments [28] and using the THz Г point data, the magnetic exchange interactions were computed. The average powder spin-wave spectra for Co4Nb2O<sup>9</sup> [Figure 4(a)] shows gapped and gapless excitations which matches accurately with the Г point of THz data. The magnetic exchange interactions (JCo4Nb2O9=-0.6 meV and DCo4Nb2O9=1.6 meV) too agree well with those depicted by the inelastic neutron experimental results. [28] Using magnetic structure of temperature above 10 K for Co4Ta2O<sup>9</sup> [29] , the powder averaged spin-wave calculations yielded gapped excitations and magnetic exchange interactions JCo4Ta2O9=-0.4 meV and DCo4Ta2O9=1.1 meV. These are at lower energy and weaker, respectively, as compared to those of Co4Nb2O<sup>9</sup> and in perfect agreement with the condition DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9 [Figure 4(b)].
In contrast to above-mentioned low-energy spin-excitations, the higher energy modes (> 5 meV) obtained from spin-wave calculations and THz experimental data do not agree for either of Co4Ta2O<sup>9</sup> and Co4Nb2O9. This is because the spin Hamiltonian accounts only for spin-excitations while the phonon contribution as well as spin-lattice coupling terms are not incorporated. This deviation is further verification of broad mode s<sup>6</sup> being [Figure 3(a)] a spin-phonon coupled mode. As Nb is systematically replaced by Ta in Co4Ta2O9 [Figure 4(c)], the gapped mode (*s4*) gradually shifts to higher energies owing to gradual enhancement of the magnetic exchange interactions (J and D) [Figure 4(d)]. Thus, magnetic exchange interactions play a prominent role in driving the spinexcitations.
Now, to shed light on the origin of excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* (Figure 3a), it is imperative to invoke comparison of some relevant properties of Co4Ta2O<sup>9</sup> from Co4Nb2O9. As noted in previous section, weaker exchange interactions in Co4Ta2O<sup>9</sup> compared to that in Co4Nb2O<sup>9</sup> render it a softer magnet. In the latter, there has been no indication of structural transition even at 5 K, [6,7,16,24] though the possibility of local lattice distortion and magnetostriction was never ruled out. [15] In the case of Co4Ta2O9, however, the structural transitions, larger local lattice distortions and magnetostriction becomes more promising owing to its sensitivity to change in magnetic structure due to weaker magnetic interactions. This deviation of Co4Ta2O<sup>9</sup> from Co4Nb2O9, below 10 K, is the source of nonlinear ME response[30] and complex magnetic state[29,30] (in χ-T curve) in the former. However, its magnetic structure is reported only down to a minimum temperature of 15 K, [29] which is higher than the complexity-rich magnetism regime of below 10K. It is this low temperature regime, wherein the complex magnetic state, magnetostriction and local lattice distortion in Co4Ta2O<sup>9</sup> create entangled magnetic moments and lattice vibrations, which consequently give rise to six spin excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* in the THz spectra [Figure 3(a, b)]. No such excitations have been observed in Co4Nb2O9. The Co4Ta2O9, thus, hosts a ground for unique correlation between magnetic exchange interactions, local lattice distortion, and magnetostriction phenomena.
As Co4Ta2O<sup>9</sup> is a magnetic-field induced ME system, it is imperative to understand the magneticfield control of THz spin-wave excitation and the ME character. Magnetic field dependence of THz spectra is plotted in Figure 5 (a). Spin-excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* and *s6<sup>c</sup>* get suppressed with increasing magnetic field which reflects the expected magnetically malleable structure of Co4Ta2O9. At 2T, all these excitations annihilate while *s4* and *s5* shift to higher frequencies. Derived from the gapped mode (*s4*), the normalized force constant (kH/k0T; k<sup>H</sup> is the force constant at magnetic-field H and k0T is force constant at zero magnetic-field) indicates the hardening of the magnetic coupling between neighboring spins as a function of increasing magnetic-field [Inset Figure 5(a)]. As magnetic field exceeds 3 T, mode *s7* appears in the detectable range of our THz spectra. This excitation, identified as goldstone (/gapless) mode, appears in the microwave region due to spontaneous symmetry-breaking at T<sup>N</sup> and it shifts linearly towards higher THz frequency with increasing field [Figure 5(a) inset]. This gapless mode is shown in the spin-excitation simulations as well as in the THz spectra. The behaviour of peak frequency of this gapless excitation yields Landé g-factor g=3.09 for Co4Ta2O<sup>9</sup> and g=2.68 for Co4Nb2O<sup>9</sup> [Figure SI 3 and 7, Supporting Information]. Clearly the value of Landé g-factor suggests unquenched orbital moments both in Co4Ta2O<sup>9</sup> and Nb counterpart.
The mechanism of the field-induced polarization in this series has been of great interest to understand the induced ME character. Knowledge of spin-phonon mode and its magnetic-field dependence from THz spectroscopy can provide valuable insights into this process. At 6 K, the peak strength of spinphonon mode of Co4Ta2O<sup>9</sup> increases with an increase in magnetic field [Figure 5 (a, b)] which is associated with the field induced electric polarization. As lattice distortion, magnetostriction, and spin-phonon coupling are highly inter-related in these materials, the induced electric polarization can be explained as follows. At zero magnetic-field, below TN, the presence of spin-phonon coupling suggests the entanglement of spin and lattice. However, the Co ions hold two inequivalent sites Co(I) and Co(II) which are in centrosymmetric positions with respect to trigonal axis, hence, lacks any net polarization. However, on the application of magnetic-field the strength of spin-phonon coupling increases [Figure 5 (b)]. This expectedly displaces the magnetic ions from their centrosymmetric positions, resulting in the manifestation of magnetically induced polarization. This scenario of fieldinduced displacement of Co-ion is depicted in Figure 5 (c) As the mass of Ta is larger than Nb (ions to which Co-ions are bonded), the effective displacement in case of Co4Ta2O<sup>9</sup> is less than that in Co4Nb2O9. This also explains why magnetic field induced polarization in Co4Nb2O<sup>9</sup> is more as compared to Co4Ta2O9. The THz characteristic features of the magnetic resonances too possess this mass effect where with increasing concentration of Nb the resonances are shifting to higher THz frequency [Figure SI 8]. To surmise, this entire mechanism based on modulation of magnetic exchange interactions provides a pathway to control the energy of spin-gapped modes, spin-phonon coupled mode, and phonon mode whereas the effective lattice displacement of cobalt ions is responsible for magnetic-field induced polarization.
From the applied pursuit, the wave nature of magnons (spin-waves) offers a pathway to encode information in amplitude, phase, or the combination of both [Figure 6(a)] which is at core of nonBoolean algebra driven spin-wave computation.[31-33] The spin excitations in THz regime offer two novel characteristics, namely, the THz magnons propagate with ultra-low dissipation as it does not involve flow of electric charge, and with ultrafast speeds, both of which are much desired attributes for futuristic technologies. The existence of multiple magnon modes, as demonstrated in this work, is a pre-requisite for efficient data transfer spin-wave logic operations. In another facet, in the direction of spin-wave computation the multitude of spin waves in Co4Ta2O<sup>9</sup> present itself as a potential candidate for multifrequency channeling in a narrow bandwidth of 0.1 – 2.5 THz. Such multi-channels allow for simultaneous transmission of multiple signals at different frequencies, increasing the overall data capacity. A schematic serving as a proof-of-concept for terahertzmagnonics-electronics multifrequency channeling is shown in Figure 6(b). Here, the frequency of THz radiation drives the resonant condition corresponding to that magnon which carries the information and provides the output as electronic signal via a spin wave to charge converter. Experimental realization of this concept requires systems having multiple magnons or other hybrid modes in THz regime. In this work, the magnetoelectric systems with non-collinear magnetic order prone to strong spin-lattice interactions provide appropriate platform for THz magnonics.
### **3. Conclusions**
A myriad of low-energy excitations in Co4Ta2O9 probed using magneto-THz spectroscopy evidence a remarkable host magnetoelectric system with a rare multitude of ten excitations comprising of magnon, phonon, and hybridized magnon-phonon modes. The THz probes and non-collinear magnetism further combine to unravel a THz magnetoelectric effect; a novel functionality not known to manifest at such high frequencies so far. The origin of magnon in a strong basal-plane anisotropy emphasized the structural, magnetic and electronic controls to all excitation modes. These experimental data are supported by theoretical spin-wave computations along with quantifiable strength of magnetic exchange interactions. Furthermore, magnetic-field induced enhanced spinphonon coupling corroborates the proposition of magnetic-ion lattice displacement being the dominant factor for the ME behavior in this family of systems. Our results emphasize that the powderaveraged THz absorption spectrum acquired on a polycrystalline sample is not a limitation, rather an advantage over single crystals to facilitate faster screening of magnetic materials for spin-wave excitation mode, thus, expediting the search for potential materials for THz magnonic applications.
# **Supporting Information**
Supporting Information is available from the Wiley Online Library or from the author.
### **Acknowledgements**
D.S.R. thanks the Science and Engineering Research Board (SERB), Department of Science and Technology, New Delhi, for financial support under research Project No. CRG/2020/002338. K.S. thanks SERB for financial support under research Project No. CRG/2021/007075. B.S.M thanks Prime Minister Research Fellowship (PMRF; 0401968) funding agency, Ministry of Education, New Delhi, and Dr. Sunil Nair for providing Mn4Ta2O<sup>9</sup> sample.
### **Conflict of Interest**
Authors declare no conflict of interest.
# **Data Availability Statement**
The data that support the findings of this study are available from the corresponding author upon reasonable request.
## **References**
- [19] N. Narayanan, A. Senyshyn, D. Mikhailova, T. Faske, T. Lu, Z. Liu, B. Weise, H. Ehrenberg, R. A. Mole, W. D. Hutchison, H. Fuess, G. J. McIntyre, Y. Liu, D. Yu, *Phys. Rev. B* **2018**, *94*, 134438.
# **SUPPORTING INFORMATION**
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
# **S1: Experimental Details:**
# **A) Sample Preparation and Magnetic Characterization:**
Polycrystalline sample of Co4Ta2O<sup>9</sup> was prepared from solid state reaction route. The stoichiometric amount of Co3O<sup>4</sup> and Ta2O<sup>5</sup> (99.99% purities) powders were ground and calcined in air at 1000°C for 10 h. Sample was reground, pressed, and sintered at 1100°C for 10 h. The outcome was phasepure disc-shaped sample (diameter ~ 7 mm & thickness ~ 600 µm). Phase purity was confirmed at room temperature by PANalytical ''Empyrean' powder X-ray diffractometer (PXRD) with Cu K<sup>α</sup> radiation (1.54 Å). [Figure SI 1] Rietveld refinement analysis provided a good fit with χ<sup>2</sup> =1.8 and lattice parameters a=b=0.5173 nm, and c=1.415 nm.
Magnetic measurements were performed using a superconducting quantum interference device [SQUID-VSM (Quantum Design)] in the temperature range of 2-80 K.
# **B) Magneto-THz time-domain Spectroscopy:**
Fiber-coupled TeraK15 THz time-domain transmission spectrometer equipped with top-loading closed-cycle He cryostat and Oxford Spectramag split-coil magnet (magnetic field up to 7T) was implemented in Faraday geometry [Figure SI 2] to measure the absorption coefficient in the spectral range 0.1-2 THz with a spectral resolution of 0.0146 THz. The path of the THz radiation is purged with nitrogen gas ten minutes before and during measurement to circumvent the water absorption peaks. THz measurement generates raw data in the form of time-dependent picosecond pulses of electric fields, which are then transformed into complex-valued frequency functions via Fast Fourier transformation. Absorption Coefficient was calculated by,
where d is the thickness of the sample, Ssample and Sreference are the spectral amplitude with and without the sample, respectively. THz study on the polycrystalline sample provides an averaged-THz spectrum permitting us to observe excitations over all the spatial directions.
# **S2: Magneto-THz time-domain Experiment:**
# **A) Co4Ta2O<sup>9</sup>**
In Co4Ta2O9, there is one magnetic-field induced excitation termed as gapless/Goldstone mode in the absorption spectrum. At 0 T it is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 3.09 was obtained which suggests the presence of unquenched orbital moments in it.
## **Goldstone Mode:**
### **B) Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup>**
Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup> are isostructural members of A4B2O<sup>9</sup> family. In the magnetic-ordered state spins of Mn2+ in Mn4Ta2O<sup>9</sup> have uniaxial anisotropy spins along the c-direction whereas Co2+ in Co4Ta2O<sup>9</sup> possess strong basal plane anisotropy [Figure SI 3 inset (a)]. Figure SI3 shows THz spectra with and without the sample at 10 K which emphasizes the presence (/absence) of the gapped modes in Co4Ta2O9 (/Mn4Ta2O9).
![*Figure SI 4: THz spectra with (Mn4Ta2O9 and Co4Ta2O9) and without the samples at 10 K. Note: [Mn4Ta2O9 sample is taken from Ref (1)]*](path)
### **C) Spin gapped and Phonon lifetime in Co4Ta2O9:**
# **D) Co4Nb2O<sup>9</sup>**
# **Goldstone Mode:**
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
| |
Figure 6: a) Types of information encoding via spin-waves: Amplitude and Phase encoding. b) Proof-of-concept of terahertz-magnonic-electronics multifrequency channelling device.
|
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
### **2. Results and Discussions**
The susceptibility versus temperature data shows a Neel's temperature (TN) of 20.5 K and a complex magnetic transition at 10 K which corroborates well with the previous reports [8,15,16] [Figure 2(a) and Inset Figure 2(a)]. THz response in three different magnetic phases [Figure 2(b)], namely, 20.5 K in paramagnetic region, 13 K in AFM region, and 6 K in complex magnetic region displays distinct
features. The strength of periodic THz oscillation in higher time scale (64-74 ps) shows abrupt increase at the onset of these regions. The time scale of this periodicity is approximately 2 ps in AFM state. This feature is absent above TN.
The normalized THz peak amplitude defined as the ratio of THz electric field peak position with and without the sample, ()(,) ()(,) , displays a sudden drop of ~12 % at the T<sup>N</sup> [Figure 2(c)] depicting a sensitivity of THz electric field to the spin-order at the magnetic transition. This feature combined with a large magnetic field dependence of normalized THz electric-field peak at 6 K [Inset Figure 2(c)] are unambiguous evidence of THz ME effect in this system. Also, The THz data yields a real refractive index of ~ 4 [Inset Figure 2(d)], which agrees well with the literature. [8] The real dielectric constant [at *ω* = 0.71 THz] increases with decreasing temperature and exhibits anomalies at both the magnetic transitions at 20.5 and 10 K [Figure 2(d)], which is consistent with the behavior of magnetization data [Inset Figure 2(a)].
In Co4Ta2O9, the magnetic symmetry lowers from trigonal in the paramagnetic state to monoclinic symmetry in the AFM state. Due to a large in-plane anisotropy, spins lie in the basal plane with an in-plane canting angle of 14° between Co(I) and Co(II) ions. [7,15] Figure 3(a) depicts the temperaturedependent THz absorption spectra of Co4Ta2O<sup>9</sup> in the frequency range 0.1-2.1 THz. As is evident, a large number of resonance absorption peaks, expectedly spin wave excitations/magnons, manifest in two different regimes of the spectra. Below TN, THz absorption spectra reveals three excitations, namely, *s4*, *s5*, and *s6* (broad mode) at 0.42, 0.54, and 1.2-1.9 THz, respectively. Below 10 K, additional excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* emerge sharply at 0.17, 0.24, 0.32, 1.44, 1.57, 1.62 THz, respectively. It may be seen that these sharp excitations (*s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* ) are superimposed on *s6* mode. These additional modes in THz spectra are in accordance with the distinct wiggles in the THz electric field tail (64 to 74 ps) at 13 and 6 K corresponding to these resonances [Figure 2(b)]. Accounting all these sharp and broad modes, it may be noted that the zero-field ground state of Co4Ta2O<sup>9</sup> at 2.5 K exhibits **nine excitations** in a narrow frequency range of 0.1-2.2 THz which is significantly larger than three zero-field excitations in Co4Nb2O9. [17] This rare manifestation of closely spaced multitude magnetic excitations in the THz frequency is potentially relevant for fundamental and applied pursuits in the field of antiferromagnetic magnonics algebra. [32-33]
Now we shed light on the origin and detailed scrutiny of thus observed magnetic modes. Starting with broad mode *s6*, we observe that it continues to grow beyond magnetic ordering [Figure 3(b)]. In the paramagnetic region, the red shift in this peak position and a larger full-width half-maximum (FWHM) [Figure 3(d)] with increasing temperature are its attributes that point towards the pure phonon mode. This was confirmed in the paramagnetic state, [Figure 3(c)] where the applied field does not affect the structure and strength of this mode. In contrast, it shows profound field-induced changes in the magnetic ordered region below T<sup>N</sup> which points towards coupling of the lattice and spin waves, consequently, giving rise to magnon-phonon excitation. This is further evidenced by the deviation of FWHM from the cubic anharmonicity of phonon-linewidth [Figure 3(d)] (in accordance with phonon-phonon anharmonic model) defined as[18]
where, ω<sup>0</sup> and Г<sup>0</sup> are the mode frequency and linewidth at absolute zero temperature, respectively. This demonstration of low-lying phonon mode and its entanglement with spins via magnetic field is an important lead to unravel its ME character in a later section.
Now we turn our attention to multiple gapped excitations *s4* and *s5* which we assign to pure spinexcitation / magnon modes, for the following reasons. As the magnetic symmetry lowers, below TN, the gapped modes emerge with their origin expected in strong in-plane single-ion anisotropy. To verify this, we collected the THz spectra of Mn4Ta2O9, which is isostructural equivalent of Co4Ta2O9. Unlike Co4Ta2O9, Mn2+ spins lie along the trigonal axis in the AFM state. [19,20] Its THz spectra clearly shows the absence of '*s4* and *s5*' type gapped modes at 10 K [Figure SI 4; Supporting Information], elucidating that the origin of gapped mode to be associated with the basal in-plane single-ion anisotropy of Co4Ta2O9. Normalized force constant as a function of temperature unveils the softening of s4 mode as temperature is lowered [Inset Figure 3(a)].
The magnon and phonon lifetime is an important factor in contemplating various THz magnonics based devices. In the present case, this was calculated using energy-time uncertainty principle. [21] For the phonon excitation, its linewidth decreases with decreasing temperature below T<sup>N</sup> owing to reduced strength of thermal fluctuation, phonon-phonon scattering, and anharmonic effect [Figure 3(d)]. Phonon lifetime [Figure SI 5(a)] in magnetic ordered phase (1 ± 0.09 ps) is smaller than that in paramagnetic phase (1.83 ± 0.07 ps). This is because at T<sup>N</sup> the linewidth begins to deviate from the pure phonon vibration as this phonon couples with magnons and hence suffers additional scattering mechanism. For the gapped spin-excitation, the strength of relevant mode should strengthen as the temperature is lowered. Exact trend can be observed in Figure SI 5(b), where the spin-gapped mode (*s4*) lifetime increases as temperature is lowered implying a long coherent length in the low temperature regime with a lifetime of 17.21 ± 2.99 ps at 2.5 K.
Using the THz gapped mode, *s4*, we tried to estimate the magnetic exchange interaction and magnetic anisotropy for Co4Ta2O9. The gapped mode originates from single ion anisotropy, = 4√, where D, J, S are the single-ion anisotropy constant, nearest neighbor interaction, and spin moments, respectively. [22] We assume that the nearest neighbor interaction in isostructural Co4Nb2O9 and Co4Ta2O9 are same (JCo4Nb2O9 = -0.7 meV and DCo4Nb2O9 = 1.8 meV). [23] From THz experiments, (Egapped)Co4Nb2O9 = 3.15 meV [Supporting Information] and, (Egapped)Co4Ta2O9 = 1.72 meV. Using the above relation, the single-ion anisotropy constant (DCo4Ta2O9) was calculated to be 0.53 meV, which turns out to be less than the absolute value of nearest neighbor exchange interaction JCo4Ta2O9 = 0.7 meV. However, it is inadmissible for the following reasons: i) Co4B2O9 (B=Nb, Ta) possesses large in-plane anisotropy such that even large value of external magnetic field along c direction cannot flop the spin from basal plane, which implies that D>J [6,23,24] and, ii) as per Goodenough-Kanamori-Anderson (GKA) rules, the super exchange interaction J is proportional to t<sup>2</sup> /U, where t is effective orbital hopping and U is the Hubbard repulsion. [25,26] The first-principle studies[15] suggest that UCo4Nb2O9 < UCo4Ta2O9 and Co are more localized in Co4Ta2O9, which implies a small spatial extent of the electron wavefunction and a reduced overlap between adjacent atomic orbital; hence, JCo4Ta2O9 < JCo4Nb2O9. Therefore, our assumption in similarity of nearest neighbor interaction does not hold suggesting that these systems behave differently. It is required that DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9.
$$H = H\_c + H\_{p,b,pb} + \Sigma\_{Co(l)} D \left( S\_{l\text{z}}^{l} \right)^2 + \Sigma\_{Co(l\text{I})} D \left( S\_{l\text{z}}^{\text{II}} \right)^2 + \Sigma\_{\text{cf,j}>} D\_{l\text{j}}. \left( \text{S}\_{l} \times \text{S}\_{\text{j}} \right) \tag{2}$$
where H<sup>c</sup> is the Heisenberg term for the nearest and next nearest neighbor along c; Hp,b,pb are the Heisenberg terms for the planar, buckled, and planar-buckled networks. Third and fourth term represent single-ion in plane anisotropy where I and II denote two inequivalent sites of cobalt [Co(I) and Co(II) sites] and Dij represent the DM interaction.
Here, the magnetic exchange interaction, single-ion anisotropy strength and high-resolution observations of magnons at Г point by THz spectroscopy underpins the magnetic structure and the magnonic dynamics. To get insights of the Brillouin zone, beyond the Г point, spin-wave calculations were performed using the above spin Hamiltonian in SPINW. [27] In-plane magnetic structure was considered as revealed by neutron diffraction experiments [28] and using the THz Г point data, the magnetic exchange interactions were computed. The average powder spin-wave spectra for Co4Nb2O<sup>9</sup> [Figure 4(a)] shows gapped and gapless excitations which matches accurately with the Г point of THz data. The magnetic exchange interactions (JCo4Nb2O9=-0.6 meV and DCo4Nb2O9=1.6 meV) too agree well with those depicted by the inelastic neutron experimental results. [28] Using magnetic structure of temperature above 10 K for Co4Ta2O<sup>9</sup> [29] , the powder averaged spin-wave calculations yielded gapped excitations and magnetic exchange interactions JCo4Ta2O9=-0.4 meV and DCo4Ta2O9=1.1 meV. These are at lower energy and weaker, respectively, as compared to those of Co4Nb2O<sup>9</sup> and in perfect agreement with the condition DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9 [Figure 4(b)].
In contrast to above-mentioned low-energy spin-excitations, the higher energy modes (> 5 meV) obtained from spin-wave calculations and THz experimental data do not agree for either of Co4Ta2O<sup>9</sup> and Co4Nb2O9. This is because the spin Hamiltonian accounts only for spin-excitations while the phonon contribution as well as spin-lattice coupling terms are not incorporated. This deviation is further verification of broad mode s<sup>6</sup> being [Figure 3(a)] a spin-phonon coupled mode. As Nb is systematically replaced by Ta in Co4Ta2O9 [Figure 4(c)], the gapped mode (*s4*) gradually shifts to higher energies owing to gradual enhancement of the magnetic exchange interactions (J and D) [Figure 4(d)]. Thus, magnetic exchange interactions play a prominent role in driving the spinexcitations.
Now, to shed light on the origin of excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* (Figure 3a), it is imperative to invoke comparison of some relevant properties of Co4Ta2O<sup>9</sup> from Co4Nb2O9. As noted in previous section, weaker exchange interactions in Co4Ta2O<sup>9</sup> compared to that in Co4Nb2O<sup>9</sup> render it a softer magnet. In the latter, there has been no indication of structural transition even at 5 K, [6,7,16,24] though the possibility of local lattice distortion and magnetostriction was never ruled out. [15] In the case of Co4Ta2O9, however, the structural transitions, larger local lattice distortions and magnetostriction becomes more promising owing to its sensitivity to change in magnetic structure due to weaker magnetic interactions. This deviation of Co4Ta2O<sup>9</sup> from Co4Nb2O9, below 10 K, is the source of nonlinear ME response[30] and complex magnetic state[29,30] (in χ-T curve) in the former. However, its magnetic structure is reported only down to a minimum temperature of 15 K, [29] which is higher than the complexity-rich magnetism regime of below 10K. It is this low temperature regime, wherein the complex magnetic state, magnetostriction and local lattice distortion in Co4Ta2O<sup>9</sup> create entangled magnetic moments and lattice vibrations, which consequently give rise to six spin excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* in the THz spectra [Figure 3(a, b)]. No such excitations have been observed in Co4Nb2O9. The Co4Ta2O9, thus, hosts a ground for unique correlation between magnetic exchange interactions, local lattice distortion, and magnetostriction phenomena.
As Co4Ta2O<sup>9</sup> is a magnetic-field induced ME system, it is imperative to understand the magneticfield control of THz spin-wave excitation and the ME character. Magnetic field dependence of THz spectra is plotted in Figure 5 (a). Spin-excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* and *s6<sup>c</sup>* get suppressed with increasing magnetic field which reflects the expected magnetically malleable structure of Co4Ta2O9. At 2T, all these excitations annihilate while *s4* and *s5* shift to higher frequencies. Derived from the gapped mode (*s4*), the normalized force constant (kH/k0T; k<sup>H</sup> is the force constant at magnetic-field H and k0T is force constant at zero magnetic-field) indicates the hardening of the magnetic coupling between neighboring spins as a function of increasing magnetic-field [Inset Figure 5(a)]. As magnetic field exceeds 3 T, mode *s7* appears in the detectable range of our THz spectra. This excitation, identified as goldstone (/gapless) mode, appears in the microwave region due to spontaneous symmetry-breaking at T<sup>N</sup> and it shifts linearly towards higher THz frequency with increasing field [Figure 5(a) inset]. This gapless mode is shown in the spin-excitation simulations as well as in the THz spectra. The behaviour of peak frequency of this gapless excitation yields Landé g-factor g=3.09 for Co4Ta2O<sup>9</sup> and g=2.68 for Co4Nb2O<sup>9</sup> [Figure SI 3 and 7, Supporting Information]. Clearly the value of Landé g-factor suggests unquenched orbital moments both in Co4Ta2O<sup>9</sup> and Nb counterpart.
The mechanism of the field-induced polarization in this series has been of great interest to understand the induced ME character. Knowledge of spin-phonon mode and its magnetic-field dependence from THz spectroscopy can provide valuable insights into this process. At 6 K, the peak strength of spinphonon mode of Co4Ta2O<sup>9</sup> increases with an increase in magnetic field [Figure 5 (a, b)] which is associated with the field induced electric polarization. As lattice distortion, magnetostriction, and spin-phonon coupling are highly inter-related in these materials, the induced electric polarization can be explained as follows. At zero magnetic-field, below TN, the presence of spin-phonon coupling suggests the entanglement of spin and lattice. However, the Co ions hold two inequivalent sites Co(I) and Co(II) which are in centrosymmetric positions with respect to trigonal axis, hence, lacks any net polarization. However, on the application of magnetic-field the strength of spin-phonon coupling increases [Figure 5 (b)]. This expectedly displaces the magnetic ions from their centrosymmetric positions, resulting in the manifestation of magnetically induced polarization. This scenario of fieldinduced displacement of Co-ion is depicted in Figure 5 (c) As the mass of Ta is larger than Nb (ions to which Co-ions are bonded), the effective displacement in case of Co4Ta2O<sup>9</sup> is less than that in Co4Nb2O9. This also explains why magnetic field induced polarization in Co4Nb2O<sup>9</sup> is more as compared to Co4Ta2O9. The THz characteristic features of the magnetic resonances too possess this mass effect where with increasing concentration of Nb the resonances are shifting to higher THz frequency [Figure SI 8]. To surmise, this entire mechanism based on modulation of magnetic exchange interactions provides a pathway to control the energy of spin-gapped modes, spin-phonon coupled mode, and phonon mode whereas the effective lattice displacement of cobalt ions is responsible for magnetic-field induced polarization.
From the applied pursuit, the wave nature of magnons (spin-waves) offers a pathway to encode information in amplitude, phase, or the combination of both [Figure 6(a)] which is at core of nonBoolean algebra driven spin-wave computation.[31-33] The spin excitations in THz regime offer two novel characteristics, namely, the THz magnons propagate with ultra-low dissipation as it does not involve flow of electric charge, and with ultrafast speeds, both of which are much desired attributes for futuristic technologies. The existence of multiple magnon modes, as demonstrated in this work, is a pre-requisite for efficient data transfer spin-wave logic operations. In another facet, in the direction of spin-wave computation the multitude of spin waves in Co4Ta2O<sup>9</sup> present itself as a potential candidate for multifrequency channeling in a narrow bandwidth of 0.1 – 2.5 THz. Such multi-channels allow for simultaneous transmission of multiple signals at different frequencies, increasing the overall data capacity. A schematic serving as a proof-of-concept for terahertzmagnonics-electronics multifrequency channeling is shown in Figure 6(b). Here, the frequency of THz radiation drives the resonant condition corresponding to that magnon which carries the information and provides the output as electronic signal via a spin wave to charge converter. Experimental realization of this concept requires systems having multiple magnons or other hybrid modes in THz regime. In this work, the magnetoelectric systems with non-collinear magnetic order prone to strong spin-lattice interactions provide appropriate platform for THz magnonics.
### **3. Conclusions**
A myriad of low-energy excitations in Co4Ta2O9 probed using magneto-THz spectroscopy evidence a remarkable host magnetoelectric system with a rare multitude of ten excitations comprising of magnon, phonon, and hybridized magnon-phonon modes. The THz probes and non-collinear magnetism further combine to unravel a THz magnetoelectric effect; a novel functionality not known to manifest at such high frequencies so far. The origin of magnon in a strong basal-plane anisotropy emphasized the structural, magnetic and electronic controls to all excitation modes. These experimental data are supported by theoretical spin-wave computations along with quantifiable strength of magnetic exchange interactions. Furthermore, magnetic-field induced enhanced spinphonon coupling corroborates the proposition of magnetic-ion lattice displacement being the dominant factor for the ME behavior in this family of systems. Our results emphasize that the powderaveraged THz absorption spectrum acquired on a polycrystalline sample is not a limitation, rather an advantage over single crystals to facilitate faster screening of magnetic materials for spin-wave excitation mode, thus, expediting the search for potential materials for THz magnonic applications.
# **Supporting Information**
Supporting Information is available from the Wiley Online Library or from the author.
### **Acknowledgements**
D.S.R. thanks the Science and Engineering Research Board (SERB), Department of Science and Technology, New Delhi, for financial support under research Project No. CRG/2020/002338. K.S. thanks SERB for financial support under research Project No. CRG/2021/007075. B.S.M thanks Prime Minister Research Fellowship (PMRF; 0401968) funding agency, Ministry of Education, New Delhi, and Dr. Sunil Nair for providing Mn4Ta2O<sup>9</sup> sample.
### **Conflict of Interest**
Authors declare no conflict of interest.
# **Data Availability Statement**
The data that support the findings of this study are available from the corresponding author upon reasonable request.
## **References**
- [19] N. Narayanan, A. Senyshyn, D. Mikhailova, T. Faske, T. Lu, Z. Liu, B. Weise, H. Ehrenberg, R. A. Mole, W. D. Hutchison, H. Fuess, G. J. McIntyre, Y. Liu, D. Yu, *Phys. Rev. B* **2018**, *94*, 134438.
# **SUPPORTING INFORMATION**
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
# **S1: Experimental Details:**
# **A) Sample Preparation and Magnetic Characterization:**
Polycrystalline sample of Co4Ta2O<sup>9</sup> was prepared from solid state reaction route. The stoichiometric amount of Co3O<sup>4</sup> and Ta2O<sup>5</sup> (99.99% purities) powders were ground and calcined in air at 1000°C for 10 h. Sample was reground, pressed, and sintered at 1100°C for 10 h. The outcome was phasepure disc-shaped sample (diameter ~ 7 mm & thickness ~ 600 µm). Phase purity was confirmed at room temperature by PANalytical ''Empyrean' powder X-ray diffractometer (PXRD) with Cu K<sup>α</sup> radiation (1.54 Å). [Figure SI 1] Rietveld refinement analysis provided a good fit with χ<sup>2</sup> =1.8 and lattice parameters a=b=0.5173 nm, and c=1.415 nm.
Magnetic measurements were performed using a superconducting quantum interference device [SQUID-VSM (Quantum Design)] in the temperature range of 2-80 K.
# **B) Magneto-THz time-domain Spectroscopy:**
Fiber-coupled TeraK15 THz time-domain transmission spectrometer equipped with top-loading closed-cycle He cryostat and Oxford Spectramag split-coil magnet (magnetic field up to 7T) was implemented in Faraday geometry [Figure SI 2] to measure the absorption coefficient in the spectral range 0.1-2 THz with a spectral resolution of 0.0146 THz. The path of the THz radiation is purged with nitrogen gas ten minutes before and during measurement to circumvent the water absorption peaks. THz measurement generates raw data in the form of time-dependent picosecond pulses of electric fields, which are then transformed into complex-valued frequency functions via Fast Fourier transformation. Absorption Coefficient was calculated by,
where d is the thickness of the sample, Ssample and Sreference are the spectral amplitude with and without the sample, respectively. THz study on the polycrystalline sample provides an averaged-THz spectrum permitting us to observe excitations over all the spatial directions.
# **S2: Magneto-THz time-domain Experiment:**
# **A) Co4Ta2O<sup>9</sup>**
In Co4Ta2O9, there is one magnetic-field induced excitation termed as gapless/Goldstone mode in the absorption spectrum. At 0 T it is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 3.09 was obtained which suggests the presence of unquenched orbital moments in it.
## **Goldstone Mode:**
### **B) Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup>**
Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup> are isostructural members of A4B2O<sup>9</sup> family. In the magnetic-ordered state spins of Mn2+ in Mn4Ta2O<sup>9</sup> have uniaxial anisotropy spins along the c-direction whereas Co2+ in Co4Ta2O<sup>9</sup> possess strong basal plane anisotropy [Figure SI 3 inset (a)]. Figure SI3 shows THz spectra with and without the sample at 10 K which emphasizes the presence (/absence) of the gapped modes in Co4Ta2O9 (/Mn4Ta2O9).
![*Figure SI 4: THz spectra with (Mn4Ta2O9 and Co4Ta2O9) and without the samples at 10 K. Note: [Mn4Ta2O9 sample is taken from Ref (1)]*](path)
### **C) Spin gapped and Phonon lifetime in Co4Ta2O9:**
# **D) Co4Nb2O<sup>9</sup>**
# **Goldstone Mode:**
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
| |
Figure SI 2: Experimental set up of magneto-THz time-domain spectroscopy in Faraday geometry.
|
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
# **S2: Magneto-THz time-domain Experiment:**
# **A) Co4Ta2O<sup>9</sup>**
In Co4Ta2O9, there is one magnetic-field induced excitation termed as gapless/Goldstone mode in the absorption spectrum. At 0 T it is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 3.09 was obtained which suggests the presence of unquenched orbital moments in it.
## **Goldstone Mode:**
### **B) Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup>**
Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup> are isostructural members of A4B2O<sup>9</sup> family. In the magnetic-ordered state spins of Mn2+ in Mn4Ta2O<sup>9</sup> have uniaxial anisotropy spins along the c-direction whereas Co2+ in Co4Ta2O<sup>9</sup> possess strong basal plane anisotropy [Figure SI 3 inset (a)]. Figure SI3 shows THz spectra with and without the sample at 10 K which emphasizes the presence (/absence) of the gapped modes in Co4Ta2O9 (/Mn4Ta2O9).
![*Figure SI 4: THz spectra with (Mn4Ta2O9 and Co4Ta2O9) and without the samples at 10 K. Note: [Mn4Ta2O9 sample is taken from Ref (1)]*](path)
### **C) Spin gapped and Phonon lifetime in Co4Ta2O9:**
# **D) Co4Nb2O<sup>9</sup>**
# **Goldstone Mode:**
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
| |
**Figure 3:** a) Absorption coefficient versus THz frequency. Normalized force constant (kN=kT/k16K; where kT is the force constant at temperature T and k16 K is the force constant at 16 K) as a function of temperature is depicted in inset. b) Temperature dynamics of *s⁶* mode. c) Absorption coefficient versus THz frequency at 6, 13, 20.5, and 50 K with magnetic field 0 and 5 T. d) FWHM of *s⁶* mode as a function of temperature. Inset shows the variation in temperature range 2-30 K. For clarity offset is provided in a, b, and c.
|
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
### **2. Results and Discussions**
The susceptibility versus temperature data shows a Neel's temperature (TN) of 20.5 K and a complex magnetic transition at 10 K which corroborates well with the previous reports [8,15,16] [Figure 2(a) and Inset Figure 2(a)]. THz response in three different magnetic phases [Figure 2(b)], namely, 20.5 K in paramagnetic region, 13 K in AFM region, and 6 K in complex magnetic region displays distinct
features. The strength of periodic THz oscillation in higher time scale (64-74 ps) shows abrupt increase at the onset of these regions. The time scale of this periodicity is approximately 2 ps in AFM state. This feature is absent above TN.
The normalized THz peak amplitude defined as the ratio of THz electric field peak position with and without the sample, ()(,) ()(,) , displays a sudden drop of ~12 % at the T<sup>N</sup> [Figure 2(c)] depicting a sensitivity of THz electric field to the spin-order at the magnetic transition. This feature combined with a large magnetic field dependence of normalized THz electric-field peak at 6 K [Inset Figure 2(c)] are unambiguous evidence of THz ME effect in this system. Also, The THz data yields a real refractive index of ~ 4 [Inset Figure 2(d)], which agrees well with the literature. [8] The real dielectric constant [at *ω* = 0.71 THz] increases with decreasing temperature and exhibits anomalies at both the magnetic transitions at 20.5 and 10 K [Figure 2(d)], which is consistent with the behavior of magnetization data [Inset Figure 2(a)].
In Co4Ta2O9, the magnetic symmetry lowers from trigonal in the paramagnetic state to monoclinic symmetry in the AFM state. Due to a large in-plane anisotropy, spins lie in the basal plane with an in-plane canting angle of 14° between Co(I) and Co(II) ions. [7,15] Figure 3(a) depicts the temperaturedependent THz absorption spectra of Co4Ta2O<sup>9</sup> in the frequency range 0.1-2.1 THz. As is evident, a large number of resonance absorption peaks, expectedly spin wave excitations/magnons, manifest in two different regimes of the spectra. Below TN, THz absorption spectra reveals three excitations, namely, *s4*, *s5*, and *s6* (broad mode) at 0.42, 0.54, and 1.2-1.9 THz, respectively. Below 10 K, additional excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* emerge sharply at 0.17, 0.24, 0.32, 1.44, 1.57, 1.62 THz, respectively. It may be seen that these sharp excitations (*s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* ) are superimposed on *s6* mode. These additional modes in THz spectra are in accordance with the distinct wiggles in the THz electric field tail (64 to 74 ps) at 13 and 6 K corresponding to these resonances [Figure 2(b)]. Accounting all these sharp and broad modes, it may be noted that the zero-field ground state of Co4Ta2O<sup>9</sup> at 2.5 K exhibits **nine excitations** in a narrow frequency range of 0.1-2.2 THz which is significantly larger than three zero-field excitations in Co4Nb2O9. [17] This rare manifestation of closely spaced multitude magnetic excitations in the THz frequency is potentially relevant for fundamental and applied pursuits in the field of antiferromagnetic magnonics algebra. [32-33]
Now we shed light on the origin and detailed scrutiny of thus observed magnetic modes. Starting with broad mode *s6*, we observe that it continues to grow beyond magnetic ordering [Figure 3(b)]. In the paramagnetic region, the red shift in this peak position and a larger full-width half-maximum (FWHM) [Figure 3(d)] with increasing temperature are its attributes that point towards the pure phonon mode. This was confirmed in the paramagnetic state, [Figure 3(c)] where the applied field does not affect the structure and strength of this mode. In contrast, it shows profound field-induced changes in the magnetic ordered region below T<sup>N</sup> which points towards coupling of the lattice and spin waves, consequently, giving rise to magnon-phonon excitation. This is further evidenced by the deviation of FWHM from the cubic anharmonicity of phonon-linewidth [Figure 3(d)] (in accordance with phonon-phonon anharmonic model) defined as[18]
where, ω<sup>0</sup> and Г<sup>0</sup> are the mode frequency and linewidth at absolute zero temperature, respectively. This demonstration of low-lying phonon mode and its entanglement with spins via magnetic field is an important lead to unravel its ME character in a later section.
Now we turn our attention to multiple gapped excitations *s4* and *s5* which we assign to pure spinexcitation / magnon modes, for the following reasons. As the magnetic symmetry lowers, below TN, the gapped modes emerge with their origin expected in strong in-plane single-ion anisotropy. To verify this, we collected the THz spectra of Mn4Ta2O9, which is isostructural equivalent of Co4Ta2O9. Unlike Co4Ta2O9, Mn2+ spins lie along the trigonal axis in the AFM state. [19,20] Its THz spectra clearly shows the absence of '*s4* and *s5*' type gapped modes at 10 K [Figure SI 4; Supporting Information], elucidating that the origin of gapped mode to be associated with the basal in-plane single-ion anisotropy of Co4Ta2O9. Normalized force constant as a function of temperature unveils the softening of s4 mode as temperature is lowered [Inset Figure 3(a)].
The magnon and phonon lifetime is an important factor in contemplating various THz magnonics based devices. In the present case, this was calculated using energy-time uncertainty principle. [21] For the phonon excitation, its linewidth decreases with decreasing temperature below T<sup>N</sup> owing to reduced strength of thermal fluctuation, phonon-phonon scattering, and anharmonic effect [Figure 3(d)]. Phonon lifetime [Figure SI 5(a)] in magnetic ordered phase (1 ± 0.09 ps) is smaller than that in paramagnetic phase (1.83 ± 0.07 ps). This is because at T<sup>N</sup> the linewidth begins to deviate from the pure phonon vibration as this phonon couples with magnons and hence suffers additional scattering mechanism. For the gapped spin-excitation, the strength of relevant mode should strengthen as the temperature is lowered. Exact trend can be observed in Figure SI 5(b), where the spin-gapped mode (*s4*) lifetime increases as temperature is lowered implying a long coherent length in the low temperature regime with a lifetime of 17.21 ± 2.99 ps at 2.5 K.
Using the THz gapped mode, *s4*, we tried to estimate the magnetic exchange interaction and magnetic anisotropy for Co4Ta2O9. The gapped mode originates from single ion anisotropy, = 4√, where D, J, S are the single-ion anisotropy constant, nearest neighbor interaction, and spin moments, respectively. [22] We assume that the nearest neighbor interaction in isostructural Co4Nb2O9 and Co4Ta2O9 are same (JCo4Nb2O9 = -0.7 meV and DCo4Nb2O9 = 1.8 meV). [23] From THz experiments, (Egapped)Co4Nb2O9 = 3.15 meV [Supporting Information] and, (Egapped)Co4Ta2O9 = 1.72 meV. Using the above relation, the single-ion anisotropy constant (DCo4Ta2O9) was calculated to be 0.53 meV, which turns out to be less than the absolute value of nearest neighbor exchange interaction JCo4Ta2O9 = 0.7 meV. However, it is inadmissible for the following reasons: i) Co4B2O9 (B=Nb, Ta) possesses large in-plane anisotropy such that even large value of external magnetic field along c direction cannot flop the spin from basal plane, which implies that D>J [6,23,24] and, ii) as per Goodenough-Kanamori-Anderson (GKA) rules, the super exchange interaction J is proportional to t<sup>2</sup> /U, where t is effective orbital hopping and U is the Hubbard repulsion. [25,26] The first-principle studies[15] suggest that UCo4Nb2O9 < UCo4Ta2O9 and Co are more localized in Co4Ta2O9, which implies a small spatial extent of the electron wavefunction and a reduced overlap between adjacent atomic orbital; hence, JCo4Ta2O9 < JCo4Nb2O9. Therefore, our assumption in similarity of nearest neighbor interaction does not hold suggesting that these systems behave differently. It is required that DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9.
$$H = H\_c + H\_{p,b,pb} + \Sigma\_{Co(l)} D \left( S\_{l\text{z}}^{l} \right)^2 + \Sigma\_{Co(l\text{I})} D \left( S\_{l\text{z}}^{\text{II}} \right)^2 + \Sigma\_{\text{cf,j}>} D\_{l\text{j}}. \left( \text{S}\_{l} \times \text{S}\_{\text{j}} \right) \tag{2}$$
where H<sup>c</sup> is the Heisenberg term for the nearest and next nearest neighbor along c; Hp,b,pb are the Heisenberg terms for the planar, buckled, and planar-buckled networks. Third and fourth term represent single-ion in plane anisotropy where I and II denote two inequivalent sites of cobalt [Co(I) and Co(II) sites] and Dij represent the DM interaction.
Here, the magnetic exchange interaction, single-ion anisotropy strength and high-resolution observations of magnons at Г point by THz spectroscopy underpins the magnetic structure and the magnonic dynamics. To get insights of the Brillouin zone, beyond the Г point, spin-wave calculations were performed using the above spin Hamiltonian in SPINW. [27] In-plane magnetic structure was considered as revealed by neutron diffraction experiments [28] and using the THz Г point data, the magnetic exchange interactions were computed. The average powder spin-wave spectra for Co4Nb2O<sup>9</sup> [Figure 4(a)] shows gapped and gapless excitations which matches accurately with the Г point of THz data. The magnetic exchange interactions (JCo4Nb2O9=-0.6 meV and DCo4Nb2O9=1.6 meV) too agree well with those depicted by the inelastic neutron experimental results. [28] Using magnetic structure of temperature above 10 K for Co4Ta2O<sup>9</sup> [29] , the powder averaged spin-wave calculations yielded gapped excitations and magnetic exchange interactions JCo4Ta2O9=-0.4 meV and DCo4Ta2O9=1.1 meV. These are at lower energy and weaker, respectively, as compared to those of Co4Nb2O<sup>9</sup> and in perfect agreement with the condition DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9 [Figure 4(b)].
In contrast to above-mentioned low-energy spin-excitations, the higher energy modes (> 5 meV) obtained from spin-wave calculations and THz experimental data do not agree for either of Co4Ta2O<sup>9</sup> and Co4Nb2O9. This is because the spin Hamiltonian accounts only for spin-excitations while the phonon contribution as well as spin-lattice coupling terms are not incorporated. This deviation is further verification of broad mode s<sup>6</sup> being [Figure 3(a)] a spin-phonon coupled mode. As Nb is systematically replaced by Ta in Co4Ta2O9 [Figure 4(c)], the gapped mode (*s4*) gradually shifts to higher energies owing to gradual enhancement of the magnetic exchange interactions (J and D) [Figure 4(d)]. Thus, magnetic exchange interactions play a prominent role in driving the spinexcitations.
Now, to shed light on the origin of excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* (Figure 3a), it is imperative to invoke comparison of some relevant properties of Co4Ta2O<sup>9</sup> from Co4Nb2O9. As noted in previous section, weaker exchange interactions in Co4Ta2O<sup>9</sup> compared to that in Co4Nb2O<sup>9</sup> render it a softer magnet. In the latter, there has been no indication of structural transition even at 5 K, [6,7,16,24] though the possibility of local lattice distortion and magnetostriction was never ruled out. [15] In the case of Co4Ta2O9, however, the structural transitions, larger local lattice distortions and magnetostriction becomes more promising owing to its sensitivity to change in magnetic structure due to weaker magnetic interactions. This deviation of Co4Ta2O<sup>9</sup> from Co4Nb2O9, below 10 K, is the source of nonlinear ME response[30] and complex magnetic state[29,30] (in χ-T curve) in the former. However, its magnetic structure is reported only down to a minimum temperature of 15 K, [29] which is higher than the complexity-rich magnetism regime of below 10K. It is this low temperature regime, wherein the complex magnetic state, magnetostriction and local lattice distortion in Co4Ta2O<sup>9</sup> create entangled magnetic moments and lattice vibrations, which consequently give rise to six spin excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* in the THz spectra [Figure 3(a, b)]. No such excitations have been observed in Co4Nb2O9. The Co4Ta2O9, thus, hosts a ground for unique correlation between magnetic exchange interactions, local lattice distortion, and magnetostriction phenomena.
As Co4Ta2O<sup>9</sup> is a magnetic-field induced ME system, it is imperative to understand the magneticfield control of THz spin-wave excitation and the ME character. Magnetic field dependence of THz spectra is plotted in Figure 5 (a). Spin-excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* and *s6<sup>c</sup>* get suppressed with increasing magnetic field which reflects the expected magnetically malleable structure of Co4Ta2O9. At 2T, all these excitations annihilate while *s4* and *s5* shift to higher frequencies. Derived from the gapped mode (*s4*), the normalized force constant (kH/k0T; k<sup>H</sup> is the force constant at magnetic-field H and k0T is force constant at zero magnetic-field) indicates the hardening of the magnetic coupling between neighboring spins as a function of increasing magnetic-field [Inset Figure 5(a)]. As magnetic field exceeds 3 T, mode *s7* appears in the detectable range of our THz spectra. This excitation, identified as goldstone (/gapless) mode, appears in the microwave region due to spontaneous symmetry-breaking at T<sup>N</sup> and it shifts linearly towards higher THz frequency with increasing field [Figure 5(a) inset]. This gapless mode is shown in the spin-excitation simulations as well as in the THz spectra. The behaviour of peak frequency of this gapless excitation yields Landé g-factor g=3.09 for Co4Ta2O<sup>9</sup> and g=2.68 for Co4Nb2O<sup>9</sup> [Figure SI 3 and 7, Supporting Information]. Clearly the value of Landé g-factor suggests unquenched orbital moments both in Co4Ta2O<sup>9</sup> and Nb counterpart.
The mechanism of the field-induced polarization in this series has been of great interest to understand the induced ME character. Knowledge of spin-phonon mode and its magnetic-field dependence from THz spectroscopy can provide valuable insights into this process. At 6 K, the peak strength of spinphonon mode of Co4Ta2O<sup>9</sup> increases with an increase in magnetic field [Figure 5 (a, b)] which is associated with the field induced electric polarization. As lattice distortion, magnetostriction, and spin-phonon coupling are highly inter-related in these materials, the induced electric polarization can be explained as follows. At zero magnetic-field, below TN, the presence of spin-phonon coupling suggests the entanglement of spin and lattice. However, the Co ions hold two inequivalent sites Co(I) and Co(II) which are in centrosymmetric positions with respect to trigonal axis, hence, lacks any net polarization. However, on the application of magnetic-field the strength of spin-phonon coupling increases [Figure 5 (b)]. This expectedly displaces the magnetic ions from their centrosymmetric positions, resulting in the manifestation of magnetically induced polarization. This scenario of fieldinduced displacement of Co-ion is depicted in Figure 5 (c) As the mass of Ta is larger than Nb (ions to which Co-ions are bonded), the effective displacement in case of Co4Ta2O<sup>9</sup> is less than that in Co4Nb2O9. This also explains why magnetic field induced polarization in Co4Nb2O<sup>9</sup> is more as compared to Co4Ta2O9. The THz characteristic features of the magnetic resonances too possess this mass effect where with increasing concentration of Nb the resonances are shifting to higher THz frequency [Figure SI 8]. To surmise, this entire mechanism based on modulation of magnetic exchange interactions provides a pathway to control the energy of spin-gapped modes, spin-phonon coupled mode, and phonon mode whereas the effective lattice displacement of cobalt ions is responsible for magnetic-field induced polarization.
From the applied pursuit, the wave nature of magnons (spin-waves) offers a pathway to encode information in amplitude, phase, or the combination of both [Figure 6(a)] which is at core of nonBoolean algebra driven spin-wave computation.[31-33] The spin excitations in THz regime offer two novel characteristics, namely, the THz magnons propagate with ultra-low dissipation as it does not involve flow of electric charge, and with ultrafast speeds, both of which are much desired attributes for futuristic technologies. The existence of multiple magnon modes, as demonstrated in this work, is a pre-requisite for efficient data transfer spin-wave logic operations. In another facet, in the direction of spin-wave computation the multitude of spin waves in Co4Ta2O<sup>9</sup> present itself as a potential candidate for multifrequency channeling in a narrow bandwidth of 0.1 – 2.5 THz. Such multi-channels allow for simultaneous transmission of multiple signals at different frequencies, increasing the overall data capacity. A schematic serving as a proof-of-concept for terahertzmagnonics-electronics multifrequency channeling is shown in Figure 6(b). Here, the frequency of THz radiation drives the resonant condition corresponding to that magnon which carries the information and provides the output as electronic signal via a spin wave to charge converter. Experimental realization of this concept requires systems having multiple magnons or other hybrid modes in THz regime. In this work, the magnetoelectric systems with non-collinear magnetic order prone to strong spin-lattice interactions provide appropriate platform for THz magnonics.
### **3. Conclusions**
A myriad of low-energy excitations in Co4Ta2O9 probed using magneto-THz spectroscopy evidence a remarkable host magnetoelectric system with a rare multitude of ten excitations comprising of magnon, phonon, and hybridized magnon-phonon modes. The THz probes and non-collinear magnetism further combine to unravel a THz magnetoelectric effect; a novel functionality not known to manifest at such high frequencies so far. The origin of magnon in a strong basal-plane anisotropy emphasized the structural, magnetic and electronic controls to all excitation modes. These experimental data are supported by theoretical spin-wave computations along with quantifiable strength of magnetic exchange interactions. Furthermore, magnetic-field induced enhanced spinphonon coupling corroborates the proposition of magnetic-ion lattice displacement being the dominant factor for the ME behavior in this family of systems. Our results emphasize that the powderaveraged THz absorption spectrum acquired on a polycrystalline sample is not a limitation, rather an advantage over single crystals to facilitate faster screening of magnetic materials for spin-wave excitation mode, thus, expediting the search for potential materials for THz magnonic applications.
# **Supporting Information**
Supporting Information is available from the Wiley Online Library or from the author.
### **Acknowledgements**
D.S.R. thanks the Science and Engineering Research Board (SERB), Department of Science and Technology, New Delhi, for financial support under research Project No. CRG/2020/002338. K.S. thanks SERB for financial support under research Project No. CRG/2021/007075. B.S.M thanks Prime Minister Research Fellowship (PMRF; 0401968) funding agency, Ministry of Education, New Delhi, and Dr. Sunil Nair for providing Mn4Ta2O<sup>9</sup> sample.
### **Conflict of Interest**
Authors declare no conflict of interest.
# **Data Availability Statement**
The data that support the findings of this study are available from the corresponding author upon reasonable request.
## **References**
- [19] N. Narayanan, A. Senyshyn, D. Mikhailova, T. Faske, T. Lu, Z. Liu, B. Weise, H. Ehrenberg, R. A. Mole, W. D. Hutchison, H. Fuess, G. J. McIntyre, Y. Liu, D. Yu, *Phys. Rev. B* **2018**, *94*, 134438.
# **SUPPORTING INFORMATION**
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
# **S1: Experimental Details:**
# **A) Sample Preparation and Magnetic Characterization:**
Polycrystalline sample of Co4Ta2O<sup>9</sup> was prepared from solid state reaction route. The stoichiometric amount of Co3O<sup>4</sup> and Ta2O<sup>5</sup> (99.99% purities) powders were ground and calcined in air at 1000°C for 10 h. Sample was reground, pressed, and sintered at 1100°C for 10 h. The outcome was phasepure disc-shaped sample (diameter ~ 7 mm & thickness ~ 600 µm). Phase purity was confirmed at room temperature by PANalytical ''Empyrean' powder X-ray diffractometer (PXRD) with Cu K<sup>α</sup> radiation (1.54 Å). [Figure SI 1] Rietveld refinement analysis provided a good fit with χ<sup>2</sup> =1.8 and lattice parameters a=b=0.5173 nm, and c=1.415 nm.
Magnetic measurements were performed using a superconducting quantum interference device [SQUID-VSM (Quantum Design)] in the temperature range of 2-80 K.
# **B) Magneto-THz time-domain Spectroscopy:**
Fiber-coupled TeraK15 THz time-domain transmission spectrometer equipped with top-loading closed-cycle He cryostat and Oxford Spectramag split-coil magnet (magnetic field up to 7T) was implemented in Faraday geometry [Figure SI 2] to measure the absorption coefficient in the spectral range 0.1-2 THz with a spectral resolution of 0.0146 THz. The path of the THz radiation is purged with nitrogen gas ten minutes before and during measurement to circumvent the water absorption peaks. THz measurement generates raw data in the form of time-dependent picosecond pulses of electric fields, which are then transformed into complex-valued frequency functions via Fast Fourier transformation. Absorption Coefficient was calculated by,
where d is the thickness of the sample, Ssample and Sreference are the spectral amplitude with and without the sample, respectively. THz study on the polycrystalline sample provides an averaged-THz spectrum permitting us to observe excitations over all the spatial directions.
# **S2: Magneto-THz time-domain Experiment:**
# **A) Co4Ta2O<sup>9</sup>**
In Co4Ta2O9, there is one magnetic-field induced excitation termed as gapless/Goldstone mode in the absorption spectrum. At 0 T it is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 3.09 was obtained which suggests the presence of unquenched orbital moments in it.
## **Goldstone Mode:**
### **B) Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup>**
Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup> are isostructural members of A4B2O<sup>9</sup> family. In the magnetic-ordered state spins of Mn2+ in Mn4Ta2O<sup>9</sup> have uniaxial anisotropy spins along the c-direction whereas Co2+ in Co4Ta2O<sup>9</sup> possess strong basal plane anisotropy [Figure SI 3 inset (a)]. Figure SI3 shows THz spectra with and without the sample at 10 K which emphasizes the presence (/absence) of the gapped modes in Co4Ta2O9 (/Mn4Ta2O9).
![*Figure SI 4: THz spectra with (Mn4Ta2O9 and Co4Ta2O9) and without the samples at 10 K. Note: [Mn4Ta2O9 sample is taken from Ref (1)]*](path)
### **C) Spin gapped and Phonon lifetime in Co4Ta2O9:**
# **D) Co4Nb2O<sup>9</sup>**
# **Goldstone Mode:**
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
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**Figure 2:** a) Magnetic susceptibility versus temperature. b) THz electric field at three different temperatures. c) Normalized THz peak amplitude as a function of temperature and magnetic field (Inset), respectively. d) Real dielectric constant versus temperature at 0.71 THz. Inset shows refractive index in the THz frequency range.
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# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
The normalized THz peak amplitude defined as the ratio of THz electric field peak position with and without the sample, ()(,) ()(,) , displays a sudden drop of ~12 % at the T<sup>N</sup> [Figure 2(c)] depicting a sensitivity of THz electric field to the spin-order at the magnetic transition. This feature combined with a large magnetic field dependence of normalized THz electric-field peak at 6 K [Inset Figure 2(c)] are unambiguous evidence of THz ME effect in this system. Also, The THz data yields a real refractive index of ~ 4 [Inset Figure 2(d)], which agrees well with the literature. [8] The real dielectric constant [at *ω* = 0.71 THz] increases with decreasing temperature and exhibits anomalies at both the magnetic transitions at 20.5 and 10 K [Figure 2(d)], which is consistent with the behavior of magnetization data [Inset Figure 2(a)].
In Co4Ta2O9, the magnetic symmetry lowers from trigonal in the paramagnetic state to monoclinic symmetry in the AFM state. Due to a large in-plane anisotropy, spins lie in the basal plane with an in-plane canting angle of 14° between Co(I) and Co(II) ions. [7,15] Figure 3(a) depicts the temperaturedependent THz absorption spectra of Co4Ta2O<sup>9</sup> in the frequency range 0.1-2.1 THz. As is evident, a large number of resonance absorption peaks, expectedly spin wave excitations/magnons, manifest in two different regimes of the spectra. Below TN, THz absorption spectra reveals three excitations, namely, *s4*, *s5*, and *s6* (broad mode) at 0.42, 0.54, and 1.2-1.9 THz, respectively. Below 10 K, additional excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* emerge sharply at 0.17, 0.24, 0.32, 1.44, 1.57, 1.62 THz, respectively. It may be seen that these sharp excitations (*s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* ) are superimposed on *s6* mode. These additional modes in THz spectra are in accordance with the distinct wiggles in the THz electric field tail (64 to 74 ps) at 13 and 6 K corresponding to these resonances [Figure 2(b)]. Accounting all these sharp and broad modes, it may be noted that the zero-field ground state of Co4Ta2O<sup>9</sup> at 2.5 K exhibits **nine excitations** in a narrow frequency range of 0.1-2.2 THz which is significantly larger than three zero-field excitations in Co4Nb2O9. [17] This rare manifestation of closely spaced multitude magnetic excitations in the THz frequency is potentially relevant for fundamental and applied pursuits in the field of antiferromagnetic magnonics algebra. [32-33]
Now we shed light on the origin and detailed scrutiny of thus observed magnetic modes. Starting with broad mode *s6*, we observe that it continues to grow beyond magnetic ordering [Figure 3(b)]. In the paramagnetic region, the red shift in this peak position and a larger full-width half-maximum (FWHM) [Figure 3(d)] with increasing temperature are its attributes that point towards the pure phonon mode. This was confirmed in the paramagnetic state, [Figure 3(c)] where the applied field does not affect the structure and strength of this mode. In contrast, it shows profound field-induced changes in the magnetic ordered region below T<sup>N</sup> which points towards coupling of the lattice and spin waves, consequently, giving rise to magnon-phonon excitation. This is further evidenced by the deviation of FWHM from the cubic anharmonicity of phonon-linewidth [Figure 3(d)] (in accordance with phonon-phonon anharmonic model) defined as[18]
where, ω<sup>0</sup> and Г<sup>0</sup> are the mode frequency and linewidth at absolute zero temperature, respectively. This demonstration of low-lying phonon mode and its entanglement with spins via magnetic field is an important lead to unravel its ME character in a later section.
Now we turn our attention to multiple gapped excitations *s4* and *s5* which we assign to pure spinexcitation / magnon modes, for the following reasons. As the magnetic symmetry lowers, below TN, the gapped modes emerge with their origin expected in strong in-plane single-ion anisotropy. To verify this, we collected the THz spectra of Mn4Ta2O9, which is isostructural equivalent of Co4Ta2O9. Unlike Co4Ta2O9, Mn2+ spins lie along the trigonal axis in the AFM state. [19,20] Its THz spectra clearly shows the absence of '*s4* and *s5*' type gapped modes at 10 K [Figure SI 4; Supporting Information], elucidating that the origin of gapped mode to be associated with the basal in-plane single-ion anisotropy of Co4Ta2O9. Normalized force constant as a function of temperature unveils the softening of s4 mode as temperature is lowered [Inset Figure 3(a)].
The magnon and phonon lifetime is an important factor in contemplating various THz magnonics based devices. In the present case, this was calculated using energy-time uncertainty principle. [21] For the phonon excitation, its linewidth decreases with decreasing temperature below T<sup>N</sup> owing to reduced strength of thermal fluctuation, phonon-phonon scattering, and anharmonic effect [Figure 3(d)]. Phonon lifetime [Figure SI 5(a)] in magnetic ordered phase (1 ± 0.09 ps) is smaller than that in paramagnetic phase (1.83 ± 0.07 ps). This is because at T<sup>N</sup> the linewidth begins to deviate from the pure phonon vibration as this phonon couples with magnons and hence suffers additional scattering mechanism. For the gapped spin-excitation, the strength of relevant mode should strengthen as the temperature is lowered. Exact trend can be observed in Figure SI 5(b), where the spin-gapped mode (*s4*) lifetime increases as temperature is lowered implying a long coherent length in the low temperature regime with a lifetime of 17.21 ± 2.99 ps at 2.5 K.
Using the THz gapped mode, *s4*, we tried to estimate the magnetic exchange interaction and magnetic anisotropy for Co4Ta2O9. The gapped mode originates from single ion anisotropy, = 4√, where D, J, S are the single-ion anisotropy constant, nearest neighbor interaction, and spin moments, respectively. [22] We assume that the nearest neighbor interaction in isostructural Co4Nb2O9 and Co4Ta2O9 are same (JCo4Nb2O9 = -0.7 meV and DCo4Nb2O9 = 1.8 meV). [23] From THz experiments, (Egapped)Co4Nb2O9 = 3.15 meV [Supporting Information] and, (Egapped)Co4Ta2O9 = 1.72 meV. Using the above relation, the single-ion anisotropy constant (DCo4Ta2O9) was calculated to be 0.53 meV, which turns out to be less than the absolute value of nearest neighbor exchange interaction JCo4Ta2O9 = 0.7 meV. However, it is inadmissible for the following reasons: i) Co4B2O9 (B=Nb, Ta) possesses large in-plane anisotropy such that even large value of external magnetic field along c direction cannot flop the spin from basal plane, which implies that D>J [6,23,24] and, ii) as per Goodenough-Kanamori-Anderson (GKA) rules, the super exchange interaction J is proportional to t<sup>2</sup> /U, where t is effective orbital hopping and U is the Hubbard repulsion. [25,26] The first-principle studies[15] suggest that UCo4Nb2O9 < UCo4Ta2O9 and Co are more localized in Co4Ta2O9, which implies a small spatial extent of the electron wavefunction and a reduced overlap between adjacent atomic orbital; hence, JCo4Ta2O9 < JCo4Nb2O9. Therefore, our assumption in similarity of nearest neighbor interaction does not hold suggesting that these systems behave differently. It is required that DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9.
$$H = H\_c + H\_{p,b,pb} + \Sigma\_{Co(l)} D \left( S\_{l\text{z}}^{l} \right)^2 + \Sigma\_{Co(l\text{I})} D \left( S\_{l\text{z}}^{\text{II}} \right)^2 + \Sigma\_{\text{cf,j}>} D\_{l\text{j}}. \left( \text{S}\_{l} \times \text{S}\_{\text{j}} \right) \tag{2}$$
where H<sup>c</sup> is the Heisenberg term for the nearest and next nearest neighbor along c; Hp,b,pb are the Heisenberg terms for the planar, buckled, and planar-buckled networks. Third and fourth term represent single-ion in plane anisotropy where I and II denote two inequivalent sites of cobalt [Co(I) and Co(II) sites] and Dij represent the DM interaction.
Here, the magnetic exchange interaction, single-ion anisotropy strength and high-resolution observations of magnons at Г point by THz spectroscopy underpins the magnetic structure and the magnonic dynamics. To get insights of the Brillouin zone, beyond the Г point, spin-wave calculations were performed using the above spin Hamiltonian in SPINW. [27] In-plane magnetic structure was considered as revealed by neutron diffraction experiments [28] and using the THz Г point data, the magnetic exchange interactions were computed. The average powder spin-wave spectra for Co4Nb2O<sup>9</sup> [Figure 4(a)] shows gapped and gapless excitations which matches accurately with the Г point of THz data. The magnetic exchange interactions (JCo4Nb2O9=-0.6 meV and DCo4Nb2O9=1.6 meV) too agree well with those depicted by the inelastic neutron experimental results. [28] Using magnetic structure of temperature above 10 K for Co4Ta2O<sup>9</sup> [29] , the powder averaged spin-wave calculations yielded gapped excitations and magnetic exchange interactions JCo4Ta2O9=-0.4 meV and DCo4Ta2O9=1.1 meV. These are at lower energy and weaker, respectively, as compared to those of Co4Nb2O<sup>9</sup> and in perfect agreement with the condition DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9 [Figure 4(b)].
In contrast to above-mentioned low-energy spin-excitations, the higher energy modes (> 5 meV) obtained from spin-wave calculations and THz experimental data do not agree for either of Co4Ta2O<sup>9</sup> and Co4Nb2O9. This is because the spin Hamiltonian accounts only for spin-excitations while the phonon contribution as well as spin-lattice coupling terms are not incorporated. This deviation is further verification of broad mode s<sup>6</sup> being [Figure 3(a)] a spin-phonon coupled mode. As Nb is systematically replaced by Ta in Co4Ta2O9 [Figure 4(c)], the gapped mode (*s4*) gradually shifts to higher energies owing to gradual enhancement of the magnetic exchange interactions (J and D) [Figure 4(d)]. Thus, magnetic exchange interactions play a prominent role in driving the spinexcitations.
Now, to shed light on the origin of excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* (Figure 3a), it is imperative to invoke comparison of some relevant properties of Co4Ta2O<sup>9</sup> from Co4Nb2O9. As noted in previous section, weaker exchange interactions in Co4Ta2O<sup>9</sup> compared to that in Co4Nb2O<sup>9</sup> render it a softer magnet. In the latter, there has been no indication of structural transition even at 5 K, [6,7,16,24] though the possibility of local lattice distortion and magnetostriction was never ruled out. [15] In the case of Co4Ta2O9, however, the structural transitions, larger local lattice distortions and magnetostriction becomes more promising owing to its sensitivity to change in magnetic structure due to weaker magnetic interactions. This deviation of Co4Ta2O<sup>9</sup> from Co4Nb2O9, below 10 K, is the source of nonlinear ME response[30] and complex magnetic state[29,30] (in χ-T curve) in the former. However, its magnetic structure is reported only down to a minimum temperature of 15 K, [29] which is higher than the complexity-rich magnetism regime of below 10K. It is this low temperature regime, wherein the complex magnetic state, magnetostriction and local lattice distortion in Co4Ta2O<sup>9</sup> create entangled magnetic moments and lattice vibrations, which consequently give rise to six spin excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* in the THz spectra [Figure 3(a, b)]. No such excitations have been observed in Co4Nb2O9. The Co4Ta2O9, thus, hosts a ground for unique correlation between magnetic exchange interactions, local lattice distortion, and magnetostriction phenomena.
As Co4Ta2O<sup>9</sup> is a magnetic-field induced ME system, it is imperative to understand the magneticfield control of THz spin-wave excitation and the ME character. Magnetic field dependence of THz spectra is plotted in Figure 5 (a). Spin-excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* and *s6<sup>c</sup>* get suppressed with increasing magnetic field which reflects the expected magnetically malleable structure of Co4Ta2O9. At 2T, all these excitations annihilate while *s4* and *s5* shift to higher frequencies. Derived from the gapped mode (*s4*), the normalized force constant (kH/k0T; k<sup>H</sup> is the force constant at magnetic-field H and k0T is force constant at zero magnetic-field) indicates the hardening of the magnetic coupling between neighboring spins as a function of increasing magnetic-field [Inset Figure 5(a)]. As magnetic field exceeds 3 T, mode *s7* appears in the detectable range of our THz spectra. This excitation, identified as goldstone (/gapless) mode, appears in the microwave region due to spontaneous symmetry-breaking at T<sup>N</sup> and it shifts linearly towards higher THz frequency with increasing field [Figure 5(a) inset]. This gapless mode is shown in the spin-excitation simulations as well as in the THz spectra. The behaviour of peak frequency of this gapless excitation yields Landé g-factor g=3.09 for Co4Ta2O<sup>9</sup> and g=2.68 for Co4Nb2O<sup>9</sup> [Figure SI 3 and 7, Supporting Information]. Clearly the value of Landé g-factor suggests unquenched orbital moments both in Co4Ta2O<sup>9</sup> and Nb counterpart.
The mechanism of the field-induced polarization in this series has been of great interest to understand the induced ME character. Knowledge of spin-phonon mode and its magnetic-field dependence from THz spectroscopy can provide valuable insights into this process. At 6 K, the peak strength of spinphonon mode of Co4Ta2O<sup>9</sup> increases with an increase in magnetic field [Figure 5 (a, b)] which is associated with the field induced electric polarization. As lattice distortion, magnetostriction, and spin-phonon coupling are highly inter-related in these materials, the induced electric polarization can be explained as follows. At zero magnetic-field, below TN, the presence of spin-phonon coupling suggests the entanglement of spin and lattice. However, the Co ions hold two inequivalent sites Co(I) and Co(II) which are in centrosymmetric positions with respect to trigonal axis, hence, lacks any net polarization. However, on the application of magnetic-field the strength of spin-phonon coupling increases [Figure 5 (b)]. This expectedly displaces the magnetic ions from their centrosymmetric positions, resulting in the manifestation of magnetically induced polarization. This scenario of fieldinduced displacement of Co-ion is depicted in Figure 5 (c) As the mass of Ta is larger than Nb (ions to which Co-ions are bonded), the effective displacement in case of Co4Ta2O<sup>9</sup> is less than that in Co4Nb2O9. This also explains why magnetic field induced polarization in Co4Nb2O<sup>9</sup> is more as compared to Co4Ta2O9. The THz characteristic features of the magnetic resonances too possess this mass effect where with increasing concentration of Nb the resonances are shifting to higher THz frequency [Figure SI 8]. To surmise, this entire mechanism based on modulation of magnetic exchange interactions provides a pathway to control the energy of spin-gapped modes, spin-phonon coupled mode, and phonon mode whereas the effective lattice displacement of cobalt ions is responsible for magnetic-field induced polarization.
From the applied pursuit, the wave nature of magnons (spin-waves) offers a pathway to encode information in amplitude, phase, or the combination of both [Figure 6(a)] which is at core of nonBoolean algebra driven spin-wave computation.[31-33] The spin excitations in THz regime offer two novel characteristics, namely, the THz magnons propagate with ultra-low dissipation as it does not involve flow of electric charge, and with ultrafast speeds, both of which are much desired attributes for futuristic technologies. The existence of multiple magnon modes, as demonstrated in this work, is a pre-requisite for efficient data transfer spin-wave logic operations. In another facet, in the direction of spin-wave computation the multitude of spin waves in Co4Ta2O<sup>9</sup> present itself as a potential candidate for multifrequency channeling in a narrow bandwidth of 0.1 – 2.5 THz. Such multi-channels allow for simultaneous transmission of multiple signals at different frequencies, increasing the overall data capacity. A schematic serving as a proof-of-concept for terahertzmagnonics-electronics multifrequency channeling is shown in Figure 6(b). Here, the frequency of THz radiation drives the resonant condition corresponding to that magnon which carries the information and provides the output as electronic signal via a spin wave to charge converter. Experimental realization of this concept requires systems having multiple magnons or other hybrid modes in THz regime. In this work, the magnetoelectric systems with non-collinear magnetic order prone to strong spin-lattice interactions provide appropriate platform for THz magnonics.
### **3. Conclusions**
A myriad of low-energy excitations in Co4Ta2O9 probed using magneto-THz spectroscopy evidence a remarkable host magnetoelectric system with a rare multitude of ten excitations comprising of magnon, phonon, and hybridized magnon-phonon modes. The THz probes and non-collinear magnetism further combine to unravel a THz magnetoelectric effect; a novel functionality not known to manifest at such high frequencies so far. The origin of magnon in a strong basal-plane anisotropy emphasized the structural, magnetic and electronic controls to all excitation modes. These experimental data are supported by theoretical spin-wave computations along with quantifiable strength of magnetic exchange interactions. Furthermore, magnetic-field induced enhanced spinphonon coupling corroborates the proposition of magnetic-ion lattice displacement being the dominant factor for the ME behavior in this family of systems. Our results emphasize that the powderaveraged THz absorption spectrum acquired on a polycrystalline sample is not a limitation, rather an advantage over single crystals to facilitate faster screening of magnetic materials for spin-wave excitation mode, thus, expediting the search for potential materials for THz magnonic applications.
# **Supporting Information**
Supporting Information is available from the Wiley Online Library or from the author.
### **Acknowledgements**
D.S.R. thanks the Science and Engineering Research Board (SERB), Department of Science and Technology, New Delhi, for financial support under research Project No. CRG/2020/002338. K.S. thanks SERB for financial support under research Project No. CRG/2021/007075. B.S.M thanks Prime Minister Research Fellowship (PMRF; 0401968) funding agency, Ministry of Education, New Delhi, and Dr. Sunil Nair for providing Mn4Ta2O<sup>9</sup> sample.
### **Conflict of Interest**
Authors declare no conflict of interest.
# **Data Availability Statement**
The data that support the findings of this study are available from the corresponding author upon reasonable request.
## **References**
- [19] N. Narayanan, A. Senyshyn, D. Mikhailova, T. Faske, T. Lu, Z. Liu, B. Weise, H. Ehrenberg, R. A. Mole, W. D. Hutchison, H. Fuess, G. J. McIntyre, Y. Liu, D. Yu, *Phys. Rev. B* **2018**, *94*, 134438.
# **SUPPORTING INFORMATION**
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
# **S1: Experimental Details:**
# **A) Sample Preparation and Magnetic Characterization:**
Polycrystalline sample of Co4Ta2O<sup>9</sup> was prepared from solid state reaction route. The stoichiometric amount of Co3O<sup>4</sup> and Ta2O<sup>5</sup> (99.99% purities) powders were ground and calcined in air at 1000°C for 10 h. Sample was reground, pressed, and sintered at 1100°C for 10 h. The outcome was phasepure disc-shaped sample (diameter ~ 7 mm & thickness ~ 600 µm). Phase purity was confirmed at room temperature by PANalytical ''Empyrean' powder X-ray diffractometer (PXRD) with Cu K<sup>α</sup> radiation (1.54 Å). [Figure SI 1] Rietveld refinement analysis provided a good fit with χ<sup>2</sup> =1.8 and lattice parameters a=b=0.5173 nm, and c=1.415 nm.
Magnetic measurements were performed using a superconducting quantum interference device [SQUID-VSM (Quantum Design)] in the temperature range of 2-80 K.
# **B) Magneto-THz time-domain Spectroscopy:**
Fiber-coupled TeraK15 THz time-domain transmission spectrometer equipped with top-loading closed-cycle He cryostat and Oxford Spectramag split-coil magnet (magnetic field up to 7T) was implemented in Faraday geometry [Figure SI 2] to measure the absorption coefficient in the spectral range 0.1-2 THz with a spectral resolution of 0.0146 THz. The path of the THz radiation is purged with nitrogen gas ten minutes before and during measurement to circumvent the water absorption peaks. THz measurement generates raw data in the form of time-dependent picosecond pulses of electric fields, which are then transformed into complex-valued frequency functions via Fast Fourier transformation. Absorption Coefficient was calculated by,
where d is the thickness of the sample, Ssample and Sreference are the spectral amplitude with and without the sample, respectively. THz study on the polycrystalline sample provides an averaged-THz spectrum permitting us to observe excitations over all the spatial directions.
# **S2: Magneto-THz time-domain Experiment:**
# **A) Co4Ta2O<sup>9</sup>**
In Co4Ta2O9, there is one magnetic-field induced excitation termed as gapless/Goldstone mode in the absorption spectrum. At 0 T it is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 3.09 was obtained which suggests the presence of unquenched orbital moments in it.
## **Goldstone Mode:**
### **B) Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup>**
Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup> are isostructural members of A4B2O<sup>9</sup> family. In the magnetic-ordered state spins of Mn2+ in Mn4Ta2O<sup>9</sup> have uniaxial anisotropy spins along the c-direction whereas Co2+ in Co4Ta2O<sup>9</sup> possess strong basal plane anisotropy [Figure SI 3 inset (a)]. Figure SI3 shows THz spectra with and without the sample at 10 K which emphasizes the presence (/absence) of the gapped modes in Co4Ta2O9 (/Mn4Ta2O9).
![*Figure SI 4: THz spectra with (Mn4Ta2O9 and Co4Ta2O9) and without the samples at 10 K. Note: [Mn4Ta2O9 sample is taken from Ref (1)]*](path)
### **C) Spin gapped and Phonon lifetime in Co4Ta2O9:**
# **D) Co4Nb2O<sup>9</sup>**
# **Goldstone Mode:**
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
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**Figure 4:** Spin wave calculations for a) Co4Nb2O<sup>9</sup> and b) Co4Ta2O9. c) Comparison of experimental and calculated value of Gapped mode *s4*, at the Г point, as a function of Nb doping in Co4Ta2-xNbxO9. d) Obtained value of magnetic exchange interactions (J=nearest neighbor interaction and D=single-ion anisotropy) for Co4Ta2-xNbxO9 (x=0, 0.3, 1, 1.7, 2).
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# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
Now, to shed light on the origin of excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* (Figure 3a), it is imperative to invoke comparison of some relevant properties of Co4Ta2O<sup>9</sup> from Co4Nb2O9. As noted in previous section, weaker exchange interactions in Co4Ta2O<sup>9</sup> compared to that in Co4Nb2O<sup>9</sup> render it a softer magnet. In the latter, there has been no indication of structural transition even at 5 K, [6,7,16,24] though the possibility of local lattice distortion and magnetostriction was never ruled out. [15] In the case of Co4Ta2O9, however, the structural transitions, larger local lattice distortions and magnetostriction becomes more promising owing to its sensitivity to change in magnetic structure due to weaker magnetic interactions. This deviation of Co4Ta2O<sup>9</sup> from Co4Nb2O9, below 10 K, is the source of nonlinear ME response[30] and complex magnetic state[29,30] (in χ-T curve) in the former. However, its magnetic structure is reported only down to a minimum temperature of 15 K, [29] which is higher than the complexity-rich magnetism regime of below 10K. It is this low temperature regime, wherein the complex magnetic state, magnetostriction and local lattice distortion in Co4Ta2O<sup>9</sup> create entangled magnetic moments and lattice vibrations, which consequently give rise to six spin excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* in the THz spectra [Figure 3(a, b)]. No such excitations have been observed in Co4Nb2O9. The Co4Ta2O9, thus, hosts a ground for unique correlation between magnetic exchange interactions, local lattice distortion, and magnetostriction phenomena.
As Co4Ta2O<sup>9</sup> is a magnetic-field induced ME system, it is imperative to understand the magneticfield control of THz spin-wave excitation and the ME character. Magnetic field dependence of THz spectra is plotted in Figure 5 (a). Spin-excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* and *s6<sup>c</sup>* get suppressed with increasing magnetic field which reflects the expected magnetically malleable structure of Co4Ta2O9. At 2T, all these excitations annihilate while *s4* and *s5* shift to higher frequencies. Derived from the gapped mode (*s4*), the normalized force constant (kH/k0T; k<sup>H</sup> is the force constant at magnetic-field H and k0T is force constant at zero magnetic-field) indicates the hardening of the magnetic coupling between neighboring spins as a function of increasing magnetic-field [Inset Figure 5(a)]. As magnetic field exceeds 3 T, mode *s7* appears in the detectable range of our THz spectra. This excitation, identified as goldstone (/gapless) mode, appears in the microwave region due to spontaneous symmetry-breaking at T<sup>N</sup> and it shifts linearly towards higher THz frequency with increasing field [Figure 5(a) inset]. This gapless mode is shown in the spin-excitation simulations as well as in the THz spectra. The behaviour of peak frequency of this gapless excitation yields Landé g-factor g=3.09 for Co4Ta2O<sup>9</sup> and g=2.68 for Co4Nb2O<sup>9</sup> [Figure SI 3 and 7, Supporting Information]. Clearly the value of Landé g-factor suggests unquenched orbital moments both in Co4Ta2O<sup>9</sup> and Nb counterpart.
The mechanism of the field-induced polarization in this series has been of great interest to understand the induced ME character. Knowledge of spin-phonon mode and its magnetic-field dependence from THz spectroscopy can provide valuable insights into this process. At 6 K, the peak strength of spinphonon mode of Co4Ta2O<sup>9</sup> increases with an increase in magnetic field [Figure 5 (a, b)] which is associated with the field induced electric polarization. As lattice distortion, magnetostriction, and spin-phonon coupling are highly inter-related in these materials, the induced electric polarization can be explained as follows. At zero magnetic-field, below TN, the presence of spin-phonon coupling suggests the entanglement of spin and lattice. However, the Co ions hold two inequivalent sites Co(I) and Co(II) which are in centrosymmetric positions with respect to trigonal axis, hence, lacks any net polarization. However, on the application of magnetic-field the strength of spin-phonon coupling increases [Figure 5 (b)]. This expectedly displaces the magnetic ions from their centrosymmetric positions, resulting in the manifestation of magnetically induced polarization. This scenario of fieldinduced displacement of Co-ion is depicted in Figure 5 (c) As the mass of Ta is larger than Nb (ions to which Co-ions are bonded), the effective displacement in case of Co4Ta2O<sup>9</sup> is less than that in Co4Nb2O9. This also explains why magnetic field induced polarization in Co4Nb2O<sup>9</sup> is more as compared to Co4Ta2O9. The THz characteristic features of the magnetic resonances too possess this mass effect where with increasing concentration of Nb the resonances are shifting to higher THz frequency [Figure SI 8]. To surmise, this entire mechanism based on modulation of magnetic exchange interactions provides a pathway to control the energy of spin-gapped modes, spin-phonon coupled mode, and phonon mode whereas the effective lattice displacement of cobalt ions is responsible for magnetic-field induced polarization.
From the applied pursuit, the wave nature of magnons (spin-waves) offers a pathway to encode information in amplitude, phase, or the combination of both [Figure 6(a)] which is at core of nonBoolean algebra driven spin-wave computation.[31-33] The spin excitations in THz regime offer two novel characteristics, namely, the THz magnons propagate with ultra-low dissipation as it does not involve flow of electric charge, and with ultrafast speeds, both of which are much desired attributes for futuristic technologies. The existence of multiple magnon modes, as demonstrated in this work, is a pre-requisite for efficient data transfer spin-wave logic operations. In another facet, in the direction of spin-wave computation the multitude of spin waves in Co4Ta2O<sup>9</sup> present itself as a potential candidate for multifrequency channeling in a narrow bandwidth of 0.1 – 2.5 THz. Such multi-channels allow for simultaneous transmission of multiple signals at different frequencies, increasing the overall data capacity. A schematic serving as a proof-of-concept for terahertzmagnonics-electronics multifrequency channeling is shown in Figure 6(b). Here, the frequency of THz radiation drives the resonant condition corresponding to that magnon which carries the information and provides the output as electronic signal via a spin wave to charge converter. Experimental realization of this concept requires systems having multiple magnons or other hybrid modes in THz regime. In this work, the magnetoelectric systems with non-collinear magnetic order prone to strong spin-lattice interactions provide appropriate platform for THz magnonics.
### **3. Conclusions**
A myriad of low-energy excitations in Co4Ta2O9 probed using magneto-THz spectroscopy evidence a remarkable host magnetoelectric system with a rare multitude of ten excitations comprising of magnon, phonon, and hybridized magnon-phonon modes. The THz probes and non-collinear magnetism further combine to unravel a THz magnetoelectric effect; a novel functionality not known to manifest at such high frequencies so far. The origin of magnon in a strong basal-plane anisotropy emphasized the structural, magnetic and electronic controls to all excitation modes. These experimental data are supported by theoretical spin-wave computations along with quantifiable strength of magnetic exchange interactions. Furthermore, magnetic-field induced enhanced spinphonon coupling corroborates the proposition of magnetic-ion lattice displacement being the dominant factor for the ME behavior in this family of systems. Our results emphasize that the powderaveraged THz absorption spectrum acquired on a polycrystalline sample is not a limitation, rather an advantage over single crystals to facilitate faster screening of magnetic materials for spin-wave excitation mode, thus, expediting the search for potential materials for THz magnonic applications.
# **Supporting Information**
Supporting Information is available from the Wiley Online Library or from the author.
### **Acknowledgements**
D.S.R. thanks the Science and Engineering Research Board (SERB), Department of Science and Technology, New Delhi, for financial support under research Project No. CRG/2020/002338. K.S. thanks SERB for financial support under research Project No. CRG/2021/007075. B.S.M thanks Prime Minister Research Fellowship (PMRF; 0401968) funding agency, Ministry of Education, New Delhi, and Dr. Sunil Nair for providing Mn4Ta2O<sup>9</sup> sample.
### **Conflict of Interest**
Authors declare no conflict of interest.
# **Data Availability Statement**
The data that support the findings of this study are available from the corresponding author upon reasonable request.
## **References**
- [19] N. Narayanan, A. Senyshyn, D. Mikhailova, T. Faske, T. Lu, Z. Liu, B. Weise, H. Ehrenberg, R. A. Mole, W. D. Hutchison, H. Fuess, G. J. McIntyre, Y. Liu, D. Yu, *Phys. Rev. B* **2018**, *94*, 134438.
# **SUPPORTING INFORMATION**
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
# **S1: Experimental Details:**
# **A) Sample Preparation and Magnetic Characterization:**
Polycrystalline sample of Co4Ta2O<sup>9</sup> was prepared from solid state reaction route. The stoichiometric amount of Co3O<sup>4</sup> and Ta2O<sup>5</sup> (99.99% purities) powders were ground and calcined in air at 1000°C for 10 h. Sample was reground, pressed, and sintered at 1100°C for 10 h. The outcome was phasepure disc-shaped sample (diameter ~ 7 mm & thickness ~ 600 µm). Phase purity was confirmed at room temperature by PANalytical ''Empyrean' powder X-ray diffractometer (PXRD) with Cu K<sup>α</sup> radiation (1.54 Å). [Figure SI 1] Rietveld refinement analysis provided a good fit with χ<sup>2</sup> =1.8 and lattice parameters a=b=0.5173 nm, and c=1.415 nm.
Magnetic measurements were performed using a superconducting quantum interference device [SQUID-VSM (Quantum Design)] in the temperature range of 2-80 K.
# **B) Magneto-THz time-domain Spectroscopy:**
Fiber-coupled TeraK15 THz time-domain transmission spectrometer equipped with top-loading closed-cycle He cryostat and Oxford Spectramag split-coil magnet (magnetic field up to 7T) was implemented in Faraday geometry [Figure SI 2] to measure the absorption coefficient in the spectral range 0.1-2 THz with a spectral resolution of 0.0146 THz. The path of the THz radiation is purged with nitrogen gas ten minutes before and during measurement to circumvent the water absorption peaks. THz measurement generates raw data in the form of time-dependent picosecond pulses of electric fields, which are then transformed into complex-valued frequency functions via Fast Fourier transformation. Absorption Coefficient was calculated by,
where d is the thickness of the sample, Ssample and Sreference are the spectral amplitude with and without the sample, respectively. THz study on the polycrystalline sample provides an averaged-THz spectrum permitting us to observe excitations over all the spatial directions.
# **S2: Magneto-THz time-domain Experiment:**
# **A) Co4Ta2O<sup>9</sup>**
In Co4Ta2O9, there is one magnetic-field induced excitation termed as gapless/Goldstone mode in the absorption spectrum. At 0 T it is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 3.09 was obtained which suggests the presence of unquenched orbital moments in it.
## **Goldstone Mode:**
### **B) Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup>**
Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup> are isostructural members of A4B2O<sup>9</sup> family. In the magnetic-ordered state spins of Mn2+ in Mn4Ta2O<sup>9</sup> have uniaxial anisotropy spins along the c-direction whereas Co2+ in Co4Ta2O<sup>9</sup> possess strong basal plane anisotropy [Figure SI 3 inset (a)]. Figure SI3 shows THz spectra with and without the sample at 10 K which emphasizes the presence (/absence) of the gapped modes in Co4Ta2O9 (/Mn4Ta2O9).
![*Figure SI 4: THz spectra with (Mn4Ta2O9 and Co4Ta2O9) and without the samples at 10 K. Note: [Mn4Ta2O9 sample is taken from Ref (1)]*](path)
### **C) Spin gapped and Phonon lifetime in Co4Ta2O9:**
# **D) Co4Nb2O<sup>9</sup>**
# **Goldstone Mode:**
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
| |
*Figure SI 6: FFT THz spectra of Co4Nb2O<sup>9</sup> which shows gapped excitations and a spin-phonon coupled vibration which becomes pure phonon vibration above TN~28 K.*
|
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
| |
Figure SI 1: Powder X-ray diffraction of Co4Ta2O9 depicting single-phase formation of Co4Ta2O9.
|
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
Magnetic measurements were performed using a superconducting quantum interference device [SQUID-VSM (Quantum Design)] in the temperature range of 2-80 K.
# **B) Magneto-THz time-domain Spectroscopy:**
Fiber-coupled TeraK15 THz time-domain transmission spectrometer equipped with top-loading closed-cycle He cryostat and Oxford Spectramag split-coil magnet (magnetic field up to 7T) was implemented in Faraday geometry [Figure SI 2] to measure the absorption coefficient in the spectral range 0.1-2 THz with a spectral resolution of 0.0146 THz. The path of the THz radiation is purged with nitrogen gas ten minutes before and during measurement to circumvent the water absorption peaks. THz measurement generates raw data in the form of time-dependent picosecond pulses of electric fields, which are then transformed into complex-valued frequency functions via Fast Fourier transformation. Absorption Coefficient was calculated by,
where d is the thickness of the sample, Ssample and Sreference are the spectral amplitude with and without the sample, respectively. THz study on the polycrystalline sample provides an averaged-THz spectrum permitting us to observe excitations over all the spatial directions.
# **S2: Magneto-THz time-domain Experiment:**
# **A) Co4Ta2O<sup>9</sup>**
In Co4Ta2O9, there is one magnetic-field induced excitation termed as gapless/Goldstone mode in the absorption spectrum. At 0 T it is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 3.09 was obtained which suggests the presence of unquenched orbital moments in it.
## **Goldstone Mode:**
### **B) Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup>**
Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup> are isostructural members of A4B2O<sup>9</sup> family. In the magnetic-ordered state spins of Mn2+ in Mn4Ta2O<sup>9</sup> have uniaxial anisotropy spins along the c-direction whereas Co2+ in Co4Ta2O<sup>9</sup> possess strong basal plane anisotropy [Figure SI 3 inset (a)]. Figure SI3 shows THz spectra with and without the sample at 10 K which emphasizes the presence (/absence) of the gapped modes in Co4Ta2O9 (/Mn4Ta2O9).
![*Figure SI 4: THz spectra with (Mn4Ta2O9 and Co4Ta2O9) and without the samples at 10 K. Note: [Mn4Ta2O9 sample is taken from Ref (1)]*](path)
### **C) Spin gapped and Phonon lifetime in Co4Ta2O9:**
# **D) Co4Nb2O<sup>9</sup>**
# **Goldstone Mode:**
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
| |
Figure 5: a) Absorption coefficient versus THz frequency at 6 K with varying magnetic field (Offset is provided for clarity). Inset highlights the normalized force constant (kH/k0T; kH is force constant at magnetic-field H and k0T is force constant at zero magnetic-field) derived from the peak position of s⁴ gapped mode. b) Peak strength of spin-phonon mode as a function of magnetic field and c) schematic illustrating magnetic-field induced polarization.
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# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
### **Abstract**
Terahertz (THz) magnonics represent the notion of mathematical algebraic operations of magnons such as addition and subtraction in THz regime – an emergent dissipation-less ultrafast alternative to existing data processing technologies. Spin-waves on antiferromagnets with a twist in spin order host such magnons in THz regime, which possess advantage of higher processing speeds, additional polarization degree of freedom and longer propagation lengths compared to that of gigahertz magnons in ferromagnets. While interaction among THz magnons is the crux of algebra operations, it requires magnetic orders with closely spaced magnon modes for easier experimental realization of their interactions. Herein, rich wealth of magnons spanning a narrow energy range of 0.4-10 meV is unraveled in Co4Ta2O<sup>9</sup> using magneto-THz spectroscopy. Rare multitude of ten excitation modes, either of magnons or hybrid magnon-phonon modes is presented. Among other attributes, spin-lattice interaction suggests a correlation among spin and local lattice distortion, magnetostriction, and magnetic exchange interaction signifying a THz magnetoelectric effect. This unification of structural, magnetic and dielectric facets, and their magnetic-field control in a narrow spectrum unwinds the mechanism underneath the system's complexity while the manifestation of multitude of spin excitation modes is a potential source to design multiple channels in spin-wave computing based devices.
### **1.Introduction**
The collective precessions of spins in a magnetically ordered material, known as spin waves with quanta as magnons, is fundamental to the pursuit of next generation low dissipation and ultrafast device operation. The non-ohmic propagation of spin waves and terahertz (THz) frequency control of antiferromagnetic (AFM) spins are the cornerstones for areas of magnonics and THz spintronics. The current focus is on the control and manipulation of the spin-waves/magnons for information processing with their use in logic-devices, low-resistance circuits, ultrafast computing, and so on. [1,2] The magnons also play a prominent role in underlying magnetic symmetric and/or antisymmetric exchange interaction and magnetic anisotropy and derive exotic non-trivial magnetic and quantum phases such as topological phases, quantum spin liquid, etc. [3,4] As this rich magnon physics in condensed matter systems is envisaged to boost the information processing technology, the search is on for materials with robust magnons along with reliable means of their control and propagation. Magnetoelectric materials (ME) could provide such platform in a way that the non-collinear magnetic order induced electric/dielectric phase will facilitate the electric and magnetic field tunable magnons in the THz frequency range.
A popular ME system possessing non-collinear magnetic order responsible for its mutual control of magnetic and electric orders, Co4Ta2O<sup>9</sup> crystallize in α-Al2O<sup>3</sup> type trigonal structure (space group P3̅c1) with Co and Ta occupation ratio 2:1. [5] Here, Co4Ta2O<sup>9</sup> exhibits ME phase below Neel's temperature (T<sup>N</sup> ~20 K), wherein Co occupies two inequivalent sites [Co(I) and Co(II)] responsible for its magnetic order. Investigations using Neutron diffraction has established that Co2+ spins lie in the basal plane contrary (magnetic space group C2/c') to the previous notion of the spins aligning along the trigonal axis. [5,6] Another investigation employing a combination of neutron diffraction and directional magnetic susceptibility reassigned the magnetic space group in Co4Ta2O<sup>9</sup> to be C2'/c. [7] It exhibits diverse properties such as i) dielectric anomaly at T<sup>N</sup> and its enhancement with applied magnetic field, [8] ii) shearing mode of cobalt ions which couples via interlayer interaction, [9] iii) complex magnetic state (weakly ferromagnetic or/and glassy state) below 10 K, [7,10] iv) magnetic field induced electric polarization, [8] v) nonlinear ME effect above spin-flop transition for in-plane magnetic fields, [10] *etc*. All these myriads of complex structural, dielectric, and magnetic properties and intercorrelation amongst them are expected to host a variety of spin-excitations due to the noncollinear nature of its AFM order. However, any experimental demonstrations of spin wave/magnons around the 'Г' point either by inelastic neutron scattering or THz spectroscopy are yet to be made. Insights on spin excitations shed light on the detailed complexity of exchange interactions that stabilizes the magnetism.
The low-energy attribute of THz radiation makes it uniquely sensitive to probe electric and magnetic phases. This combined with its spectral range appropriate to host spin-excitation modes makes it a powerful tool to investigate the presence of spin waves as well as the dynamics of electric/dielectric medium underneath. This versatile contactless technique spans not only the energy range of variety of quasiparticles in condensed matter system such as low-lying phonon mode, charge density waves, Higg's mode, superconducting gap and so on[11–14] but also probes various symmetric and antisymmetric magnetic interactions which are the building blocks of magnetic Hamiltonian in physical sciences. Here, we report a record *ten* excitations pertaining to magnon, phonon, and hybridized magnon-phonon modes in Co4Ta2O<sup>9</sup> using magneto-THz-time domain spectroscopy [Figure 1]. Zerofield ME ground state unveiled rich wealth of spin-excitations including multiple gapped modes and a pure lattice vibration which couples with the magnetic structure at the AFM transition temperature. We demonstrated that magnetic ions' lattice displacement is vital in accounting for magnetically induced polarization. Theoretical spin-wave calculations were performed to determine the strength of exchange interactions. Evidence of optical ME effect are also presented along with the multitude of magnon and magnon-phonon modes.
### **2. Results and Discussions**
The susceptibility versus temperature data shows a Neel's temperature (TN) of 20.5 K and a complex magnetic transition at 10 K which corroborates well with the previous reports [8,15,16] [Figure 2(a) and Inset Figure 2(a)]. THz response in three different magnetic phases [Figure 2(b)], namely, 20.5 K in paramagnetic region, 13 K in AFM region, and 6 K in complex magnetic region displays distinct
features. The strength of periodic THz oscillation in higher time scale (64-74 ps) shows abrupt increase at the onset of these regions. The time scale of this periodicity is approximately 2 ps in AFM state. This feature is absent above TN.
The normalized THz peak amplitude defined as the ratio of THz electric field peak position with and without the sample, ()(,) ()(,) , displays a sudden drop of ~12 % at the T<sup>N</sup> [Figure 2(c)] depicting a sensitivity of THz electric field to the spin-order at the magnetic transition. This feature combined with a large magnetic field dependence of normalized THz electric-field peak at 6 K [Inset Figure 2(c)] are unambiguous evidence of THz ME effect in this system. Also, The THz data yields a real refractive index of ~ 4 [Inset Figure 2(d)], which agrees well with the literature. [8] The real dielectric constant [at *ω* = 0.71 THz] increases with decreasing temperature and exhibits anomalies at both the magnetic transitions at 20.5 and 10 K [Figure 2(d)], which is consistent with the behavior of magnetization data [Inset Figure 2(a)].
In Co4Ta2O9, the magnetic symmetry lowers from trigonal in the paramagnetic state to monoclinic symmetry in the AFM state. Due to a large in-plane anisotropy, spins lie in the basal plane with an in-plane canting angle of 14° between Co(I) and Co(II) ions. [7,15] Figure 3(a) depicts the temperaturedependent THz absorption spectra of Co4Ta2O<sup>9</sup> in the frequency range 0.1-2.1 THz. As is evident, a large number of resonance absorption peaks, expectedly spin wave excitations/magnons, manifest in two different regimes of the spectra. Below TN, THz absorption spectra reveals three excitations, namely, *s4*, *s5*, and *s6* (broad mode) at 0.42, 0.54, and 1.2-1.9 THz, respectively. Below 10 K, additional excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* emerge sharply at 0.17, 0.24, 0.32, 1.44, 1.57, 1.62 THz, respectively. It may be seen that these sharp excitations (*s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* ) are superimposed on *s6* mode. These additional modes in THz spectra are in accordance with the distinct wiggles in the THz electric field tail (64 to 74 ps) at 13 and 6 K corresponding to these resonances [Figure 2(b)]. Accounting all these sharp and broad modes, it may be noted that the zero-field ground state of Co4Ta2O<sup>9</sup> at 2.5 K exhibits **nine excitations** in a narrow frequency range of 0.1-2.2 THz which is significantly larger than three zero-field excitations in Co4Nb2O9. [17] This rare manifestation of closely spaced multitude magnetic excitations in the THz frequency is potentially relevant for fundamental and applied pursuits in the field of antiferromagnetic magnonics algebra. [32-33]
Now we shed light on the origin and detailed scrutiny of thus observed magnetic modes. Starting with broad mode *s6*, we observe that it continues to grow beyond magnetic ordering [Figure 3(b)]. In the paramagnetic region, the red shift in this peak position and a larger full-width half-maximum (FWHM) [Figure 3(d)] with increasing temperature are its attributes that point towards the pure phonon mode. This was confirmed in the paramagnetic state, [Figure 3(c)] where the applied field does not affect the structure and strength of this mode. In contrast, it shows profound field-induced changes in the magnetic ordered region below T<sup>N</sup> which points towards coupling of the lattice and spin waves, consequently, giving rise to magnon-phonon excitation. This is further evidenced by the deviation of FWHM from the cubic anharmonicity of phonon-linewidth [Figure 3(d)] (in accordance with phonon-phonon anharmonic model) defined as[18]
where, ω<sup>0</sup> and Г<sup>0</sup> are the mode frequency and linewidth at absolute zero temperature, respectively. This demonstration of low-lying phonon mode and its entanglement with spins via magnetic field is an important lead to unravel its ME character in a later section.
Now we turn our attention to multiple gapped excitations *s4* and *s5* which we assign to pure spinexcitation / magnon modes, for the following reasons. As the magnetic symmetry lowers, below TN, the gapped modes emerge with their origin expected in strong in-plane single-ion anisotropy. To verify this, we collected the THz spectra of Mn4Ta2O9, which is isostructural equivalent of Co4Ta2O9. Unlike Co4Ta2O9, Mn2+ spins lie along the trigonal axis in the AFM state. [19,20] Its THz spectra clearly shows the absence of '*s4* and *s5*' type gapped modes at 10 K [Figure SI 4; Supporting Information], elucidating that the origin of gapped mode to be associated with the basal in-plane single-ion anisotropy of Co4Ta2O9. Normalized force constant as a function of temperature unveils the softening of s4 mode as temperature is lowered [Inset Figure 3(a)].
The magnon and phonon lifetime is an important factor in contemplating various THz magnonics based devices. In the present case, this was calculated using energy-time uncertainty principle. [21] For the phonon excitation, its linewidth decreases with decreasing temperature below T<sup>N</sup> owing to reduced strength of thermal fluctuation, phonon-phonon scattering, and anharmonic effect [Figure 3(d)]. Phonon lifetime [Figure SI 5(a)] in magnetic ordered phase (1 ± 0.09 ps) is smaller than that in paramagnetic phase (1.83 ± 0.07 ps). This is because at T<sup>N</sup> the linewidth begins to deviate from the pure phonon vibration as this phonon couples with magnons and hence suffers additional scattering mechanism. For the gapped spin-excitation, the strength of relevant mode should strengthen as the temperature is lowered. Exact trend can be observed in Figure SI 5(b), where the spin-gapped mode (*s4*) lifetime increases as temperature is lowered implying a long coherent length in the low temperature regime with a lifetime of 17.21 ± 2.99 ps at 2.5 K.
Using the THz gapped mode, *s4*, we tried to estimate the magnetic exchange interaction and magnetic anisotropy for Co4Ta2O9. The gapped mode originates from single ion anisotropy, = 4√, where D, J, S are the single-ion anisotropy constant, nearest neighbor interaction, and spin moments, respectively. [22] We assume that the nearest neighbor interaction in isostructural Co4Nb2O9 and Co4Ta2O9 are same (JCo4Nb2O9 = -0.7 meV and DCo4Nb2O9 = 1.8 meV). [23] From THz experiments, (Egapped)Co4Nb2O9 = 3.15 meV [Supporting Information] and, (Egapped)Co4Ta2O9 = 1.72 meV. Using the above relation, the single-ion anisotropy constant (DCo4Ta2O9) was calculated to be 0.53 meV, which turns out to be less than the absolute value of nearest neighbor exchange interaction JCo4Ta2O9 = 0.7 meV. However, it is inadmissible for the following reasons: i) Co4B2O9 (B=Nb, Ta) possesses large in-plane anisotropy such that even large value of external magnetic field along c direction cannot flop the spin from basal plane, which implies that D>J [6,23,24] and, ii) as per Goodenough-Kanamori-Anderson (GKA) rules, the super exchange interaction J is proportional to t<sup>2</sup> /U, where t is effective orbital hopping and U is the Hubbard repulsion. [25,26] The first-principle studies[15] suggest that UCo4Nb2O9 < UCo4Ta2O9 and Co are more localized in Co4Ta2O9, which implies a small spatial extent of the electron wavefunction and a reduced overlap between adjacent atomic orbital; hence, JCo4Ta2O9 < JCo4Nb2O9. Therefore, our assumption in similarity of nearest neighbor interaction does not hold suggesting that these systems behave differently. It is required that DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9.
$$H = H\_c + H\_{p,b,pb} + \Sigma\_{Co(l)} D \left( S\_{l\text{z}}^{l} \right)^2 + \Sigma\_{Co(l\text{I})} D \left( S\_{l\text{z}}^{\text{II}} \right)^2 + \Sigma\_{\text{cf,j}>} D\_{l\text{j}}. \left( \text{S}\_{l} \times \text{S}\_{\text{j}} \right) \tag{2}$$
where H<sup>c</sup> is the Heisenberg term for the nearest and next nearest neighbor along c; Hp,b,pb are the Heisenberg terms for the planar, buckled, and planar-buckled networks. Third and fourth term represent single-ion in plane anisotropy where I and II denote two inequivalent sites of cobalt [Co(I) and Co(II) sites] and Dij represent the DM interaction.
Here, the magnetic exchange interaction, single-ion anisotropy strength and high-resolution observations of magnons at Г point by THz spectroscopy underpins the magnetic structure and the magnonic dynamics. To get insights of the Brillouin zone, beyond the Г point, spin-wave calculations were performed using the above spin Hamiltonian in SPINW. [27] In-plane magnetic structure was considered as revealed by neutron diffraction experiments [28] and using the THz Г point data, the magnetic exchange interactions were computed. The average powder spin-wave spectra for Co4Nb2O<sup>9</sup> [Figure 4(a)] shows gapped and gapless excitations which matches accurately with the Г point of THz data. The magnetic exchange interactions (JCo4Nb2O9=-0.6 meV and DCo4Nb2O9=1.6 meV) too agree well with those depicted by the inelastic neutron experimental results. [28] Using magnetic structure of temperature above 10 K for Co4Ta2O<sup>9</sup> [29] , the powder averaged spin-wave calculations yielded gapped excitations and magnetic exchange interactions JCo4Ta2O9=-0.4 meV and DCo4Ta2O9=1.1 meV. These are at lower energy and weaker, respectively, as compared to those of Co4Nb2O<sup>9</sup> and in perfect agreement with the condition DCo4Ta2O9 > JCo4Ta2O9 and JCo4Ta2O9 < JCo4Nb2O9 [Figure 4(b)].
In contrast to above-mentioned low-energy spin-excitations, the higher energy modes (> 5 meV) obtained from spin-wave calculations and THz experimental data do not agree for either of Co4Ta2O<sup>9</sup> and Co4Nb2O9. This is because the spin Hamiltonian accounts only for spin-excitations while the phonon contribution as well as spin-lattice coupling terms are not incorporated. This deviation is further verification of broad mode s<sup>6</sup> being [Figure 3(a)] a spin-phonon coupled mode. As Nb is systematically replaced by Ta in Co4Ta2O9 [Figure 4(c)], the gapped mode (*s4*) gradually shifts to higher energies owing to gradual enhancement of the magnetic exchange interactions (J and D) [Figure 4(d)]. Thus, magnetic exchange interactions play a prominent role in driving the spinexcitations.
Now, to shed light on the origin of excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* (Figure 3a), it is imperative to invoke comparison of some relevant properties of Co4Ta2O<sup>9</sup> from Co4Nb2O9. As noted in previous section, weaker exchange interactions in Co4Ta2O<sup>9</sup> compared to that in Co4Nb2O<sup>9</sup> render it a softer magnet. In the latter, there has been no indication of structural transition even at 5 K, [6,7,16,24] though the possibility of local lattice distortion and magnetostriction was never ruled out. [15] In the case of Co4Ta2O9, however, the structural transitions, larger local lattice distortions and magnetostriction becomes more promising owing to its sensitivity to change in magnetic structure due to weaker magnetic interactions. This deviation of Co4Ta2O<sup>9</sup> from Co4Nb2O9, below 10 K, is the source of nonlinear ME response[30] and complex magnetic state[29,30] (in χ-T curve) in the former. However, its magnetic structure is reported only down to a minimum temperature of 15 K, [29] which is higher than the complexity-rich magnetism regime of below 10K. It is this low temperature regime, wherein the complex magnetic state, magnetostriction and local lattice distortion in Co4Ta2O<sup>9</sup> create entangled magnetic moments and lattice vibrations, which consequently give rise to six spin excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* , and *s6<sup>c</sup>* in the THz spectra [Figure 3(a, b)]. No such excitations have been observed in Co4Nb2O9. The Co4Ta2O9, thus, hosts a ground for unique correlation between magnetic exchange interactions, local lattice distortion, and magnetostriction phenomena.
As Co4Ta2O<sup>9</sup> is a magnetic-field induced ME system, it is imperative to understand the magneticfield control of THz spin-wave excitation and the ME character. Magnetic field dependence of THz spectra is plotted in Figure 5 (a). Spin-excitations *s1*, *s2*, *s3*, *s6<sup>a</sup>* , *s6<sup>b</sup>* and *s6<sup>c</sup>* get suppressed with increasing magnetic field which reflects the expected magnetically malleable structure of Co4Ta2O9. At 2T, all these excitations annihilate while *s4* and *s5* shift to higher frequencies. Derived from the gapped mode (*s4*), the normalized force constant (kH/k0T; k<sup>H</sup> is the force constant at magnetic-field H and k0T is force constant at zero magnetic-field) indicates the hardening of the magnetic coupling between neighboring spins as a function of increasing magnetic-field [Inset Figure 5(a)]. As magnetic field exceeds 3 T, mode *s7* appears in the detectable range of our THz spectra. This excitation, identified as goldstone (/gapless) mode, appears in the microwave region due to spontaneous symmetry-breaking at T<sup>N</sup> and it shifts linearly towards higher THz frequency with increasing field [Figure 5(a) inset]. This gapless mode is shown in the spin-excitation simulations as well as in the THz spectra. The behaviour of peak frequency of this gapless excitation yields Landé g-factor g=3.09 for Co4Ta2O<sup>9</sup> and g=2.68 for Co4Nb2O<sup>9</sup> [Figure SI 3 and 7, Supporting Information]. Clearly the value of Landé g-factor suggests unquenched orbital moments both in Co4Ta2O<sup>9</sup> and Nb counterpart.
The mechanism of the field-induced polarization in this series has been of great interest to understand the induced ME character. Knowledge of spin-phonon mode and its magnetic-field dependence from THz spectroscopy can provide valuable insights into this process. At 6 K, the peak strength of spinphonon mode of Co4Ta2O<sup>9</sup> increases with an increase in magnetic field [Figure 5 (a, b)] which is associated with the field induced electric polarization. As lattice distortion, magnetostriction, and spin-phonon coupling are highly inter-related in these materials, the induced electric polarization can be explained as follows. At zero magnetic-field, below TN, the presence of spin-phonon coupling suggests the entanglement of spin and lattice. However, the Co ions hold two inequivalent sites Co(I) and Co(II) which are in centrosymmetric positions with respect to trigonal axis, hence, lacks any net polarization. However, on the application of magnetic-field the strength of spin-phonon coupling increases [Figure 5 (b)]. This expectedly displaces the magnetic ions from their centrosymmetric positions, resulting in the manifestation of magnetically induced polarization. This scenario of fieldinduced displacement of Co-ion is depicted in Figure 5 (c) As the mass of Ta is larger than Nb (ions to which Co-ions are bonded), the effective displacement in case of Co4Ta2O<sup>9</sup> is less than that in Co4Nb2O9. This also explains why magnetic field induced polarization in Co4Nb2O<sup>9</sup> is more as compared to Co4Ta2O9. The THz characteristic features of the magnetic resonances too possess this mass effect where with increasing concentration of Nb the resonances are shifting to higher THz frequency [Figure SI 8]. To surmise, this entire mechanism based on modulation of magnetic exchange interactions provides a pathway to control the energy of spin-gapped modes, spin-phonon coupled mode, and phonon mode whereas the effective lattice displacement of cobalt ions is responsible for magnetic-field induced polarization.
From the applied pursuit, the wave nature of magnons (spin-waves) offers a pathway to encode information in amplitude, phase, or the combination of both [Figure 6(a)] which is at core of nonBoolean algebra driven spin-wave computation.[31-33] The spin excitations in THz regime offer two novel characteristics, namely, the THz magnons propagate with ultra-low dissipation as it does not involve flow of electric charge, and with ultrafast speeds, both of which are much desired attributes for futuristic technologies. The existence of multiple magnon modes, as demonstrated in this work, is a pre-requisite for efficient data transfer spin-wave logic operations. In another facet, in the direction of spin-wave computation the multitude of spin waves in Co4Ta2O<sup>9</sup> present itself as a potential candidate for multifrequency channeling in a narrow bandwidth of 0.1 – 2.5 THz. Such multi-channels allow for simultaneous transmission of multiple signals at different frequencies, increasing the overall data capacity. A schematic serving as a proof-of-concept for terahertzmagnonics-electronics multifrequency channeling is shown in Figure 6(b). Here, the frequency of THz radiation drives the resonant condition corresponding to that magnon which carries the information and provides the output as electronic signal via a spin wave to charge converter. Experimental realization of this concept requires systems having multiple magnons or other hybrid modes in THz regime. In this work, the magnetoelectric systems with non-collinear magnetic order prone to strong spin-lattice interactions provide appropriate platform for THz magnonics.
### **3. Conclusions**
A myriad of low-energy excitations in Co4Ta2O9 probed using magneto-THz spectroscopy evidence a remarkable host magnetoelectric system with a rare multitude of ten excitations comprising of magnon, phonon, and hybridized magnon-phonon modes. The THz probes and non-collinear magnetism further combine to unravel a THz magnetoelectric effect; a novel functionality not known to manifest at such high frequencies so far. The origin of magnon in a strong basal-plane anisotropy emphasized the structural, magnetic and electronic controls to all excitation modes. These experimental data are supported by theoretical spin-wave computations along with quantifiable strength of magnetic exchange interactions. Furthermore, magnetic-field induced enhanced spinphonon coupling corroborates the proposition of magnetic-ion lattice displacement being the dominant factor for the ME behavior in this family of systems. Our results emphasize that the powderaveraged THz absorption spectrum acquired on a polycrystalline sample is not a limitation, rather an advantage over single crystals to facilitate faster screening of magnetic materials for spin-wave excitation mode, thus, expediting the search for potential materials for THz magnonic applications.
# **Supporting Information**
Supporting Information is available from the Wiley Online Library or from the author.
### **Acknowledgements**
D.S.R. thanks the Science and Engineering Research Board (SERB), Department of Science and Technology, New Delhi, for financial support under research Project No. CRG/2020/002338. K.S. thanks SERB for financial support under research Project No. CRG/2021/007075. B.S.M thanks Prime Minister Research Fellowship (PMRF; 0401968) funding agency, Ministry of Education, New Delhi, and Dr. Sunil Nair for providing Mn4Ta2O<sup>9</sup> sample.
### **Conflict of Interest**
Authors declare no conflict of interest.
# **Data Availability Statement**
The data that support the findings of this study are available from the corresponding author upon reasonable request.
## **References**
- [19] N. Narayanan, A. Senyshyn, D. Mikhailova, T. Faske, T. Lu, Z. Liu, B. Weise, H. Ehrenberg, R. A. Mole, W. D. Hutchison, H. Fuess, G. J. McIntyre, Y. Liu, D. Yu, *Phys. Rev. B* **2018**, *94*, 134438.
# **SUPPORTING INFORMATION**
# **Myriad of Terahertz Magnons with All-Optical Magnetoelectric Functionality for Efficient Spin-Wave Computing in Honeycomb Magnet Co4Ta2O<sup>9</sup>**
*Brijesh Singh Mehra<sup>1</sup> , Sanjeev Kumar<sup>1</sup> , Gaurav Dubey<sup>1</sup> , Ayyappan Shyam<sup>1</sup> , Ankit Kumar<sup>1</sup> , K Anirudh<sup>1</sup> , Kiran Singh<sup>2</sup> , Dhanvir Singh Rana<sup>1</sup> \**
1 Indian Institute of Science Education and Research Bhopal, 462066, India <sup>2</sup>Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India Email: [dsrana@iiserb.ac.in](mailto:dsrana@iiserb.ac.in)
# **S1: Experimental Details:**
# **A) Sample Preparation and Magnetic Characterization:**
Polycrystalline sample of Co4Ta2O<sup>9</sup> was prepared from solid state reaction route. The stoichiometric amount of Co3O<sup>4</sup> and Ta2O<sup>5</sup> (99.99% purities) powders were ground and calcined in air at 1000°C for 10 h. Sample was reground, pressed, and sintered at 1100°C for 10 h. The outcome was phasepure disc-shaped sample (diameter ~ 7 mm & thickness ~ 600 µm). Phase purity was confirmed at room temperature by PANalytical ''Empyrean' powder X-ray diffractometer (PXRD) with Cu K<sup>α</sup> radiation (1.54 Å). [Figure SI 1] Rietveld refinement analysis provided a good fit with χ<sup>2</sup> =1.8 and lattice parameters a=b=0.5173 nm, and c=1.415 nm.
Magnetic measurements were performed using a superconducting quantum interference device [SQUID-VSM (Quantum Design)] in the temperature range of 2-80 K.
# **B) Magneto-THz time-domain Spectroscopy:**
Fiber-coupled TeraK15 THz time-domain transmission spectrometer equipped with top-loading closed-cycle He cryostat and Oxford Spectramag split-coil magnet (magnetic field up to 7T) was implemented in Faraday geometry [Figure SI 2] to measure the absorption coefficient in the spectral range 0.1-2 THz with a spectral resolution of 0.0146 THz. The path of the THz radiation is purged with nitrogen gas ten minutes before and during measurement to circumvent the water absorption peaks. THz measurement generates raw data in the form of time-dependent picosecond pulses of electric fields, which are then transformed into complex-valued frequency functions via Fast Fourier transformation. Absorption Coefficient was calculated by,
where d is the thickness of the sample, Ssample and Sreference are the spectral amplitude with and without the sample, respectively. THz study on the polycrystalline sample provides an averaged-THz spectrum permitting us to observe excitations over all the spatial directions.
# **S2: Magneto-THz time-domain Experiment:**
# **A) Co4Ta2O<sup>9</sup>**
In Co4Ta2O9, there is one magnetic-field induced excitation termed as gapless/Goldstone mode in the absorption spectrum. At 0 T it is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 3.09 was obtained which suggests the presence of unquenched orbital moments in it.
## **Goldstone Mode:**
### **B) Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup>**
Co4Ta2O<sup>9</sup> and Mn4Ta2O<sup>9</sup> are isostructural members of A4B2O<sup>9</sup> family. In the magnetic-ordered state spins of Mn2+ in Mn4Ta2O<sup>9</sup> have uniaxial anisotropy spins along the c-direction whereas Co2+ in Co4Ta2O<sup>9</sup> possess strong basal plane anisotropy [Figure SI 3 inset (a)]. Figure SI3 shows THz spectra with and without the sample at 10 K which emphasizes the presence (/absence) of the gapped modes in Co4Ta2O9 (/Mn4Ta2O9).
![*Figure SI 4: THz spectra with (Mn4Ta2O9 and Co4Ta2O9) and without the samples at 10 K. Note: [Mn4Ta2O9 sample is taken from Ref (1)]*](path)
### **C) Spin gapped and Phonon lifetime in Co4Ta2O9:**
# **D) Co4Nb2O<sup>9</sup>**
# **Goldstone Mode:**
In Co4Nb2O9, like Co4Ta2O9, at 0 T the gapless excitation is not present but as the magnetic-field is increased it linearly blue shifts and appears in our detectable spectrum. Using its frequency versus magnetic-field trace, Landé g-factor of 2.68 was obtained which suggests the presence of unquenched orbital moments in it as well.
# **References:**
| |
Figure S7. (a) Volume-temperature and (b) volumetric thermal expansion coefficienttemperature relations in TiRhBi, TiPtSn and NbPtTl, respectively.
|
# **Screening of half-Heuslers with temperature-induced band convergence and enhanced thermoelectric properties**
#### **Corresponding Author:**
#### **Abstract**
Enhancing band convergence is an effective way to optimize the thermoelectric (TE) properties of materials. However, the temperature-induced band renormalization is commonly ignored. By employing the recently-developed electron-phonon renormalization (EPR) method, the nature of band renormalization in half-Heusler (HH) compounds TiCoSb and NbFeSb is revealed, and the key factors for temperatureinduced conduction band convergence in HH are found out. Using these as the screening criteria, 3 out of 274 HHs (TiRhBi, TiPtSn, NbPtTl) are then stood out from our *MatHub-3d* database. Taking TiPtSn as the example, it shows the conduction band convergence at mid-high temperature, and further resulting in enhanced Seebeck coefficient *S*: *e.g.*, at 600 K with electron concentration 10<sup>20</sup> cm-3 , the predicted *S* with and without renormalized band is 352.83 μV/K and 289.52 μV/K, respectively. Herein, the former is closer to our measurement value of 338.79 μV/K. Besides, the effective masses obtained from calculation and experiment are both enlarged with temperature, indicating the existence of band convergence. Our work demonstrates for the first time the significance of adding the temperature effect on electronic structure in the design of potential high-performance TE materials.
#### **Introduction**
Thermoelectric (TE) materials have attracted enormous attention by the advantages in refrigeration and waste heat recovery. [1,2] The TE performance of a material is characterized by the dimensionless figure of merit *ZT* = *S* 2 *σT*/(*κ*<sup>e</sup> + *κ*L), where *S* is the Seebeck coefficient, *σ* is the electrical conductivity, *T* is the absolute temperature, *κ*<sup>e</sup> and *κ*<sup>L</sup> are the electronic and lattice contributions to the total thermal conductivity *κ*, respectively. Obviously, obtaining a high *ZT* requires a high *S*, a high *σ* and a low *κ* simultaneously. But it is a great challenge because of the strong coupling of these parameters.[3,4] The most commonly pursued approaches to enable high *ZT* include the manipulation of the density of states (DOS) by band engineering for high power factor (*S* 2 *σ*),[5] such as doping,[6-8] introducing resonant states in the vicinity of the Fermi level,[9,10] and achieving band convergence/degeneracy,[11-19] *etc*. Especially, band engineering to converge multiple band valleys has been demonstrated to be a robust strategy for achieving a high power factor,[11] and thus it is good for TE materials.[20]
Temperature is one of the intrinsic factors for affecting band convergence and further the TE properties. For instance, in PbX (X = S, Se, and Te), the change of band gap is positively correlated with temperature, and the convergence of the valence band maximum (VBM) at **L** and **Σ** occurs at a high temperature.[21] For *n*-type CoSb<sup>3</sup> skutterudites, a secondary conduction band with 12 conducting carrier pockets (which converges with the primary band at high temperatures) is responsible for its extraordinary TE performance.[22] In principle, the temperature effect on the band structure is related to two major mechanisms:[23] the lattice thermal expansion, and the lattice dynamics, such as phonon-induced atomic vibrations. Generally, the latter is defined as the electron-phonon renormalization (EPR).[24-27] So far, the temperaturedependent band gap in lots of semiconductors has been verified in experiments and theoretical calculations.[23,28-39] Recently, we have developed the state-of-art EPR method, and applied it to study the temperature effect on the band structure in traditional semiconductors,[23] TE skutterudites[34,35] and Mg2Si1-*x*Sn*x*, [36] as well as optoelectronic perovskites[37,38] and pyrite FeS2. [39] Especially for MAPbI<sup>3</sup> perovskite, the temperature-induced band dispersion (that is, carrier effective mass) renormalization and further its effect on the charge mobility have been firstly discussed.[37] However, the design and screening of functional materials based on the temperature-dependent band structure has been barely as yet. For TE materials, there are two questions: (1) how does the temperature affect the band convergence and what is its nature; (2) can we efficiently screen some materials with temperature-induced band convergence and so that excellent TE properties.
In order to answer the questions above, the half-Heusler (HH) compounds are studied as the examples in present work. Due to the good TE properties, HHs have emerged as the potential TE materials over the past few decades.[40-42] However, the temperature-dependent band structure, and the possible temperature-induced band convergence which is beneficial to enhance TE properties, have never been fully explored. Here, TiCoSb and NbFeSb are firstly selected as the examples, and we apply the multiple methods[23,26] of EPR to reveal the different temperature responses on the electronic structure properties of the 1st and 2nd conduction band minimum (CBM1, CBM2) in two systems. The two key factors for conduction band convergence at a given temperature for HHs (*ABX* type) are further found out: (1) *A* and *B* sites elements both contribute to the CBM2, while CBM1 mainly comes from *A*; (2) the energy difference between CBM2 and CBM1 should be small enough by the calculation without temperature effect. Using these as the criteria, 3 HHs, namely TiRhBi, TiPtSn and NbPtTl, are screened out from our *MatHub-3d* database.[43,44] They all have the conduction band convergence at mid-high temperature by the further EPR calculations. Taking TiPtSn as the example, the predicted Seebeck coefficient is obviously improved at mid-high temperature. Finally, our experimental transport measurement of TiPtSn verifies the theoretical results. Our work is significant as considering the EPR effect, which is a full understanding of the electronic structure and an accurate prediction of electrical transport at a given temperature. We provide a clearer route forward to the band engineering in the HHs for further improvement of *ZT*.
#### **Result and discussions**
intermetallic compound, which is usually expressed by the chemical formula *ABX* with the space group of F4̅3m. For TE HHs, *A* is commonly an early transition (IIIB or IVB) or rare-earth metal, *X* is a main group element (IVA or VA), and *B* is normally a transition metal between *A* and *X* in the Periodic Table.[40] The high symmetry of this kind of material makes it having a large band degeneracy and a large DOS. Therefore, it often has the high electrical transport properties and becoming a kind of TE material with full development prospects.[41,42] Among the typical HHs, TiCoSb and NbFeSb are selected in this work to study the temperature-dependent band structure.
By using the quasi-harmonic approximation (QHA),[45] the lattice parameters of TiCoSb and NbFeSb at different temperatures are determined (Figure S1 in the Supporting Information). Then, the band structures of TiCoSb and NbFeSb at different temperatures are calculated by using the Allen-Heine-Cardona (AHC) theory[26] (Figures S2 and S3), and the cases at 700 K as well as without temperature effect (defined as DFT) are shown in Figure 1a. As increasing to 700 K, the energy difference *E*<sup>c</sup> between CBM1 and CBM2 at **X** point increases from 0.12 eV to 0.20 eV for TiCoSb, while it decreases from 0.68 eV to 0.48 eV for NbFeSb. Although the so large *E*<sup>c</sup> (comparing with 2*k*B*T*) indicates no band convergence in two HHs, the opposite phenomenon is drawn our attention. As analyzed in our previous works, [34-39] the temperature-induced band gap change or band convergence is due to the different responses of the band energy levels to the temperature. More fundamentally, it originates from the destruction of chemical bonds caused by the temperature-induced lattice expansion and vibration. Thus, we firstly examine the chemical characteristics of CBM1 and CBM2 in TiCoSb and NbFeSb by taking advantages of the wavefunction at CBM (Figure 1b), the projected band structure (Figure S4a) and band-resolved projected crystal orbital Hamilton (pCOHP, Figure S4b). It is found that the CBM1 of TiCoSb and CBM2 of NbFeSb mainly come from the contributions of *A* (Ti/Nb) and *B* (Co/Fe) elements, showing the antibonding between *A* and *B*. Differently, only *A* element Ti or Nb contributes to the CBM2 of TiCoSb or CBM1 of NbFeSb. As mentioned before,[37,38] the antibonding is unstable and its energy would decrease by considering the temperature-induced bond change. Further understanding the temperature effect, the wavefunction of structure at 700 K is shown in Figure 1c. To obtain the structure as including the EPR effect at 700 K, the one-shot method is used.[23] Interestingly, the morphology and distribution of wavefunctions for CBM2 of TiCoSb and CBM1 of NbFeSb at 700 K are almost the same to these without temperature effect (Figure 1b). However, these for CBM1 of TiCoSb and CBM2 of NbFeSb are affected more severely, showing a larger electronic structural disorder. Therefore, the antibonding states are broken, and the energy level of CBM1 of TiCoSb (CBM2 of NbFeSb) drops down with temperature, while that of CBM2 of TiCoSb (CBM1 of NbFeSb) has relatively small changes (Figure S5), and resulting to the increase (decrease) of *E*c. The case in NbFeSb is purposeful, however, there is no band convergence occurred even at high temperature, which should be due to the large *E*<sup>c</sup> even that without temperature effect (0.68 eV).
The band renormalization by temperature in TiCoSb and NbFeSb gives us the inspiration. That is, the HHs may have the conduction band convergence on a **k**-point band edge at a given temperature if (1) the antibonding of *A* and *B* elements mainly contributes to the CBM2, and CBM1 only comes from the contribution of *A* element; (2) the energy difference between CBM1 and CBM2 by the calculation without temperature effect is small. In the next section, we will screen the HHs following these criteria.
**Screening HHs with band convergence.** Figure 2 is the workflow of HHs screening. In order to obtain the HHs with semiconductor characteristic and structural stability, the band gap *E*<sup>g</sup> > 0.1 eV and phonon frequency *ω* > 0 are added as the first two screening criteria, and we get 109 out of the 274 HHs from the *MatHub-3d* database. Further considering the screening criteria for band convergence as discussed above, 3 HHs are stood out, which are TiRhBi, TiPtSn and NbPtTl. Specifically, 10*k*B*T* at 300 K (~0.26 eV) is used as the threshold value of *E*<sup>c</sup> for the calculation without temperature effect. The corresponding chemical characteristic analysis of three systems are shown in Figure S6. Then, the band structures at different temperatures for the three HHs are calculated, and they all exhibit band convergence at mid-high temperature indeed (Figures S7-S10). As the example, the electrical transport prediction and corresponding experimental measurement in TiPtSn are finally carried out to show the effect of temperature-induced band convergence on TE properties. The details of TiPtSn are discussed in the next section. In addition, 109 HHs' band structures at different temperatures are calculated, and will be stored in *MatHub-3d* for the future study.
**Temperature-dependent band structure and electrical transport properties in TiPtSn.** The band structures of TiPtSn at 300 K and 700 K are shown in Figure 3a. The case without temperature effect is also plotted for comparing. As expected, the energy of CBM1 and CBM2 at **X** point is obviously overlapped at 700 K. In order to further explore the temperature range of band convergence, the energy difference *E*<sup>c</sup> between CBM1 and CBM2 as the function of temperature is examined (Figure 3b). With the increase of temperature, *E*<sup>c</sup> decreases gradually and then increases. The effective band convergence occurs at ~ 340 K and above, where *E*<sup>c</sup> < 2*k*B*T*. Because the energy level of CBM2 is even lower than that of CBM1 at high temperature (Figure S8), *E*<sup>c</sup> increases at > 700 K. The corresponding results for TiRhBi and NbPtTl are shown in Figures S11 and S12, which have the similar temperature law of *E*c.
In order to confirm the improvement of TE properties by band convergence, the electrical transport properties in TiPtSn are carried out based on the Boltzmann transport theory and relaxation time approximation.[46] To simplify the calculation of relaxation time, the constant electron-phonon coupling such as deformation potential theory is used.[47-50] Notably, it is our first time that using the renormalized electron energy and velocity to predict the transport parameters. It is updated in our *TransOpt* code[51] and the details can be found in the section of Method. Comparing with other electrical transport parameters, the Seebeck coefficient *S* is highly dependent on the band structure and less dependent on the relaxation time, thus we mainly focus on it. Figures 4a exhibits the predicted *S* as the function of electron concentration at 700 K. Due to the degenerate bands and thus larger DOS near the Fermi level, the *S* with 700 K band is larger than that with 300 K as well as without temperature effect. Further using the *S* and the single parabolic band model, [52] the predicted effective mass enlarges as considering the temperature effect. The similar behavior is found for transport at 300 K (Figure S13). Especially, the effective mass increases from 2.79 *m*<sup>0</sup> at 300 K to 6.49 *m*<sup>0</sup> at 700 K (*m*<sup>0</sup> is the bare electron mass). Meanwhile, the temperaturedependent *S* at different electron concentration (Figure 4b) is examined. The temperature-induced band convergence makes *S* enlarged at mid-high temperature, *e.g.*, at 600 K with 10<sup>20</sup> cm-3 , the *S* with and without renormalized band is 352.83 μV/K and 289.52 μV/K, respectively. In particular, due to the band gap reduction with temperature (Figure S9), there is a significant bipolar effect near ~800 K with 10<sup>20</sup> cm-3 as considering the renormalized band (red-solid symbol in Figure 4b). Therefore, the temperature effect plays an important role on HH's band structure and even electrical transport, and it should not be neglected in the theoretical calculation.
To further verify the theoretical screening and prediction, the samples of TiPtSn and its 1% Sb doping TiPtSn0.99Sb0.01 are synthetized (X-ray diffraction patterns in Figure S14a), and the electrical transport properties are then measured. As shown in Figure 4c, the experimental *S* of TiPtSn increases from 300 K to 500 K, afterwards, it is almost unchanged until obviously decreasing > 750 K, resulting in a bipolar effect. The *S* of doping 1% Sb TiPtSn0.99Sb0.01 with the higher electron concentration has the similar temperature law, while the value becomes smaller. Because of the larger electrical conductivity in TiPtSn0.99Sb0.01 (Figure S14b), its power factor maximum is somehow larger than that of TiPtSn (Figure S14d). Besides the electrical transport properties, the thermal part is also measured, and finally the *ZT* is predicted (Figure S15). Although the power factor and further the *ZT* in TiPtSn systems are small as comparing to other outstanding TE materials, the purpose of our experiment is to illustrate the temperature-induced band convergence and the enhanced electrical transport properties caused by it. It is worth noting that the predicted *S* with renormalized band is closer to the experiment one especially at mid temperature. For example: the measured *S* at ~ 370 K is 281.56 μV/K with 2.2 × 10<sup>20</sup> cm-3 in TiPtSn (Figure 4c and 4d) and 155.33 μV/K with 1.2 × 10<sup>21</sup> cm-3 in TiPtSn0.99Sb0.01 (Figures 4c and S16), respectively; the calculated values at the same temperature are ~ 229.80 μV/K with 1 × 10<sup>20</sup> cm-3 and ~ 110.76 μV/K with 1 × 10<sup>21</sup> cm-3 . Furthermore, the temperature dependence of the effective mass *m* \* in TiPtSn and TiPtSn0.99Sb0.01 are deduced from the measurements of the electrical transport (Figures 4d and S16). Especially for TiPtSn, the *m* \* enlarges with temperature, indicating the increase of DOS near the Fermi level, which is also demonstrated by above calculation. Therefore, the experiment confirms the theoretical prediction, that is, the increase of temperature causes the conduction band convergence in TiPtSn, and further the enlarged DOS and Seebeck.
Worthy of note is that the *m* \* in TiPtSn follows ~ *T* 0.77, and the temperature dependence of *m* \* in TE materials is widely known for a long time, such as in lead chalcogenides with ~ *T* 0.4 . [53,54] However, there is no in-depth theoretical explanation or full understanding. As performing the EPR calculation, our work is the first time that revealing the origin of temperature dependence of *m* \* , and more detailed studies in more TE materials will be carried out in the future.
#### **Conclusions**
In this work, we propose a new strategy that is optimizing TE performance through screening HH compounds with possible temperature-induced band convergence. Taking the TiCoSb and NbFeSb as the examples, two key factors for conduction band convergence at a given temperature are revealed. Using these as the criteria, TiRhBi, TiPtSn, and NbPtTl are then screened out from 274 HHs in *MatHub3d*, and they all show the conduction band convergence at mid-high temperature. Further the electrical transport calculation definitely shows the enlarged Seebeck coefficient in TiPtSn, which is due to the temperature-induced band convergence. The finally experimental measurement verifies the theoretical results. Hence, the temperature plays an important role on the band structure and further the electrical transport, and cannot be neglected in theoretical prediction. Our work has the deep understanding of temperaturedependent electronic structures, and screen out the HHs with band convergence and fine electrical transport properties. It can provide a clearer route forward to band structure engineering as well as the extension to more studies of the basic TE properties in the HHs.
#### **Methods**
**Computational model and parameter setting.** The band structure is influenced by the temperature effect from two aspects: the lattice thermal expansion and phonon vibration.[23] In this study, the QHA[45] method is used to determine the lattice constant at a given temperature *T*, which is implemented by using the Vienna *ab initio* Simulation Package (VASP)[55,56] and Phonopy code.[57] Wherein, Perdew-Burke-Ernzerhof (PBE)[58] type exchange-correlation functional is used, the projector augmented wave method[59] is applied with the plane-wave cutoff energy of 520 eV, and the 4 × 4 × 4 supercell is used for phonon calculation. Therefore, the structure with lattice parameters at *T* is obtained (Figures S1 and S7). Then, in order to consider the contribution from phonon vibration, the many-body perturbation approach: AHC theory is employed as implemented in ABINIT package.[60] In the framework of AHC theory, the electron-phonon coupling is evaluated by the density functional perturbation theory (DFPT).[61] The electron-nucleus interactions are described by using the normconserving pseudopotentials[62] with the plane-wave cut off of 35 Hartree, **k**-mesh of 6 × 6 × 6 and **q**-mesh of 10 × 10 × 10. After the DFPT calculation at PBE level, the electron self-energy Σ () for the *n* th band and the wave-vector **k** at *T* can be determined by the AHC theory[26]
$$\Sigma\_{n\mathbf{k}}^{\rm FM}(T) = \Sigma\_{m,\nu} \int \frac{d\mathbf{q}}{\Omega\_{BZ}} |g\_{mn\nu}(\mathbf{k}, \mathbf{q})|^2 \left[ \frac{n\_{\mathbf{q}\nu}(T) + f\_{m\mathbf{k}+\mathbf{q}}(\varepsilon\_{\mathbf{F}}, T)}{\varepsilon\_{n\mathbf{k}} - \varepsilon\_{m\mathbf{k}+\mathbf{q}} + \omega\_{\mathbf{q}\nu} + i\eta} + \frac{n\_{\mathbf{q}\nu}(T) + 1 - f\_{m\mathbf{k}+\mathbf{q}}(\varepsilon\_{\mathbf{F}}, T)}{\varepsilon\_{n\mathbf{k}} - \varepsilon\_{m\mathbf{k}+\mathbf{q}} - \omega\_{\mathbf{q}\nu} + i\eta} \right], \qquad (2)$$
$$\Sigma\_{n\mathbf{k}}^{\rm DW}(T) = \Sigma\_{m,\nu} \int \frac{d\mathbf{q}}{\Omega\_{BZ}} \left[ 2n\_{\mathbf{q}\nu}(T) + 1 \right] \frac{g\_{mn\nu}^{2\beta\mathcal{W}}(\mathbf{k}, \mathbf{q})}{\varepsilon\_{n\mathbf{k}} - \varepsilon\_{m\mathbf{k}+\mathbf{q}}}. \tag{3}$$
Where + (, ) and () are the Fermi-Dirac and Bose-Einstein occupation functions with *T* and the Fermi level . The integration is performed over the **q**-points in the Brillouin zone (BZ) of volume Ω, is the phonon frequency on the branch and wave-vector **q**, is a positive real infinitesimal. 2,(, ) is an effective matrix element that, within the rigid-ion approximation, can be expressed in terms of the standard first-order (, ) matrix elements by exploiting the invariance of the quasi-particle energies under infinitesimal translation. The renormalized electron energy ̃ at *T* is the sum of the bare Kohn-Sham eigenvalue and the real part of Σ () as following:
By using the ̃, the electrical transport parameters as considering the electron energy renormalization can be determined under the Boltzmann transport theory as implemented in *TransOpt*[51] code. Specifically, electrical conductivity and Seebeck coefficient *S* can be calculated as following:[50,51]
\sigma\_{\alpha\beta}(\varepsilon\_F, T) = \sum\_{n} \int \frac{d\mathbf{k}}{\Omega\_{BZ}} \tilde{\upsilon}\_{n\mathbf{k}\alpha} \tilde{\upsilon}\_{n\mathbf{k}\beta} \,\tilde{\tau}\_{n\mathbf{k}} \left[ -\frac{\partial \dot{\tilde{f}}\_{n\mathbf{k}}(\varepsilon\_F, T)}{\partial \varepsilon\_{n\mathbf{k}}} \right], \tag{5}
$$S\_{\alpha\beta}(\varepsilon\_F, T) = \frac{1}{eT} \sigma\_{\alpha\beta}(\varepsilon\_F, T)^{-1} \sum\_{n} \int \frac{d\mathbf{k}}{\Omega\_{\mathbf{BZ}}} \tilde{\boldsymbol{\nu}}\_{n\mathbf{k}a} \tilde{\boldsymbol{\nu}}\_{n\mathbf{k}\beta} \tilde{\boldsymbol{\tau}}\_{n\mathbf{k}} (\varepsilon\_F - \tilde{\varepsilon}\_{n\mathbf{k}}) \left[ -\frac{\partial f\_{n\mathbf{k}}(\varepsilon\_F, T)}{\partial \boldsymbol{\xi}\_{n\mathbf{k}}} \right], \qquad (6)$$
where the electron group velocity ̃, the electron relaxation time ̃, and the Fermi-Dirac occupation function ̃ are obtained as replacing the with ̃. Especially, ̃ is calculated by using the deformation potential approximation, which is written as[49-51]
$$\frac{1}{\tau\_{\text{nk}}} = \frac{2\pi k\_B T D\_{\text{def}}^2}{\hbar \mathcal{C}} \sum\_m \int \frac{d\mathbf{k} \nu}{\Omega\_{\text{BZ}}} \delta(\tilde{\varepsilon}\_{n\text{k}} - \tilde{\varepsilon}\_{m\text{k}}),\tag{7}$$
here *k*<sup>B</sup> is the Boltzmann constant, *ħ* is the reduced Planck constant, *Ddef* is the deformation potential of the band edge state, and *C* is the Young's modulus. According to ∆ = ∆Ω Ω and ∆ Ω = 1 2 ( ∆Ω Ω ) 2 (Δ*Etot* is the change in total energy, Δ*Eband edg*<sup>e</sup> is the change in absolute energy level of the band edge, and ∆Ω Ω is the relative change in the lattice constant at *T*),[48] *Ddef* and *C* can be determined by linear fitting and parabolic fitting at each *T* with corresponding lattice constant, respectively, and the values at each *T* are summarized in Table S1. To satisfy the convergence of integrals, the **k**-mesh used in the calculations of the transport properties is 40 × 40× 40. The *n*type doping in TiPtSn with different electron concentrations are considered by the rigid shift of the Fermi level.
In order to examine the temperature effect on the wavefunction as shown in Figures 1c and S6, the one-shot method is used for obtaining the effective structure at *T*. Specifically, the vibration-induced atomic displacement ∆*τκα* (*κ* and *α* indicate the atom and the Cartesian direction, respectively) at *T* is determined as following:[23,63]
where , = [(ℏ⁄) − 1] −1 is the Bose-Einstein distribution. It considers the contributions from all phonon vibrations to the structure, and the details can be found in our previous work.[23] Besides, the band-resolved pCOHP in Figures S4 and S5 is implemented using the LOBSTER code. [64]
**Experimental sample preparation and TE properties measurement.** *Sample Synthesis:* Polycrystalline samples TiPtSn1-*x*Sb*x* (*x* = 0, 0.01) are synthesized under an argon atmosphere by arc melting stoichiometric amounts of high-purity elements Ti (granules, 99.98%), Pt (filaments, 99.999%), and Sn (granules, 99.99%). The ingots are remelted 3 times to ensure compositional homogeneity. Additional 3 wt% Sn is added to compensate for the evaporation loss during arc melting. Then the arc melted ingot is crushed and ball-milled for 5 hours by a FRITSCH Pulverisette-7 Premium Line ballmilling machine. The as-milled fine ground powders are then loaded into a graphite die with an inner diameter of 12.7 mm and compacted into dense pellets by spark plasma sintering (LABOX-325GH-C1, Japan) at 1223 K for 15 min under an axial pressure of 50 MPa in vacuum. The as-sintered samples with relative densities over 98% are cut into different shapes for measuring the thermal diffusivity (Φ10 mm × 1 mm), Hall effect (0.6 mm × 4 mm × 8 mm), Seebeck coefficient, and electrical conductivity (2 mm × 3 mm × 12 mm).
*Sample characterization*: X-ray diffraction (XRD) patterns of all samples are obtained by the Cu-Kα (λ = 1.54185 Å) radiation (Rigaku SmartLab, Japan) at room temperature. The Seebeck coefficient and electrical conductivity are measured in helium atmosphere utilizing a commercially available instrument (ZEM-3, ULVAC-RIKO, Japan). The carrier concentration and mobility are measured by a comprehensive physical property measuring system (PPMS, Quantum Design, USA). and the Hall carrier concentration *n*<sup>H</sup> is calculated according to *n*<sup>H</sup> = 1/(*eR*H). The calculated DOS effective mass *m* \* is by the single parabolic band model. This is using the equation[52]
#### **Acknowledgements**
This work was supported by the National Key Research and Development Program of China (no. 2021YFB3502200), and the National Natural Science Foundation of China (grant no. 52172216, 92163212, and 52302282). Numerical computations were performed on Hefei Advanced Computing Center and Shanghai Technical Service Center of Science and Engineering Computing, Shanghai University.
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## **Supporting Information**
### **for**
# **Screening of half-Heuslers with temperature-induced band convergence and enhanced thermoelectric properties**
#### **Corresponding Author:**
**Thermal conductivity measurement.** The thermal diffusivity *λ* of a disk sample with a diameter of 12.7 mm and a thickness of about 1 mm was measured using an automatic pulsed laser thermal conductivity measurement system (LFA457, NETZSCH, Germany). Mass density *ρ* was measured by the Archimedean method, specific heat capacity (*C*P) was calculated by Dulonn-Petit law, and total thermal conductivity *κ* was calculated by *κ* = *ρλC*p. The lattice thermal conductivity <sup>L</sup> is normally obtained by subtracting the electronic thermal conductivity <sup>e</sup> from the total thermal conductivity through the Wiedemann–Franz law <sup>L</sup> = - <sup>e</sup> = - *LσT*, where *σ*, *L* and *T* are the electrical conductivity, Lorenz number, and absolute temperature, respectively. However, the bipolar thermal conductivity <sup>b</sup> should be taken into account if the intrinsic excitation presents, which gives the relationship <sup>L</sup> + <sup>b</sup> = - *LσT*. The Lorenz number is estimated under the framework of single parabolic band model with the assumption of electron-phonon interaction. The employed equations for the Lorenz number can be written as
$$L = (\frac{\kappa\_{\mathbb{B}}}{e})^2 \left| \frac{\left(r + \frac{\gamma}{2}\right) \boldsymbol{F}\_{r + \frac{\gamma}{2}}(\boldsymbol{\eta})}{\left(r + \frac{3}{2}\right) \boldsymbol{F}\_{r + \frac{3}{2}}(\boldsymbol{\eta})} - \frac{\left(r + \frac{5}{2}\right) \boldsymbol{F}\_{r + \frac{3}{2}}(\boldsymbol{\eta})}{\left(r + \frac{3}{2}\right) \boldsymbol{F}\_{r + \frac{1}{2}}(\boldsymbol{\eta})} \right|,\tag{S2}$$
where *S* is the Seebeck coefficient, *k*<sup>B</sup> the Boltzmann constant, *e* the free electron charge, *r* the scattering factor, *F<sup>i</sup>* the *i*-th Fermi integral, *η* the reduced Fermi level (Fermi level over *k*B*T*). The scattering factor *r* is equal to -1/2 assuming that the acoustic phonon scattering dominates the charge transport process.
#### temperature, respectively.
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