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2004-12-18
Fluctuations of the Magnetization in Thin Films due to Conduction Electrons
A detailed analysis of damping and noise due to a {\it sd}-interaction in a thin ferromagnetic film sandwiched between two large normal metal layers is carried out. The magnetization is shown to obey in general a non-local equation of motion which differs from the the Gilbert equation and is extended to the non-adiabatic regime. To lowest order in the exchange interaction and in the limit where the Gilbert equation applies, we show that the damping term is enhanced due to interfacial effects but it also shows oscillations as a function of the film thickness. The noise calculation is however carried out to all orders in the exchange coupling constant. The ellipticity of the precession of the magnetization is taken into account. The damping is shown to have a Gilbert form only in the adiabatic limit while the relaxation time becomes strongly dependent on the geometry of the thin film. It is also shown that the induced noise characteristic of sd-exchange is inherently colored in character and depends on the symmetry of the Hamiltonian of the magnetization in the film. We show that the sd-noise can be represented in terms of an external stochastic field which is white only in the adiabatic regime. The temperature is also renormalized by the spin accumulation in the system. For large intra-atomic exchange interactions, the Gilbert-Brown equation is no longer valid.
0412510v1
2018-04-02
Anisotropic Gilbert damping in perovskite La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ thin film
The viscous Gilbert damping parameter governing magnetization dynamics is of primary importance for various spintronics applications. Although, the damping constant is believed to be anisotropic by theories. It is commonly treated as a scalar due to lack of experimental evidence. Here, we present an elaborate angle dependent broadband ferromagnetic resonance study of high quality epitaxial La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ films. Extrinsic effects are suppressed and we show convincing evidence of anisotropic damping with twofold symmetry at room temperature. The observed anisotropic relaxation is attributed to the magnetization orientation dependence of the band structure. In addition, we demonstrated that such anisotropy can be tailored by manipulating the stain. This work provides new insights to understand the mechanism of magnetization relaxation.
1804.00554v1
2009-04-21
Tensor damping in metallic magnetic multilayers
The mechanism of spin-pumping, described by Tserkovnyak et al., is formally analyzed in the general case of a magnetic multilayer consisting of two or more metallic ferromagnetic (FM) films separated by normal metal (NM) layers. It is shown that the spin-pumping-induced dynamic coupling between FM layers modifies the linearized Gilbert equations in a way that replaces the scalar Gilbert damping constant with a nonlocal matrix of Cartesian damping tensors. The latter are shown to be methodically calculable from a matrix algebra solution of the Valet-Fert transport equations. As an example, explicit analytical results are obtained for a 5-layer (spin-valve) of form NM/FM/NM'/FM/NM. Comparisons with earlier well known results of Tserkovnyak et al. for the related 3-layer FM/NM/FM indicate that the latter inadvertently hid the tensor character of the damping, and instead singled out the diagonal element of the local damping tensor along the axis normal to the plane of the two magnetization vectors. For spin-valve devices of technological interest, the influence of the tensor components of the damping on thermal noise or spin-torque critical currents are strongly weighted by the relative magnitude of the elements of the nonlocal, anisotropic stiffness-field tensor-matrix, and for in-plane magnetized spin-valves are generally more sensitive to the in-plane element of the damping tensor.
0904.3150v2
2023-12-20
An effective field theory of damped ferromagnetic systems
Using the in-in formalism, we generalize the recently constructed magnetoelastic EFT arXiv:2112.13873 [hep-th] to describe the damping dynamics of ferromagnetic systems at long wavelengths. We find that the standard Gilbert damping term naturally arises as the simplest leading-order symmetry-consistent non-conservative contribution within the in-in framework. The EFT is easily generalized to scenarios with anisotropy and inhomogeneity. In particular, we find the classic Landau-Lifshitz damping term emerges when isotropy is broken by a constant external background field. This provides a first principle explanation for distinguishing the two types of damping dynamics that were originally constructed phenomenologically. Furthermore, the EFT framework could also incorporate intrinsic anisotropy of the material in a straightforward way using the spurion method. For systems with inhomogeneity such as nontrivial spin textures, we find that the leading order derivative correction yields the generalized Gilbert damping equations that were found in condensed matter literature. This shows that the EFT approach enables us to derive the form of higher-derivative-order corrections in a systematic way. Lastly, using the phonon-magnon coupling deduced in the magnetoelastic EFT, we are able to make a prediction for the generic form of the phononic contribution to the damping equation.
2312.13093v1
2019-09-06
The interplay of large two-magnon ferromagnetic resonance linewidths and low Gilbert damping in Heusler thin films
We report on broadband ferromagnetic resonance linewidth measurements performed on epitaxial Heusler thin films. A large and anisotropic two-magnon scattering linewidth broadening is observed for measurements with the magnetization lying in the film plane, while linewidth measurements with the magnetization saturated perpendicular to the sample plane reveal low Gilbert damping constants of $(1.5\pm0.1)\times 10^{-3}$, $(1.8\pm0.2)\times 10^{-3}$, and $<8\times 10^{-4}$ for Co$_2$MnSi/MgO, Co$_2$MnAl/MgO, and Co$_2$FeAl/MgO, respectively. The in-plane measurements are fit to a model combining Gilbert and two-magnon scattering contributions to the linewidth, revealing a characteristic disorder lengthscale of 10-100 nm.
1909.02738v2
2018-02-15
Damping's effect on the magnetodynamics of spin Hall nano-oscillators
We study the impact of spin wave damping ($\alpha$) on the auto-oscillation properties of nano-constriction based spin Hall nano-oscillators (SHNOs). The SHNOs are based on a 5 nm Pt layer interfaced to a 5 nm Py$_{100-x-y}$Pt$_{x}$Ag$_{y}$ magnetic layer, where the Pt and Ag contents are co-varied to keep the saturation magnetization constant (within 10 %), while $\alpha$ varies close to a factor of three. We systematically investigate the influence of the Gilbert damping on the magnetodynamics of these SHNOs by means of electrical microwave measurements. Under the condition of a constant field, the threshold current scales with the damping in the magnetic layer. The threshold current as a function of field shows a parabolic-like behavior, which we attribute to the evolution of the spatial profile of the auto-oscillation mode. The signal linewidth is smaller for the high-damping materials in low magnetic fields, although the lowest observed linewidth was measured for the alloy with least damping.
1802.05548v1
2015-09-06
Study of spin dynamics and damping on the magnetic nanowire arrays with various nanowire widths
We investigate the spin dynamics including Gilbert damping in the ferromagnetic nanowire arrays. We have measured the ferromagnetic resonance of ferromagnetic nanowire arrays using vector-network analyzer ferromagnetic resonance (VNA-FMR) and analyzed the results with the micromagnetic simulations. We find excellent agreement between the experimental VNA-FMR spectra and micromagnetic simulations result for various applied magnetic fields. We find that the demagnetization factor for longitudinal conditions, Nz (Ny) increases (decreases) as decreasing the nanowire width in the micromagnetic simulations. For the transverse magnetic field, Nz (Ny) increases (decreases) as increasing the nanowire width. We also find that the Gilbert damping constant increases from 0.018 to 0.051 as the increasing nanowire width for the transverse case, while it is almost constant as 0.021 for the longitudinal case.
1509.01807v1
2005-03-24
Fast magnetization switching of Stoner particles: A nonlinear dynamics picture
The magnetization reversal of Stoner particles is investigated from the point of view of nonlinear dynamics within the Landau-Lifshitz-Gilbert formulation. The following results are obtained. 1) We clarify that the so-called Stoner-Wohlfarth (SW) limit becomes exact when damping constant is infinitely large. Under the limit, the magnetization moves along the steepest energy descent path. The minimal switching field is the one at which there is only one stable fixed point in the system. 2) For a given magnetic anisotropy, there is a critical value for the damping constant, above which the minimal switching field is the same as that of the SW-limit. 3) We illustrate how fixed points and their basins change under a field along different directions. This change explains well why a non-parallel field gives a smaller minimal switching field and a short switching time. 4) The field of a ballistic magnetization reversal should be along certain direction window in the presence of energy dissipation. The width of the window depends on both of the damping constant and the magnetic anisotropy. The upper and lower bounds of the direction window increase with the damping constant. The window width oscillates with the damping constant for a given magnetic anisotropy. It is zero for both zero and infinite damping. Thus, the perpendicular field configuration widely employed in the current experiments is not the best one since the damping constant in a real system is far from zero.
0503594v1
2018-08-20
Gilbert damping of [Co/Pd]n/Py multilayer thin films
Understanding the Gilbert damping in exchange-coupled multilayer materials is particularly important to develop future fast switching spintronics devices. Here, we report an experimental investigation of temperature-dependent Gilbert damping in [Co/Pd]n/Py multilayer films of varying the number of Co/Pd repetitions by ferromagnetic resonance. The results demonstrate that three independent contributions to the Gilbert damping are identified, namely the intrinsic Gilbert damping, the inhomogeneous linewidth broadening and the two-magnon scattering contribution. Of particular interest, the two-magnon scattering intensity increases as the enlargement of number repetitions of Co/Pd due to the larger pinning effect at the interface between Py and the Co/Pd layers. The Gilbert damping increases monotonically as the temperature decreases from 300K to 50K. Our findings open the door to comprehend the physical origin of the Gilbert damping in ultrathin exchange-coupled multilayer films.
1808.06515v2
2023-05-17
Material Parameters for Faster Ballistic Switching of an In-plane Magnetized Nanomagnet
High-speed magnetization switching of a nanomagnet is necessary for faster information processing. The ballistic switching by a pulsed magnetic filed is a promising candidate for the high-speed switching. It is known that the switching speed of the ballistic switching can be increased by increasing the magnitude of the pulsed magnetic field. However it is difficult to generate a strong and short magnetic field pulse in a small device. Here we explore another direction to achieve the high-speed ballistic switching by designing material parameters such as anisotropy constant, saturation magnetization, and the Gilbert damping constant. We perform the macrospin simulations for the ballistic switching of in-plane magnetized nano magnets with varying material parameters. The results are analyzed based on the switching dynamics on the energy density contour. We show that the pulse width required for the ballistic switching can be reduced by increasing the magnetic anisotropy constant or by decreasing the saturation magnetization. We also show that there exists an optimal value of the Gilbert damping constant that minimizes the pulse width required for the ballistic switching.
2305.10111v1
2015-11-16
Determination of intrinsic damping of perpendicularly magnetized ultrathin films from time resolved precessional magnetization measurements
Magnetization dynamics are strongly influenced by damping. An effective damping constant {\alpha}eff is often determined experimentally from the spectral linewidth of the free induction decay of the magnetization after the system is excited to its non-equilibrium state. Such an {\alpha}eff, however, reflects both intrinsic damping as well as inhomogeneous broadening. In this paper we compare measurements of the magnetization dynamics in ultrathin non-epitaxial films having perpendicular magnetic anisotropy using two different techniques, time-resolved magneto optical Kerr effect (TRMOKE) and hybrid optical-electrical ferromagnetic resonance (OFMR). By using an external magnetic field that is applied at very small angles to the film plane in the TRMOKE studies, we develop an explicit closed-form analytical expression for the TRMOKE spectral linewidth and show how this can be used to reliably extract the intrinsic Gilbert damping constant. The damping constant determined in this way is in excellent agreement with that determined from the OFMR method on the same samples. Our studies indicate that the asymptotic high-field approach that is often used in the TRMOKE method to distinguish the intrinsic damping from the effective damping may result in significant error, because such high external magnetic fields are required to make this approach valid that they are out of reach. The error becomes larger the lower is the intrinsic damping constant, and thus may account for the anomalously high damping constants that are often reported in TRMOKE studies. In conventional ferromagnetic resonance (FMR) studies, inhomogeneous contributions can be readily distinguished from intrinsic damping contributions from the magnetic field dependence of the FMR linewidth. Using the analogous approach, we show how reliable values of the intrinsic damping can be extracted from TRMOKE.
1511.04802v1
2016-03-25
Large spin pumping effect in antisymmetric precession of Ni$_{79}$Fe$_{21}$/Ru/Ni$_{79}$Fe$_{21}$
In magnetic trilayer structures, a contribution to the Gilbert damping of ferromagnetic resonance arises from spin currents pumped from one layer to another. This contribution has been demonstrated for layers with weakly coupled, separated resonances, where magnetization dynamics are excited predominantly in one layer and the other layer acts as a spin sink. Here we show that trilayer structures in which magnetizations are excited simultaneously, antisymmetrically, show a spin-pumping effect roughly twice as large. The antisymmetric (optical) mode of antiferromagnetically coupled Ni$_{79}$Fe$_{21}$(8nm)/Ru/Ni$_{79}$Fe$_{21}$(8nm) trilayers shows a Gilbert damping constant greater than that of the symmetric (acoustic) mode by an amount as large as the intrinsic damping of Py ($\Delta \alpha\simeq\textrm{0.006}$). The effect is shown equally in field-normal and field-parallel to film plane geometries over 3-25 GHz. The results confirm a prediction of the spin pumping model and have implications for the use of synthetic antiferromagnets (SAF)-structures in GHz devices.
1603.07977v1
2015-11-13
Magnified Damping under Rashba Spin Orbit Coupling
The spin orbit coupling spin torque consists of the field-like [REF: S.G. Tan et al., arXiv:0705.3502, (2007).] and the damping-like terms [REF: H. Kurebayashi et al., Nature Nanotechnology 9, 211 (2014).] that have been widely studied for applications in magnetic memory. We focus, in this article, not on the spin orbit effect producing the above spin torques, but on its magnifying the damping constant of all field like spin torques. As first order precession leads to second order damping, the Rashba constant is naturally co-opted, producing a magnified field-like damping effect. The Landau-Liftshitz-Gilbert equations are written separately for the local magnetization and the itinerant spin, allowing the progression of magnetization to be self-consistently locked to the spin.
1511.04227v1
2022-05-13
Precession dynamics of a small magnet with non-Markovian damping: Theoretical proposal for an experiment to determine the correlation time
Recent advances in experimental techniques have made it possible to manipulate and measure the magnetization dynamics on the femtosecond time scale which is the same order as the correlation time of the bath degrees of freedom. In the equations of motion of magnetization, the correlation of the bath is represented by the non-Markovian damping. For development of the science and technologies based on the ultrafast magnetization dynamics it is important to understand how the magnetization dynamics depend on the correlation time. It is also important to determine the correlation time experimentally. Here we study the precession dynamics of a small magnet with the non-Markovian damping. Extending the theoretical analysis of Miyazaki and Seki [J. Chem. Phys. 108, 7052 (1998)] we obtain analytical expressions of the precession angular velocity and the effective damping constant for any values of the correlation time under assumption of small Gilbert damping constant. We also propose a possible experiment for determination of the correlation time.
2205.06399v1
2002-07-19
Gilbert Damping in Magnetic Multilayers
We study the enhancement of the ferromagnetic relaxation rate in thin films due to the adjacent normal metal layers. Using linear response theory, we derive the dissipative torque produced by the s-d exchange interaction at the ferromagnet-normal metal interface. For a slow precession, the enhancement of Gilbert damping constant is proportional to the square of the s-d exchange constant times the zero-frequency limit of the frequency derivative of the local dynamic spin susceptibility of the normal metal at the interface. Electron-electron interactions increase the relaxation rate by the Stoner factor squared. We attribute the large anisotropic enhancements of the relaxation rate observed recently in multilayers containing palladium to this mechanism. For free electrons, the present theory compares favorably with recent spin-pumping result of Tserkovnyak et al. [Phys. Rev. Lett. \textbf{88},117601 (2002)].
0207471v1
2018-10-17
Perpendicularly magnetized YIG films with small Gilbert damping constant and anomalous spin transport properties
The Y3Fe5O12 (YIG) films with perpendicular magnetic anisotropy (PMA) have recently attracted a great deal of attention for spintronics applications. Here, we report the induced PMA in the ultrathin YIG films grown on (Gd2.6Ca0.4)(Ga4.1Mg0.25Zr0.65)O12 (SGGG) substrates by epitaxial strain without preprocessing. Reciprocal space mapping shows that the films are lattice-matched to the substrates without strain relaxation. Through ferromagnetic resonance and polarized neutron reflectometry measurements, we find that these YIG films have ultra-low Gilbert damping constant with a magnetic dead layer as thin as about 0.3 nm at the YIG/SGGG interfaces. Moreover, the transport behavior of the Pt/YIG/SGGG films reveals an enhancement of spin mixing conductance and a large non-monotonic magnetic field dependence of anomalous Hall effect as compared with the Pt/YIG/Gd3Ga5O12 (GGG) films. The non-monotonic anomalous Hall signal is extracted in the temperature range from 150 to 350 K, which has been ascribed to the possible non-collinear magnetic order at the Pt/YIG interface induced by uniaxial strain.
1810.07384v2
2017-06-14
Temperature-dependent Gilbert damping of Co2FeAl thin films with different degree of atomic order
Half-metallicity and low magnetic damping are perpetually sought for in spintronics materials and full Heusler alloys in this respect provide outstanding properties. However, it is challenging to obtain the well-ordered half-metallic phase in as-deposited full Heusler alloys thin films and theory has struggled to establish a fundamentals understanding of the temperature dependent Gilbert damping in these systems. Here we present a study of the temperature dependent Gilbert damping of differently ordered as-deposited Co2FeAl full Heusler alloy thin films. The sum of inter- and intraband electron scattering in conjunction with the finite electron lifetime in Bloch states govern the Gilbert damping for the well-ordered phase in contrast to the damping of partially-ordered and disordered phases which is governed by interband electronic scattering alone. These results, especially the ultralow room temperature intrinsic damping observed for the well-ordered phase provide new fundamental insights to the physical origin of the Gilbert damping in full Heusler alloy thin films.
1706.04670v2
2023-11-27
Gilbert damping in two-dimensional metallic anti-ferromagnets
A finite spin life-time of conduction electrons may dominate Gilbert damping of two-dimensional metallic anti-ferromagnets or anti-ferromagnet/metal heterostructures. We investigate the Gilbert damping tensor for a typical low-energy model of a metallic anti-ferromagnet system with honeycomb magnetic lattice and Rashba spin-orbit coupling for conduction electrons. We distinguish three regimes of spin relaxation: exchange-dominated relaxation for weak spin-orbit coupling strength, Elliot-Yafet relaxation for moderate spin-orbit coupling, and Dyakonov-Perel relaxation for strong spin-orbit coupling. We show, however, that the latter regime takes place only for the in-plane Gilbert damping component. We also show that anisotropy of Gilbert damping persists for any finite spin-orbit interaction strength provided we consider no spatial variation of the N\'eel vector. Isotropic Gilbert damping is restored only if the electron spin-orbit length is larger than the magnon wavelength. Our theory applies to MnPS3 monolayer on Pt or to similar systems.
2311.16268v2
2018-07-31
Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences
Relaxation effects are of primary importance in the description of magnetic excitations, leading to a myriad of methods addressing the phenomenological damping parameters. In this work, we consider several well-established forms of calculating the intrinsic Gilbert damping within a unified theoretical framework, mapping out their connections and the approximations required to derive each formula. This scheme enables a direct comparison of the different methods on the same footing and a consistent evaluation of their range of validity. Most methods lead to very similar results for the bulk ferromagnets Fe, Co and Ni, due to the low spin-orbit interaction strength and the absence of the spin pumping mechanism. The effects of inhomogeneities, temperature and other sources of finite electronic lifetime are often accounted for by an empirical broadening of the electronic energy levels. We show that the contribution to the damping introduced by this broadening is additive, and so can be extracted by comparing the results of the calculations performed with and without spin-orbit interaction. Starting from simulated ferromagnetic resonance spectra based on the underlying electronic structure, we unambiguously demonstrate that the damping parameter obtained within the constant broadening approximation diverges for three-dimensional bulk magnets in the clean limit, while it remains finite for monolayers. Our work puts into perspective the several methods available to describe and compute the Gilbert damping, building a solid foundation for future investigations of magnetic relaxation effects in any kind of material.
1807.11808v3
2003-10-13
Domain wall mobility in nanowires: transverse versus vortex walls
The motion of domain walls in ferromagnetic, cylindrical nanowires is investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole-dipole interaction, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. The transverse domain wall is observed for diameters smaller than the exchange length of the given material. Here, the system behaves effectively one-dimensional and the domain wall mobility agrees with a result derived for a one-dimensional wall by Slonczewski. For low damping the domain wall mobility decreases with decreasing damping constant. With increasing diameter, a crossover to a vortex wall sets in which enhances the domain wall mobility drastically. For a vortex wall the domain wall mobility is described by the Walker-formula, with a domain wall width depending on the diameter of the wire. The main difference is the dependence on damping: for a vortex wall the domain wall mobility can be drastically increased for small values of the damping constant up to a factor of $1/\alpha^2$.
0310277v1
2017-09-21
Low Gilbert Damping Constant in Perpendicularly Magnetized W/CoFeB/MgO Films with High Thermal Stability
Perpendicular magnetic materials with low damping constant and high thermal stability have great potential for realizing high-density, non-volatile, and low-power consumption spintronic devices, which can sustain operation reliability for high processing temperatures. In this work, we study the Gilbert damping constant ({\alpha}) of perpendicularly magnetized W/CoFeB/MgO films with a high perpendicular magnetic anisotropy (PMA) and superb thermal stability. The {\alpha} of these PMA films annealed at different temperatures is determined via an all-optical Time-Resolved Magneto-Optical Kerr Effect method. We find that {\alpha} of these W/CoFeB/MgO PMA films decreases with increasing annealing temperature, reaches a minimum of {\alpha} = 0.016 at an annealing temperature of 350 {\deg}C, and then increases to 0.024 after post-annealing at 400 {\deg}C. The minimum {\alpha} observed at 350 {\deg}C is rationalized by two competing effects as the annealing temperature becomes higher: the enhanced crystallization of CoFeB and dead-layer growth occurring at the two interfaces of the CoFeB layer. We further demonstrate that {\alpha} of the 400 {\deg}C-annealed W/CoFeB/MgO film is comparable to that of a reference Ta/CoFeB/MgO PMA film annealed at 300 {\deg}C, justifying the enhanced thermal stability of the W-seeded CoFeB films.
1709.07483v1
2008-07-31
Scattering Theory of Gilbert Damping
The magnetization dynamics of a single domain ferromagnet in contact with a thermal bath is studied by scattering theory. We recover the Landau-Liftshitz-Gilbert equation and express the effective fields and Gilbert damping tensor in terms of the scattering matrix. Dissipation of magnetic energy equals energy current pumped out of the system by the time-dependent magnetization, with separable spin-relaxation induced bulk and spin-pumping generated interface contributions. In linear response, our scattering theory for the Gilbert damping tensor is equivalent with the Kubo formalism.
0807.5009v1
2006-11-22
Magnetization damping in a local-density approximation
The linear response of itinerant transition metal ferromagnets to transverse magnetic fields is studied in a self-consistent adiabatic local-density approximation. The susceptibility is calculated from a microscopic Hamiltonian, including spin-conserving impurities, impurity induced spin-orbit interaction and magnetic impurities using the Keldysh formalism. The Gilbert damping constant in the Landau-Lifshitz-Gilbert equation is identified, parametrized by an effective transverse spin dephasing rate, and is found to be inversely proportional to the exchange splitting. Our result justify the phenomenological treatment of transverse spin dephasing in the study of current-induced magnetization dynamics in weak, itinerant ferromagnets by Tserkovnyak \textit{et al.}. We show that neglect of gradient corrections in the quasiclassical transport equations leads to incorrect results when the exchange potential becomes of the order of the Fermi energy.
0611588v1
2020-08-14
Large enhancement of spin pumping due to the surface bound states in normal metal/superconductor structures
We show that the spin pumping from ferromagnetic insulator into the adjacent metallic spin sink can be strongly stimulated by the superconducting correlations. The key physical mechanism responsible for this effect is the presence of quasiparticle surface states at the ferromagnetic insulator/superconductor interface. We consider the minimal model when these states appear because of the suppressed pairing constant within the interfacial normal layer. For thin normal layers we obtain a strongly peaked temperature dependence of the Gilbert damping coefficient which has been recently observed in such systems. For thicker normal layers the Gilbert damping monotonically increases down to the temperatures much smaller than the critical one. The suggested model paves the way to controlling the temperature dependence of the spin pumping by fabricating hybrid normal metal/superconductor spin sinks.
2008.06253v1
2024-01-18
Real-space nonlocal Gilbert damping from exchange torque correlation applied to bulk ferromagnets and their surfaces
In this work we present an ab initio scheme based on linear response theory of exchange torque correlation, implemented into the real-space Korringa-Kohn-Rostoker (RS-KKR) framework to calculate diagonal elements of the atomic-site-dependent intrinsic Gilbert damping tensor. The method is first applied to bcc iron and fcc cobalt bulk systems. Beside reproducing earlier results from the literature for those bulk magnets, the effect of the lattice compression is also studied for Fe bulk, and significant changes for the Gilbert damping are found. Furthermore, (001)-oriented surfaces of Fe and Co are also investigated. It is found that the on-site Gilbert damping increases in the surface atomic layer and decreases in the subsurface layer, and approaches the bulk value moving further inside the magnets. Realistic atomic relaxation of the surface layers enhances the identified effects. The first-neighbor damping parameters are extremely sensitive to the surface relaxation. Despite their inhomogeneity caused by the surface, the transverse Gilbert damping tensor components remain largely insensitive to the magnetization direction.
2401.09938v2
2007-06-12
Gilbert and Landau-Lifshitz damping in the presense of spin-torque
A recent article by Stiles et al. (cond-mat/0702020) argued in favor of the Landau-Lifshitz damping term in the micromagnetic equations of motion over that of the more commonly accepted Gilbert damping form. Much of their argument revolved around spin-torque driven domain wall motion in narrow magnetic wires, since the presence of spin-torques can more acutely draw a distinction between the two forms of damping. In this article, the author uses simple arguments and examples to offer an alternative point of view favoring Gilbert.
0706.1736v1
2008-04-04
Inhomogeneous Gilbert damping from impurities and electron-electron interactions
We present a unified theory of magnetic damping in itinerant electron ferromagnets at order $q^2$ including electron-electron interactions and disorder scattering. We show that the Gilbert damping coefficient can be expressed in terms of the spin conductivity, leading to a Matthiessen-type formula in which disorder and interaction contributions are additive. In a weak ferromagnet regime, electron-electron interactions lead to a strong enhancement of the Gilbert damping.
0804.0820v2
2015-03-04
Critical current destabilizing perpendicular magnetization by the spin Hall effect
The critical current needed to destabilize the magnetization of a perpendicular ferromagnet via the spin Hall effect is studied. Both the dampinglike and fieldlike torques associated with the spin current generated by the spin Hall effect is included in the Landau-Lifshitz-Gilbert equation to model the system. In the absence of the fieldlike torque, the critical current is independent of the damping constant and is much larger than that of conventional spin torque switching of collinear magnetic systems, as in magnetic tunnel junctions. With the fieldlike torque included, we find that the critical current scales with the damping constant as $\alpha^{0}$ (i.e., damping independent),$\alpha$, and $\alpha^{1/2}$ depending on the sign of the fieldlike torque and other parameters such as the external field. Numerical and analytical results show that the critical current can be significantly reduced when the fieldlike torque possesses the appropriate sign, i.e. when the effective field associated with the fieldlike torque is pointing opposite to the spin direction of the incoming electrons. These results provide a pathway to reducing the current needed to switch magnetization using the spin Hall effect.
1503.01478v2
2015-10-23
Laser-induced THz magnetization precession for a tetragonal Heusler-like nearly compensated ferrimagnet
Laser-induced magnetization precessional dynamics was investigated in epitaxial films of Mn$_3$Ge, which is a tetragonal Heusler-like nearly compensated ferrimagnet. The ferromagnetic resonance (FMR) mode was observed, the precession frequency for which exceeded 0.5 THz and originated from the large magnetic anisotropy field of approximately 200 kOe for this ferrimagnet. The effective damping constant was approximately 0.03. The corresponding effective Landau-Lifshitz constant of approximately 60 Mrad/s and is comparable to those of the similar Mn-Ga materials. The physical mechanisms for the Gilbert damping and for the laser-induced excitation of the FMR mode were also discussed in terms of the spin-orbit-induced damping and the laser-induced ultrafast modulation of the magnetic anisotropy, respectively.
1510.06793v1
2017-04-11
CoFeAlB alloy with low damping and low magnetization for spin transfer torque switching
We investigate the effect of Al doping on the magnetic properties of the alloy CoFeB. Comparative measurements of the saturation magnetization, the Gilbert damping parameter $\alpha$ and the exchange constant as a function of the annealing temperature for CoFeB and CoFeAlB thin films are presented. Our results reveal a strong reduction of the magnetization for CoFeAlB in comparison to CoFeB. If the prepared CoFeAlB films are amorphous, the damping parameter $\alpha$ is unaffected by the Al doping in comparison to the CoFeB alloy. In contrast, in the case of a crystalline CoFeAlB film, $\alpha$ is found to be reduced. Furthermore, the x-ray characterization and the evolution of the exchange constant with the annealing temperature indicate a similar crystallization process in both alloys. The data proves the suitability of CoFeAlB for spin torque switching properties where a reduction of the switching current in comparison with CoFeB is expected.
1704.03326v1
2021-01-07
Mechanisms behind large Gilbert damping anisotropies
A method with which to calculate the Gilbert damping parameter from a real-space electronic structure method is reported here. The anisotropy of the Gilbert damping with respect to the magnetic moment direction and local chemical environment is calculated for bulk and surfaces of Fe$_{50}$Co$_{50}$ alloys from first principles electronic structure in a real space formulation. The size of the damping anisotropy for Fe$_{50}$Co$_{50}$ alloys is demonstrated to be significant. Depending on details of the simulations, it reaches a maximum-minimum damping ratio as high as 200%. Several microscopic origins of the strongly enhanced Gilbert damping anisotropy have been examined, where in particular interface/surface effects stand out, as do local distortions of the crystal structure. Although theory does not reproduce the experimentally reported high ratio of 400% [Phys. Rev. Lett. 122, 117203 (2019)], it nevertheless identifies microscopic mechanisms that can lead to huge damping anisotropies.
2101.02794v2
2018-08-13
Gilbert damping phenomenology for two-sublattice magnets
We present a systematic phenomenological description of Gilbert damping in two-sublattice magnets. Our theory covers the full range of materials from ferro- via ferri- to antiferromagnets. Following a Rayleigh dissipation functional approach within a Lagrangian classical field formulation, the theory captures intra- as well as cross-sublattice terms in the Gilbert damping, parameterized by a 2$\times$2 matrix. When spin-pumping into an adjacent conductor causes dissipation, we obtain the corresponding Gilbert damping matrix in terms of the interfacial spin-mixing conductances. Our model reproduces the experimentally observed enhancement of the ferromagnetic resonance linewidth in a ferrimagnet close to its compensation temperature without requiring an increased Gilbert parameter. It also predicts new contributions to damping in an antiferromagnet and suggests the resonance linewidths as a direct probe of the sublattice asymmetry, which may stem from boundary or bulk.
1808.04385v2
2021-07-02
Anomalous Gilbert Damping and Duffing Features of the SFS {\boldmath $\varphi_0$} Josephson Junction
We demonstrate unusual features of phase dynamics, IV-characteristics and magnetization dynamics of the $\varphi_0$ Josephson junction at small values of spin-orbit interaction, ratio of Josephson to magnetic energy and Gilbert damping. In particular, an anomalous shift of the ferromagnetic resonance frequency with an increase of Gilbert damping is found. The ferromagnetic resonance curves show the Duffing oscillator behaviour, reflecting the nonlinear nature of Landau-Lifshitz-Gilbert (LLG) equation. Based on the numerical analysis of each term in LLG equation we obtained an approximated equation demonstrated both damping effect and Duffing oscillator features. The resulting Duffing equation incorporates the Gilbert damping in a special way across the dissipative term and the restoring force. A resonance method for the determination of spin-orbit interaction in noncentrosymmetric materials which play the role of barrier in $\varphi_0$ junctions is proposed.
2107.00982v3
2023-03-07
Electrically tunable Gilbert damping in van der Waals heterostructures of two-dimensional ferromagnetic metals and ferroelectrics
Tuning the Gilbert damping of ferromagnetic (FM) metals via a nonvolatile way is of importance to exploit and design next-generation novel spintronic devices. Through systematical first-principles calculations, we study the magnetic properties of the van der Waals heterostructure of two-dimensional FM metal CrTe2 and ferroelectric (FE) In2Te3 monolayers. The ferromagnetism of CrTe2 is maintained in CrTe2/In2Te3 and its magnetic easy axis can be switched from in-plane to out-of-plane by reversing the FE polarization of In2Te3. Excitingly, we find that the Gilbert damping of CrTe2 is tunable when the FE polarization of In2Te3 is reversed from upward to downward. By analyzing the k-dependent contributions to the Gilbert damping, we unravel that such tunability results from the changed intersections between the bands of CrTe2 and Fermi level on the reversal of the FE polarizations of In2Te3 in CrTe2/In2Te3. Our work provides an appealing way to electrically tailor Gilbert dampings of two-dimensional FM metals by contacting them with ferroelectrics.
2303.03852v1
2014-05-19
Comparison of micromagnetic parameters of ferromagnetic semiconductors (Ga,Mn)(As,P) and (Ga,Mn)As
We report on the determination of micromagnetic parameters of epilayers of the ferromagnetic semiconductor (Ga,Mn)As, which has easy axis in the sample plane, and (Ga,Mn)(As,P) which has easy axis perpendicular to the sample plane. We use an optical analog of ferromagnetic resonance where the laser-pulse-induced precession of magnetization is measured directly in the time domain. By the analysis of a single set of pump-and-probe magneto-optical data we determined the magnetic anisotropy fields, the spin stiffness and the Gilbert damping constant in these two materials. We show that incorporation of 10% of phosphorus in (Ga,Mn)As with 6% of manganese leads not only to the expected sign change of the perpendicular to plane anisotropy field but also to an increase of the Gilbert damping and to a reduction of the spin stiffness. The observed changes in the micromagnetic parameters upon incorporating P in (Ga,Mn)As are consistent with the reduced hole density, conductivity, and Curie temperature of the (Ga,Mn)(As,P) material. We report that the magnetization precession damping is stronger for the n = 1 spin wave resonance mode than for the n = 0 uniform magnetization precession mode.
1405.4677v1
2015-03-24
Spin dynamics and frequency dependence of magnetic damping study in soft ferromagnetic FeTaC film with a stripe domain structure
Perpendicular magnetic anisotropy (PMA) and low magnetic damping are the key factors for the free layer magnetization switching by spin transfer torque technique in magnetic tunnel junction devices. The magnetization precessional dynamics in soft ferromagnetic FeTaC thin film with a stripe domain structure was explored in broad band frequency range by employing micro-strip ferromagnetic resonance technique. The polar angular variation of resonance field and linewidth at different frequencies have been analyzed numerically using Landau-Lifshitz-Gilbert equation by taking into account the total free energy density of the film. The numerically estimated parameters Land\'{e} $g$-factor, PMA constant, and effective magnetization are found to be 2.1, 2$\times10^{5}$ erg/cm$^{3}$ and 7145 Oe, respectively. The frequency dependence of Gilbert damping parameter ($\alpha$) is evaluated by considering both intrinsic and extrinsic effects into the total linewidth analysis. The value of $\alpha$ is found to be 0.006 at 10 GHz and it increases with decreasing precessional frequency.
1503.07043v5
2015-08-28
The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space
We prove that in dimensions three and higher the Landau-Lifshitz- Gilbert equation with small initial data in the critical Besov space is globally wellposed in a uniform way with respect to the Gilbert damping parameter. Then we show that the global solution converges to that of the Schrodinger maps in the natural space as the Gilbert damping term vanishes. The proof is based on some studies on the derivative Ginzburg-Landau equations.
1508.07118v3
2006-06-05
Phenomenological theory of current driven exchange switching in ferromagnetic nanojunctions
Phenomenological approach is developed in the theory of spin-valve type ferromagnetic junctions to describe exchange switching by current flowing perpendicular to interfaces. Forward and backward current switching effects are described and they may be principally different in nature. Mobile electron spins are considered as being free in all the contacting ferromagnetic layers. Joint action of the following two current effects is investigated: the nonequilibrium longitudinal spin-injection effective field and the transverse spin-transfer surface torque. Dispersion relation for fluctuations is derived and solved for a junction model having spatially localized spin transfer torque: depth of the torque penetration into the free layer is assumed much smaller than the total free layer thickness. Some critical value of the well known Gilbert damping constant is established for the first time. Spin transfer torque dominates in the instability threshold determination for small enough damping constants, while the spin-injection effective field dominates for high damping. Fine interplay between spin transfer torque and spin injection is necessary to provide a hysteretic behavior of the resistance versus current dependence. The state diagram building up shows the possibility of non-stationary (time dependent) nonlinear states arising due to instability development. Calculations lead to the instability rise time values of the order of 0.1 ns. Spin wave resonance frequency spectrum softening occurs under the current growing to the instability threshold. Magnetization fluctuations above the threshold rise oscillating with time for low damping, but rise aperiodically and much more rapid for high damping.
0606102v2
2005-01-27
Current-induced macrospin vs spin-wave excitations in spin valves
The mode dependence of current-induced magnetic excitations in spin valves is studied theoretically. The torque exerted on the magnetization by transverse spin currents as well as the Gilbert damping constant are found to depend strongly on the wave length of the excitation (spin wave). Analytic expressions are presented for the critical currents that excite a selected spin wave. The onset of macrospin (zero wavelength) vs finite wavelength instabilities depends on the device parameters and the current direction, in agreement with recent experimental findings.
0501672v3
2011-04-15
Lagrangian approach and dissipative magnetic systems
A Lagrangian is introduced which includes the coupling between magnetic moments $\mathbf{m}$ and the degrees of freedom $\boldsymbol{\sigma}$ of a reservoir. In case the system-reservoir coupling breaks the time reversal symmetry the magnetic moments perform a damped precession around an effective field which is self-organized by the mutual interaction of the moments. The resulting evolution equation has the form of the Landau-Lifshitz-Gilbert equation. In case the bath variables are constant vector fields the moments $\mathbf{m}$ fulfill the reversible Landau-Lifshitz equation. Applying Noether's theorem we find conserved quantities under rotation in space and within the configuration space of the moments.
1104.3002v1
2011-07-04
Minimization of the Switching Time of a Synthetic Free Layer in Thermally Assisted Spin Torque Switching
We theoretically studied the thermally assisted spin torque switching of a synthetic free layer and showed that the switching time is minimized if the condition H_J=|H_s|/(2 alpha) is satisfied, where H_J, H_s and alpha are the coupling field of two ferromagnetic layers, the amplitude of the spin torque, and the Gilbert damping constant. We also showed that the coupling field of the synthetic free layer can be determined from the resonance frequencies of the spin-torque diode effect.
1107.0753v2
2013-03-12
Thermally excited spin waves in a nano-structure: thermal gradient vs. constant temperature
Using micromagnetic simulations, we have investigated spin dynamics in a nanostructure in the presence of thermal fluctuations. In particular, we have studied the effects of a uniform temperature and of a uniform thermal gradient. In both cases, the stochastic field leads to an increase of the precession angle of the magnetization, and to a mild decreas of the linewidth of the resonance peaks. Our results indicate that the Gilbert damping parameter plays the role of control parameter for the amplification of spin waves.
1303.2895v1
2015-07-24
Boosting Domain Wall Propagation by Notches
We report a counter-intuitive finding that notches in an otherwise homogeneous magnetic nanowire can boost current-induced domain wall (DW) propagation. DW motion in notch-modulated wires can be classified into three phases: 1) A DW is pinned around a notch when the current density is below the depinning current density. 2) DW propagation velocity is boosted by notches above the depinning current density and when non-adiabatic spin-transfer torque strength $\beta$ is smaller than the Gilbert damping constant $\alpha$. The boost can be manyfold. 3) DW propagation velocity is hindered when $\beta > \alpha$. The results are explained by using the Thiele equation.
1507.06748v1
2020-01-17
Fermi Level Controlled Ultrafast Demagnetization Mechanism in Half-Metallic Heusler Alloy
The electronic band structure-controlled ultrafast demagnetization mechanism in Co2FexMn1-xSi Heusler alloy is underpinned by systematic variation of composition. We find the spin-flip scattering rate controlled by spin density of states at Fermi level is responsible for non-monotonic variation of ultrafast demagnetization time ({\tau}M) with x with a maximum at x = 0.4. Furthermore, Gilbert damping constant exhibits an inverse relationship with {\tau}M due to the dominance of inter-band scattering mechanism. This establishes a unified mechanism of ultrafast spin dynamics based on Fermi level position.
2001.06217v1
2019-06-25
Conductivity-Like Gilbert Damping due to Intraband Scattering in Epitaxial Iron
Confirming the origin of Gilbert damping by experiment has remained a challenge for many decades, even for simple ferromagnetic metals. In this Letter, we experimentally identify Gilbert damping that increases with decreasing electronic scattering in epitaxial thin films of pure Fe. This observation of conductivity-like damping, which cannot be accounted for by classical eddy current loss, is in excellent quantitative agreement with theoretical predictions of Gilbert damping due to intraband scattering. Our results resolve the longstanding question about a fundamental damping mechanism and offer hints for engineering low-loss magnetic metals for cryogenic spintronics and quantum devices.
1906.10326v2
2008-08-28
Gilbert Damping in Conducting Ferromagnets II: Model Tests of the Torque-Correlation Formula
We report on a study of Gilbert damping due to particle-hole pair excitations in conducting ferromagnets. We focus on a toy two-band model and on a four-band spherical model which provides an approximate description of ferromagnetic (Ga,Mn)As. These models are sufficiently simple that disorder-ladder-sum vertex corrections to the long-wavelength spin-spin response function can be summed to all orders. An important objective of this study is to assess the reliability of practical approximate expressions which can be combined with electronic structure calculations to estimate Gilbert damping in more complex systems.
0808.3923v1
2010-01-26
Effect of spin-conserving scattering on Gilbert damping in ferromagnetic semiconductors
The Gilbert damping in ferromagnetic semiconductors is theoretically investigated based on the $s$-$d$ model. In contrast to the situation in metals, all the spin-conserving scattering in ferromagnetic semiconductors supplies an additional spin relaxation channel due to the momentum dependent effective magnetic field of the spin-orbit coupling, thereby modifies the Gilbert damping. In the presence of a pure spin current, we predict a new contribution due to the interplay of the anisotropic spin-orbit coupling and a pure spin current.
1001.4576v1
2020-10-15
Spin injection characteristics of Py/graphene/Pt by gigahertz and terahertz magnetization dynamics driven by femtosecond laser pulse
Spin transport characteristics of graphene has been extensively studied so far. The spin transport along c-axis is however reported by rather limited number of papers. We have studied spin transport characteristics through graphene along c-axis with permalloy(Py)/graphene(Gr)/Pt by gigahertz (GHz) and terahertz (THz) magnetization dynamics driven by femtosecond laser pulses. The relatively simple sample structure does not require electrodes on the sample. The graphene layer was prepared by chemical vapor deposition and transferred on Pt film. The quality of graphene layer was characterized by Raman microscopy. Time resolved magneto-optical Kerr effect is used to characterize gigahertz magnetization dynamics. Magnetization precession is clearly observed both for Pt/Py and Pt/Gr/Py. The Gilbert damping constant of Pt/Py was 0.015, indicates spin pumping effect from Py to Pt. The Gilbert damping constant of Pt/Gr/Py is found to be 0.011, indicates spin injection is blocked by graphene layer. We have also performed the measurement of THz emission for Pt/Py and Pt/Gr/Py. While the THz emission is clearly observed for Pt/Py, a strong reduction of THz emission is observed for Pt/Gr/Py. With these two different experiments, and highly anisotropic resistivity of graphite, we conclude that the vertical spin transport is strongly suppressed by the graphene layer.
2010.07694v1
2015-02-05
Nonlinear analysis of magnetization dynamics excited by spin Hall effect
We investigate the possibility of exciting self-oscillation in a perpendicular ferromagnet by the spin Hall effect on the basis of a nonlinear analysis of the Landau-Lifshitz-Gilbert (LLG) equation. In the self-oscillation state, the energy supplied by the spin torque during a precession on a constant energy curve should equal the dissipation due to damping. Also, the current to balance the spin torque and the damping torque in the self-oscillation state should be larger than the critical current to destabilize the initial state. We find that the second condition in the spin Hall system is not satisfied by deriving analytical solutions of the energy supplied by the spin transfer effect and the dissipation due to the damping from the nonlinear LLG equation. This indicates that the self-oscillation of a perpendicular ferromagnet cannot be excited solely by the spin Hall torque.
1502.01420v2
2008-12-17
Origin of intrinsic Gilbert damping
The damping of magnetization, represented by the rate at which it relaxes to equilibrium, is successfully modeled as a phenomenological extension in the Landau-Lifschitz-Gilbert equation. This is the damping torque term known as Gilbert damping and its direction is given by the vector product of the magnetization and its time derivative. Here we derive the Gilbert term from first principles by a non-relativistic expansion of the Dirac equation. We find that the Gilbert term arises when one calculates the time evolution of the spin observable in the presence of the full spin-orbital coupling terms, while recognizing the relationship between the curl of the electric field and the time varying magnetic induction.
0812.3184v2
2019-07-01
Magnon decay theory of Gilbert damping in metallic antiferromagnets
Gilbert damping is a key property governing magnetization dynamics in ordered magnets. We present a theoretical study of intrinsic Gilbert damping induced by magnon decay in antiferromagnetic metals through $s$-$d$ exchange interaction. Our theory delineates the qualitative features of damping in metallic antiferromagnets owing to their bipartite nature, in addition to providing analytic expressions for the damping parameters. Magnon-induced intraband electron scattering is found to predominantly cause magnetization damping, whereas the N\'eel field is found to be damped via disorder. Depending on the conduction electron band structure, we predict that magnon-induced interband electron scattering around band crossings may be exploited to engineer a strong N\'eel field damping.
1907.01045v1
2022-11-24
Influence of non-local damping on magnon properties of ferromagnets
We study the influence of non-local damping on magnon properties of Fe, Co, Ni and Fe$_{1-x}$Co$_{x}$ ($x=30\%,50\%$) alloys. The Gilbert damping parameter is typically considered as a local scalar both in experiment and in theoretical modelling. However, recent works have revealed that Gilbert damping is a non-local quantity that allows for energy dissipation between atomic sites. With the Gilbert damping parameters calculated from a state-of-the-art real-space electronic structure method, magnon lifetimes are evaluated from spin dynamics and linear response, where a good agreement is found between these two methods. It is found that non-local damping affects the magnon lifetimes in different ways depending on the system. Specifically, we find that in Fe, Co, and Ni the non-local damping decreases the magnon lifetimes, while in $\rm Fe_{70}Co_{30}$ and Fe$_{50}$Co$_{50}$ an opposite, non-local damping effect is observed, and our data show that it is much stronger in the former.
2211.13486v1
2005-07-20
All-optical probe of precessional magnetization dynamics in exchange biased NiFe/FeMn bilayers
An internal anisotropy pulse field is launched by an 8.3 ps short laser excitation, which triggers precessional magnetization dynamics of a polycrystalline NiFe/FeMn exchange bias system on the picosecond timescale. Due to the excitation the unidirectional anisotropy and, thus, the exchange coupling across the interface between the ferromagnetic and the antiferromagnetic layer is reduced, leading to a fast reduction of the exchange bias field and to a dramatic increase of the zero-field susceptibility. The fast optical unpinning is followed by a slower recovery of the interfacial exchange coupling dominated by spin-lattice and heat flow relaxation with a time constant of the order of 160 ps. The measured picosecond time evolution of the exchange decoupling and restoration is interpreted as an anisotropy pulse field giving rise to fast precessional magnetization dynamics of the ferromagnetic layer. The strength of the internal pulse field and even the initial magnetization deflection direction from the equilibrium orientation can be controlled by the absorbed photons. The dependence of the effective Gilbert damping on both small and large angle precessional motion was studied, yielding that both cases can be modeled with reasonable accuracy within the Landau-Lifshitz and Gilbert framework.
0507475v1
2013-09-21
Patterns formation in axially symmetric Landau-Lifshitz-Gilbert-Slonczewski equations
The Landau-Lifshitz-Gilbert-Slonczewski equation describes magnetization dynamics in the presence of an applied field and a spin polarized current. In the case of axial symmetry and with focus on one space dimension, we investigate the emergence of space-time patterns in the form of wavetrains and coherent structures, whose local wavenumber varies in space. A major part of this study concerns existence and stability of wavetrains and of front- and domain wall-type coherent structures whose profiles asymptote to wavetrains or the constant up-/down-magnetizations. For certain polarization the Slonczewski term can be removed which allows for a more complete charaterization, including soliton-type solutions. Decisive for the solution structure is the polarization parameter as well as size of anisotropy compared with the difference of field intensity and current intensity normalized by the damping.
1309.5523v4
2017-03-28
Temperature dependent magnetic damping of yttrium iron garnet spheres
We investigate the temperature dependent microwave absorption spectrum of an yttrium iron garnet sphere as a function of temperature (5 K to 300 K) and frequency (3 GHz to 43.5 GHz). At temperatures above 100 K, the magnetic resonance linewidth increases linearly with temperature and shows a Gilbert-like linear frequency dependence. At lower temperatures, the temperature dependence of the resonance linewidth at constant external magnetic fields exhibits a characteristic peak which coincides with a non-Gilbert-like frequency dependence. The complete temperature and frequency evolution of the linewidth can be modeled by the phenomenology of slowly relaxing rare-earth impurities and either the Kasuya-LeCraw mechanism or the scattering with optical magnons. Furthermore, we extract the temperature dependence of the saturation magnetization, the magnetic anisotropy and the g-factor.
1703.09444v2
2017-12-10
Magnetic field gradient driven dynamics of isolated skyrmions and antiskyrmions in frustrated magnets
The study of skyrmion/antiskyrmion motion in magnetic materials is very important in particular for the spintronics applications. In this work, we study the dynamics of isolated skyrmions and antiskyrmions in frustrated magnets driven by magnetic field gradient, using the Landau-Lifshitz-Gilbert simulations on the frustrated classical Heisenberg model on the triangular lattice. A Hall-like motion induced by the gradient is revealed in bulk system, similar to that in the well-studied chiral magnets. More interestingly, our work suggests that the lateral confinement in nano-stripes of the frustrated system can completely suppress the Hall motion and significantly speed up the motion along the gradient direction. The simulated results are well explained by the Thiele theory. It is demonstrated that the acceleration of the motion is mainly determined by the Gilbert damping constant, which provides useful information for finding potential materials for skyrmion-based spintronics.
1712.03550v1
2010-02-26
Correlation Effects in the Stochastic Landau-Lifshitz-Gilbert Equation
We analyze the Landau-Lifshitz-Gilbert equation when the precession motion of the magnetic moments is additionally subjected to an uniaxial anisotropy and is driven by a multiplicative coupled stochastic field with a finite correlation time $\tau$. The mean value for the spin wave components offers that the spin-wave dispersion relation and its damping is strongly influenced by the deterministic Gilbert damping parameter $\alpha$, the strength of the stochastic forces $D$ and its temporal range $\tau$. The spin-spin-correlation function can be calculated in the low correlation time limit by deriving an evolution equation for the joint probability function. The stability analysis enables us to find the phase diagram within the $\alpha-D$ plane for different values of $\tau$ where damped spin wave solutions are stable. Even for zero deterministic Gilbert damping the magnons offer a finite lifetime. We detect a parameter range where the deterministic and the stochastic damping mechanism are able to compensate each other leading to undamped spin-waves. The onset is characterized by a critical value of the correlation time. An enhancement of $\tau$ leads to an increase of the oscillations of the correlation function.
1002.4958v1
2014-10-02
Investigation of the temperature-dependence of ferromagnetic resonance and spin waves in Co2FeAl0.5Si0.5
Co2FeAl0.5Si0.5 (CFAS) is a Heusler compound that is of interest for spintronics applications, due to its high spin polarization and relatively low Gilbert damping constant. In this study, the behavior of ferromagnetic resonance as a function of temperature was investigated in CFAS, yielding a decreasing trend of damping constant as the temperature was increased from 13 to 300 K. Furthermore, we studied spin waves in CFAS using both frequency domain and time domain techniques, obtaining group velocities and attenuation lengths as high as 26 km/s and 23.3 um, respectively, at room temperature.
1410.0439v1
2018-10-11
Propagating spin waves in nanometer-thick yttrium iron garnet films: Dependence on wave vector, magnetic field strength and angle
We present a comprehensive investigation of propagating spin waves in nanometer-thick yttrium iron garnet (YIG) films. We use broadband spin-wave spectroscopy with integrated coplanar waveguides (CPWs) and microstrip antennas on top of continuous and patterned YIG films to characterize spin waves with wave vectors up to 10 rad/$\mu$m. All films are grown by pulsed laser deposition. From spin-wave transmission spectra, parameters such as the Gilbert damping constant, spin-wave dispersion relation, group velocity, relaxation time, and decay length are derived and their dependence on magnetic bias field strength and angle is systematically gauged. For a 40-nm-thick YIG film, we obtain a damping constant of $3.5 \times 10^{-4}$ and a maximum decay length of 1.2 mm. Our experiments reveal a strong variation of spin-wave parameters with magnetic bias field and wave vector. Spin-wave properties change considerably up to a magnetic bias field of about 30 mT and above a field angle of $\theta_{H} = 20^{\circ}$, where $\theta_{H} = 0^{\circ}$ corresponds to the Damon-Eshbach configuration.
1810.04973v1
2019-02-26
Enhanced Gilbert Damping in Re doped FeCo Films: A Combined Experimental and Theoretical Study
The effects of rhenium doping in the range 0 to 10 atomic percent on the static and dynamic magnetic properties of Fe65Co35 thin films have been studied experimentally as well as with first principles electronic structure calculations focusing on the change of the saturation magnetization and the Gilbert damping parameter. Both experimental and theoretical results show that the saturation magnetization decreases with increasing Re doping level, while at the same time Gilbert damping parameter increases. The experimental low temperature saturation magnetic induction exhibits a 29 percent decrease, from 2.31 T to 1.64 T, in the investigated doping concentration range, which is more than predicted by the theoretical calculations. The room temperature value of the damping parameter obtained from ferromagnetic resonance measurements, correcting for extrinsic contributions to the damping, is for the undoped sample 0.0027, which is close to the theoretically calculated Gilbert damping parameter. With 10 atomic percent Re doping, the damping parameter increases to 0.0090, which is in good agreement with the theoretical value of 0.0073. The increase in damping parameter with Re doping is explained by the increase in density of states at Fermi level, mostly contributed by the spin-up channel of Re. Moreover, both experimental and theoretical values for the damping parameter are observed to be weakly decreasing with decreasing temperature.
1902.09896v1
2021-09-13
Control of magnetization dynamics by substrate orientation in YIG thin films
Yttrium Iron Garnet (YIG) and bismuth (Bi) substituted YIG (Bi0.1Y2.9Fe5O12, BYG) films are grown in-situ on single crystalline Gadolinium Gallium Garnet (GGG) substrates [with (100) and (111) orientations] using pulsed laser deposition (PLD) technique. As the orientation of the Bi-YIG film changes from (100) to (111), the lattice constant is enhanced from 12.384 {\AA} to 12.401 {\AA} due to orientation dependent distribution of Bi3+ ions at dodecahedral sites in the lattice cell. Atomic force microscopy (AFM) images show smooth film surfaces with roughness 0.308 nm in Bi-YIG (111). The change in substrate orientation leads to the modification of Gilbert damping which, in turn, gives rise to the enhancement of ferromagnetic resonance (FMR) line width. The best values of Gilbert damping are found to be (0.54)*10-4, for YIG (100) and (6.27)*10-4, for Bi-YIG (111) oriented films. Angle variation measurements of the Hr are also performed, that shows a four-fold symmetry for the resonance field in the (100) grown film. In addition, the value of effective magnetization (4{\pi}Meff) and extrinsic linewidth ({\Delta}H0) are observed to be dependent on substrate orientation. Hence PLD growth can assist single-crystalline YIG and BYG films with a perfect interface that can be used for spintronics and related device applications.
2109.05901v1
2022-09-01
Growth parameters of Bi0.1Y2.9Fe5O12 thin films for high frequency applications
The growth and characterization of Bismuth (Bi) substituted YIG (Bi-YIG, Bi0.1Y2.9Fe5O12) thin films are reported. Pulsed laser deposited (PLD) films with thicknesses ranging from 20 to 150 nm were grown on Gadolinium Gallium Garnet substrates. Two substrate orientations of (100) and (111) were considered. The enhanced distribution of Bi3+ ions at dodecahedral site along (111) is observed to lead to an increment in lattice constant from 12.379 angstrom in (100) to 12.415 angstrom in (111) oriented films. Atomic force microscopy images showed decreasing roughness with increasing film thickness. Compared to (100) grown films, (111) oriented films showed an increase in ferromagnetic resonance linewidth and consequent increase in Gilbert damping. The lowest Gilbert damping values are found to be (1.06) * 10E-4 for (100) and (2.30) * 10E-4 for (111) oriented films with thickness of 150 nm. The observed values of extrinsic linewidth, effective magnetization, and anisotropic field are related to thickness of the films and substrate orientation. In addition, the in-plane angular variation established four-fold symmetry for the (100) deposited films unlike the case of (111) deposited films. This study prescribes growth conditions for PLD grown single-crystalline Bi-YIG films towards desired high frequency and magneto-optical device applications.
2209.00558v1
2023-06-07
Helicity-dependent optical control of the magnetization state emerging from the Landau-Lifshitz-Gilbert equation
It is well known that the Gilbert relaxation time of a magnetic moment scales inversely with the magnitude of the externally applied field, H, and the Gilbert damping, {\alpha}. Therefore, in ultrashort optical pulses, where H can temporarily be extremely large, the Gilbert relaxation time can momentarily be extremely short, reaching even picosecond timescales. Here we show that for typical ultrashort pulses, the optical control of the magnetization emerges by merely considering the optical magnetic field in the Landau-Lifshitz-Gilbert (LLG) equation. Surprisingly, when circularly polarized optical pulses are introduced to the LLG equation, an optically induced helicity-dependent torque results. We find that the strength of the interaction is determined by {\eta}={\alpha}{\gamma}H/f_opt, where f_opt and {\gamma} are the optical frequency and gyromagnetic ratio. Our results illustrate the generality of the LLG equation to the optical limit and the pivotal role of the Gilbert damping in the general interaction between optical magnetic fields and spins in solids.
2306.04617v2
2018-04-03
Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms
The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term and the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy-Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.
1804.09242v1
2016-08-02
Ferromagnetic Damping/Anti-damping in a Periodic 2D Helical surface; A Non-Equilibrium Keldysh Green Function Approach
In this paper, we investigate theoretically the spin-orbit torque as well as the Gilbert damping for a two band model of a 2D helical surface state with a Ferromagnetic (FM) exchange coupling. We decompose the density matrix into the Fermi sea and Fermi surface components and obtain their contributions to the electronic transport as well as the spin-orbit torque (SOT). Furthermore, we obtain the expression for the Gilbert damping due to the surface state of a 3D Topological Insulator (TI) and predicted its dependence on the direction of the magnetization precession axis.
1608.00984v2
2016-02-19
A systematic study of magnetodynamic properties at finite temperatures in doped permalloy from first principles calculations
By means of first principles calculations, we have systematically investigated how the magnetodynamic properties Gilbert damping, magnetization and exchange stiffness are affected when permalloy (Py) (Fe$_{0.19}$Ni$_{0.81}$) is doped with 4d or 5d transition metal impurities. We find that the trends in the Gilbert damping can be understood from relatively few basic parameters such as the density of states at the Fermi level, the spin-orbit coupling and the impurity concentration. % The temperature dependence of the Gilbert damping is found to be very weak which we relate to the lack of intraband transitions in alloys. % Doping with $4d$ elements has no major impact on the studied Gilbert damping, apart from diluting the host. However, the $5d$ elements have a profound effect on the damping and allows it to be tuned over a large interval while maintaining the magnetization and exchange stiffness. % As regards spin stiffness, doping with early transition metals results in considerable softening, whereas late transition metals have a minor impact. % Our result agree well with earlier calculations where available. In comparison to experiments, the computed Gilbert damping appears slightly underestimated while the spin stiffness show good general agreement.
1602.06201v2
2002-11-01
Exploring dynamical magnetism with time-dependent density-functional theory: from spin fluctuations to Gilbert damping
We use time-dependent spin-density-functional theory to study dynamical magnetic phenomena. First, we recall that the local-spin-density approximation (LSDA) fails to account correctly for magnetic fluctuations in the paramagnetic state of iron and other itinerant ferromagnets. Next, we construct a gradient-dependent density functional that does not suffer from this problem of the LSDA. This functional is then used to derive, for the first time, the phenomenological Gilbert equation of micromagnetics directly from time-dependent density-functional theory. Limitations and extensions of Gilbert damping are discussed on this basis, and some comparisons with phenomenological theories and experiments are made.
0211021v1
2012-04-24
Nonlocal feedback in ferromagnetic resonance
Ferromagnetic resonance in thin films is analyzed under the influence of spatiotemporal feedback effects. The equation of motion for the magnetization dynamics is nonlocal in both space and time and includes isotropic, anisotropic and dipolar energy contributions as well as the conserved Gilbert- and the non-conserved Bloch-damping. We derive an analytical expression for the peak-to-peak linewidth. It consists of four separate parts originated by Gilbert damping, Bloch-damping, a mixed Gilbert-Bloch component and a contribution arising from retardation. In an intermediate frequency regime the results are comparable with the commonly used Landau-Lifshitz-Gilbert theory combined with two-magnon processes. Retardation effects together with Gilbert damping lead to a linewidth the frequency dependence of which becomes strongly nonlinear. The relevance and the applicability of our approach to ferromagnetic resonance experiments is discussed.
1204.5342v1
2017-04-24
Spin injection into silicon detected by broadband ferromagnetic resonance spectroscopy
We studied the spin injection in a NiFe(Py)/Si system using broadband ferromagnetic resonance spectroscopy. The Gilbert damping parameter of the Py layer on top of the Si channel was determined as a function of the Si doping concentration and Py layer thickness. For fixed Py thickness we observed an increase of the Gilbert damping parameter with decreasing resistivity of the Si channel. For a fixed Si doping concentration we measured an increasing Gilbert damping parameter for decreasing Py layer thickness. No increase of the Gilbert damping parameter was found Py/Si samples with an insulating interlayer. We attribute our observations to an enhanced spin injection into the low-resistivity Si by spin pumping.
1704.07006v1
2021-03-11
Magnetoelastic Gilbert damping in magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films
We report an enhanced magnetoelastic contribution to the Gilbert damping in highly magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films. This effect is mitigated for perpendicular-to-plane fields, leading to a large anisotropy of the Gilbert damping in all of the films (up to a factor of 10 at room temperature). These claims are supported by broadband measurements of the ferromagnetic resonance linewidths over a range of temperatures (5 to 400 K), which serve to elucidate the effect of both the magnetostriction and phonon relaxation on the magnetoelastic Gilbert damping.
2103.07008v1
2022-01-27
Effect of vertex corrections on the enhancement of Gilbert damping in spin pumping into a two-dimensional electron gas
We theoretically consider the effect of vertex correction on spin pumping from a ferromagnetic insulator (FI) into a two-dimensional electron gas (2DEG) in which the Rashba and Dresselhaus spin-orbit interactions coexist. The Gilbert damping in the FI is enhanced by elastic spin-flipping or magnon absorption. We show that the Gilbert damping due to elastic spin-flipping is strongly enhanced by the vertex correction when the ratio of the two spin-orbit interactions is near a special value at which the spin relaxation time diverges while that due to magnon absorption shows only small modification. We also show that the shift in the resonant frequency due to elastic spin-flipping is strongly enhanced in a similar way as the Gilbert damping.
2201.11498v3
2016-02-22
Effects of Landau-Lifshitz-Gilbert damping on domain growth
Domain patterns are simulated by the Landau-Lifshitz-Gilbert (LLG) equation with an easy-axis anisotropy. If the Gilbert damping is removed from the LLG equation, it merely describes the precession of magnetization with a ferromagnetic interaction. However, even without the damping, domains that look similar to those of scalar fields are formed, and they grow with time. It is demonstrated that the damping has no significant effects on domain growth laws and large-scale domain structure. In contrast, small-scale domain structure is affected by the damping. The difference in small-scale structure arises from energy dissipation due to the damping.
1602.06673v3
2023-06-22
Gilbert damping in metallic ferromagnets from Schwinger-Keldysh field theory: Intrinsically nonlocal and nonuniform, and made anisotropic by spin-orbit coupling
Understanding the origin of damping mechanisms in magnetization dynamics of metallic ferromagnets is a fundamental problem for nonequilibrium many-body physics of systems where quantum conduction electrons interact with localized spins assumed to be governed by the classical Landau-Lifshitz-Gilbert (LLG) equation. It is also of critical importance for applications, as damping affects energy consumption and speed of spintronic and magnonic devices. Since the 1970s, a variety of linear-response and scattering theory approaches have been developed to produce widely used formulas for computation of spatially-independent Gilbert scalar parameter as the magnitude of the Gilbert damping term in the LLG equation. The largely unexploited for this purpose Schwinger-Keldysh field theory (SKFT) offers additional possibilities, such as to rigorously derive an extended LLG equation by integrating quantum electrons out. Here we derive such equation whose Gilbert damping for metallic ferromagnets is nonlocal, i.e., dependent on all localized spins at a given time, and nonuniform, even if all localized spins are collinear and spin-orbit coupling (SOC) is absent. This is in sharp contrast to standard lore, where nonlocal damping is considered to emerge only if localized spins are noncollinear; for such situations, direct comparison on the example of magnetic domain wall shows that SKFT-derived nonlocal damping is an order of magnitude larger than the previously considered one. Switching on SOC makes such nonlocal damping anisotropic, in contrast to standard lore where SOC is usually necessary to obtain nonzero Gilbert damping scalar parameter. Our analytical formulas, with their nonlocality being more prominent in low spatial dimensions, are fully corroborated by numerically exact quantum-classical simulations.
2306.13013v4
2014-12-12
Spin waves in micro-structured yttrium iron garnet nanometer-thick films
We investigated the spin-wave propagation in a micro-structured yttrium iron garnet waveguide of $40$ nm thickness. Utilizing spatially-resolved Brillouin light scattering microscopy, an exponential decay of the spin-wave amplitude of $(10.06 \pm 0.83)$ $\mu$m was observed. This leads to an estimated Gilbert damping constant of $\alpha=(8.79\pm 0.73)\times 10^{-4}$, which is larger than damping values obtained through ferromagnetic resonance measurements in unstructured films. The theoretically calculated spatial interference of waveguide modes was compared to the spin-wave pattern observed experimentally by means of Brillouin light scattering spectroscopy.
1412.4032v1
2017-06-05
Consistent microscopic analysis of spin pumping effects
We present a consistent microscopic study of spin pumping effects for both metallic and insulating ferromagnets. As for metallic case, we present a simple quantum mechanical picture of the effect as due to the electron spin flip as a result of a nonadiabatic (off-diagonal) spin gauge field. The effect of interface spin-orbit interaction is briefly discussed. We also carry out field-theoretic calculation to discuss on the equal footing the spin current generation and torque effects such as enhanced Gilbert damping constant and shift of precession frequency both in metallic and insulating cases. For thick ferromagnetic metal, our study reproduces results of previous theories such as the correspondence between the dc component of the spin current and enhancement of the damping. For thin metal and insulator, the relation turns out to be modified. For the insulating case, driven locally by interface $sd$ exchange interaction due to magnetic proximity effect, physical mechanism is distinct from the metallic case. Further study of proximity effect and interface spin-orbit interaction would be crucial to interpret experimental results in particular for insulators.
1706.01185v1
2019-05-30
Predicting New Iron Garnet Thin Films with Perpendicular Magnetic Anisotropy
Perpendicular magnetic anisotropy (PMA) is a necessary condition for many spintronic applications like spin-orbit torques switching, logic and memory devices. An important class of magnetic insulators with low Gilbert damping at room temperature are iron garnets, which only have a few PMA types such as terbium and samarium iron garnet. More and stable PMA garnet options are necessary for researchers to be able to investigate new spintronic phenomena. In this study, we predict 20 new substrate/magnetic iron garnet film pairs with stable PMA at room temperature. The effective anisotropy energies of 10 different garnet films that are lattice-matched to 5 different commercially available garnet substrates have been calculated using shape, magnetoelastic and magnetocrystalline anisotropy terms. Strain type, tensile or compressive depending on substrate choice, as well as the sign and the magnitude of the magnetostriction constants of garnets determine if a garnet film may possess PMA. We show the conditions in which Samarium, Gadolinium, Terbium, Holmium, Dysprosium and Thulium garnets may possess PMA on the investigated garnet substrate types. Guidelines for obtaining garnet films with low damping are presented. New PMA garnet films with tunable saturation moment and field may improve spin-orbit torque memory and compensated magnonic thin film devices.
1905.13042v1
2019-07-17
Inhomogeneous domain walls in spintronic nanowires
In case of a spin-polarized current, the magnetization dynamics in nanowires are governed by the classical Landau-Lifschitz equation with Gilbert damping term, augmented by a typically non-variational Slonczewski term. Taking axial symmetry into account, we study the existence of domain wall type coherent structure solutions, with focus on one space dimension and spin-polarization, but our results also apply to vanishing spin-torque term. Using methods from bifurcation theory for arbitrary constant applied fields, we prove the existence of domain walls with non-trivial azimuthal profile, referred to as inhomogeneous. We present an apparently new type of domain wall, referred to as non-flat, whose approach of the axial magnetization has a certain oscillatory character. Additionally, we present the leading order mechanism for the parameter selection of flat and non-flat inhomogeneous domain walls for an applied field below a threshold, which depends on anisotropy, damping, and spin-transfer. Moreover, numerical continuation results of all these domain wall solutions are presented.
1907.07470v2
2021-11-16
Ultrathin ferrimagnetic GdFeCo films with very low damping
Ferromagnetic materials dominate as the magnetically active element in spintronic devices, but come with drawbacks such as large stray fields, and low operational frequencies. Compensated ferrimagnets provide an alternative as they combine the ultrafast magnetization dynamics of antiferromagnets with a ferromagnet-like spin-orbit-torque (SOT) behavior. However to use ferrimagnets in spintronic devices their advantageous properties must be retained also in ultrathin films (t < 10 nm). In this study, ferrimagnetic Gdx(Fe87.5Co12.5)1-x thin films in the thickness range t = 2-20 nm were grown on high resistance Si(100) substrates and studied using broadband ferromagnetic resonance measurements at room temperature. By tuning their stoichiometry, a nearly compensated behavior is observed in 2 nm Gdx(Fe87.5Co12.5)1-x ultrathin films for the first time, with an effective magnetization of Meff = 0.02 T and a low effective Gilbert damping constant of {\alpha} = 0.0078, comparable to the lowest values reported so far in 30 nm films. These results show great promise for the development of ultrafast and energy efficient ferrimagnetic spintronic devices.
2111.08768v1
2021-11-30
First and second order magnetic anisotropy and damping of europium iron garnet under high strain
Understanding and tailoring static and dynamic properties of magnetic insulator thin films is important for spintronic device applications. Here, we grow atomically flat epitaxial europium iron garnet (EuIG) thin films by pulsed laser deposition on (111)-oriented garnet substrates with a range of lattice parameters. By controlling the lattice mismatch between EuIG and the substrates, we tune the strain in EuIG films from compressive to tensile regime, which is characterized by X-ray diffraction. Using ferromagnetic resonance, we find that in addition to the first-order perpendicular magnetic anisotropy which depends linearly on the strain, there is a significant second-order one that has a quadratic strain dependence. Inhomogeneous linewidth of the ferromagnetic resonance increases notably with increasing strain, while the Gilbert damping parameter remains nearly constant (~ 2x10^-2). These results provide valuable insight into the spin dynamics in ferrimagnetic insulators and useful guidance for material synthesis and engineering of next-generation spintronics applications.
2111.15142v1
2011-11-18
Charge and Spin Transport in Magnetic Tunnel Junctions: Microscopic Theory
We study the charge and spin currents passing through a magnetic tunnel junction (MTJ) on the basis of a tight-binding model. The currents are evaluated perturbatively with respect to the tunnel Hamiltonian. The charge current has the form $A[\bm M_1(t)\times\dot{\bm M}_1(t)]\cdot\bm M_2+B\dot{\bm M}_1(t)\cdot\bm M_2$, where $\bm M_1(t)$ and $\bm M_2$ denote the directions of the magnetization in the free layer and fixed layer, respectively. The constant $A$ vanishes when one or both layers are insulators, {while the constant $B$ disappears when both layers are insulators or the same ferromagnets.} The first term in the expression for charge current represents dissipation driven by the effective electric field induced by the dynamic magnetization. In addition, from an investigation of the spin current, we obtain the microscopic expression for the enhanced Gilbert damping constant $\varDelta \alpha$. We show that $\varDelta\alpha$ is proportional to the tunnel conductance and depends on the bias voltage.
1111.4295v2
2017-05-21
Dynamical depinning of chiral domain walls
The domain wall depinning field represents the minimum magnetic field needed to move a domain wall, typically pinned by samples' disorder or patterned constrictions. Conventionally, such field is considered independent on the Gilbert damping since it is assumed to be the field at which the Zeeman energy equals the pinning energy barrier (both damping independent). Here, we analyse numerically the domain wall depinning field as function of the Gilbert damping in a system with perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction. Contrary to expectations, we find that the depinning field depends on the Gilbert damping and that it strongly decreases for small damping parameters. We explain this dependence with a simple one-dimensional model and we show that the reduction of the depinning field is related to the internal domain wall dynamics, proportional to the Dzyaloshinskii-Moriya interaction, and the finite size of the pinning barriers.
1705.07489v2
2019-01-07
Giant anisotropy of Gilbert damping in epitaxial CoFe films
Tailoring Gilbert damping of metallic ferromagnetic thin films is one of the central interests in spintronics applications. Here we report a giant Gilbert damping anisotropy in epitaxial Co$_{50}$Fe$_{50}$ thin film with a maximum-minimum damping ratio of 400 \%, determined by broadband spin-torque as well as inductive ferromagnetic resonance. We conclude that the origin of this damping anisotropy is the variation of the spin orbit coupling for different magnetization orientations in the cubic lattice, which is further corroborate from the magnitude of the anisotropic magnetoresistance in Co$_{50}$Fe$_{50}$.
1901.01941v1
2019-11-02
Tuning Non-Gilbert-type damping in FeGa films on MgO(001) via oblique deposition
The ability to tailor the damping factor is essential for spintronic and spin-torque applications. Here, we report an approach to manipulate the damping factor of FeGa/MgO(001) films by oblique deposition. Owing to the defects at the surface or interface in thin films, two-magnon scattering (TMS) acts as a non-Gilbert damping mechanism in magnetization relaxation. In this work, the contribution of TMS was characterized by in-plane angular dependent ferromagnetic resonance (FMR). It is demonstrated that the intrinsic Gilbert damping is isotropic and invariant, while the extrinsic mechanism related to TMS is anisotropic and can be tuned by oblique deposition. Furthermore, the two and fourfold TMS related to the uniaxial magnetic anisotropy (UMA) and magnetocrystalline anisotropy were discussed. Our results open an avenue to manipulate magnetization relaxation in spintronic devices.
1911.00728v1
2001-10-11
Enhanced Gilbert Damping in Thin Ferromagnetic Films
Using a scattering matrix approach, the precession of the magnetization of a ferromagnet is shown to transfer spins into adjacent normal metal layers. This ``pumping'' of spins slows down the precession corresponding to an enhanced Gilbert damping factor in the Landau-Lifshitz equation. The damping is expressed in terms of the scattering matrix of the ferromagnet-normal metal interface, which is accessible to model and first-principles calculations. Our estimates for permalloy thin films explain the trends observed in recent experiments.
0110247v2
2002-02-11
Radiation Induced Landau-Lifshitz-Gilbert Damping in Ferromagnets
The Landau-Lifshitz-Gilbert damping coefficient employed in the analysis of spin wave ferromagnetic resonance is related to the electrical conductivity of the sample. The changing magnetization (with time) radiates electromagnetic fields. The electromagnetic energy is then absorbed by the sample and the resulting heating effect describes magnetic dissipative damping. The ferromagnetic resonance relaxation rate theoretically depends on the geometry (shape and size) of the sample as well as temperature in agreement with experiment.
0202181v1
2006-01-10
Voltage dependence of Landau-Lifshitz-Gilbert damping of a spin in a current driven tunnel junction
We present a theory of Landau-Lifshitz-Gilbert damping $\alpha$ for a localized spin ${\vec S}$ in the junction coupled to the conduction electrons in both leads under an applied volatege $V$. We find the voltage dependence of the damping term reflecting the energy dependence of the density of states. We find the effect is linear in the voltage and cotrolled by particle-hole asymmetry of the leads.
0601185v1
2015-02-06
Microscopic theory of Gilbert damping in metallic ferromagnets
We present a microscopic theory for magnetization relaxation in metallic ferromagnets of nanoscopic dimensions that is based on the dynamic spin response matrix in the presence of spin-orbit coupling. Our approach allows the calculation of the spin excitation damping rate even for perfectly crystalline systems, where existing microscopic approaches fail. We demonstrate that the relaxation properties are not completely determined by the transverse susceptibility alone, and that the damping rate has a non-negligible frequency dependence in experimentally relevant situations. Our results indicate that the standard Landau-Lifshitz-Gilbert phenomenology is not always appropriate to describe spin dynamics of metallic nanostructure in the presence of strong spin-orbit coupling.
1502.02068v1
2011-09-22
Hole spin relaxation and coefficients in Landau-Lifshitz-Gilbert equation in ferromagnetic GaMnAs
We investigate the temperature dependence of the coefficients in the Landau-Lifshitz-Gilbert equation in ferromagnetic GaMnAs by employing the Zener model. We first calculate the hole spin relaxation time based on the microscopic kinetic equation. We find that the hole spin relaxation time is typically several tens femtoseconds and can present a nonmonotonic temperature dependence due to the variation of the interband spin mixing, influenced by the temperature related Zeeman splitting. With the hole spin relaxation time, we are able to calculate the coefficients in the Landau-Lifshitz-Gilbert equation, such as the Gilbert damping, nonadiabatic spin torque, spin stiffness and vertical spin stiffness coefficients. We find that the nonadiabatic spin torque coefficient $\beta$ is around $0.1\sim 0.3$ at low temperature, which is consistent with the experiment [Adam {\em et al.}, Phys. Rev. B {\bf 80}, 193204 (2009)]. As the temperature increases, $\beta$ monotonically increases and can exceed one in the vicinity of the Curie temperature. In the low temperature regime with $\beta<1$, the Gilbert damping coefficient $\alpha$ increases with temperature, showing good agreement with the experiments [Sinova {\em et al.}, Phys. Rev. B {\bf 69}, 085209 (2004); Khazen {\em et al.}, {\em ibid.} {\bf 78}, 195210 (2008)]. Furthermore, we predict that $\alpha$ decreases with increasing temperature once $\beta>1$ near the Curie temperature. We also find that the spin stiffness decreases with increasing temperature, especially near the Curie temperature due to the modification of the finite $\beta$. Similar to the Gilbert damping, the vertical spin stiffness coefficient is also found to be nonmonotonically dependent on the temperature.
1109.4964v1
2011-04-08
Magnetization Dissipation in Ferromagnets from Scattering Theory
The magnetization dynamics of ferromagnets are often formulated in terms of the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation describes the response of the magnetization in terms of effective fields, whereas the dissipative part is parameterized by the Gilbert damping tensor. We formulate a scattering theory for the magnetization dynamics and map this description on the linearized LLG equation by attaching electric contacts to the ferromagnet. The reactive part can then be expressed in terms of the static scattering matrix. The dissipative contribution to the low-frequency magnetization dynamics can be described as an adiabatic energy pumping process to the electronic subsystem by the time-dependent magnetization. The Gilbert damping tensor depends on the time derivative of the scattering matrix as a function of the magnetization direction. By the fluctuation-dissipation theorem, the fluctuations of the effective fields can also be formulated in terms of the quasistatic scattering matrix. The theory is formulated for general magnetization textures and worked out for monodomain precessions and domain wall motions. We prove that the Gilbert damping from scattering theory is identical to the result obtained by the Kubo formalism.
1104.1625v1
2022-02-12
Generalization of the Landau-Lifshitz-Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets
We propose a systematic and sequential expansion of the Landau-Lifshitz-Gilbert equation utilizing the dependence of the Gilbert damping tensor on the angle between magnetic moments, which arises from multi-body scattering processes. The tensor consists of a damping-like term and a correction to the gyromagnetic ratio. Based on electronic structure theory, both terms are shown to depend on e.g. the scalar, anisotropic, vector-chiral and scalar-chiral products of magnetic moments: $\vec{e}_i\cdot\vec{e}_j$, $(\vec{n}_{ij}\cdot\vec{e}_i)(\vec{n}_{ij}\cdot\vec{e}_j)$, $\vec{n}_{ij}\cdot(\vec{e}_i\times\vec{e}_j)$, $(\vec{e}_i\cdot\vec{e}_j)^2$, $\vec{e}_i\cdot(\vec{e}_j\times\vec{e}_k)$..., where some terms are subjected to the spin-orbit field $\vec{n}_{ij}$ in first and second order. We explore the magnitude of the different contributions using both the Alexander-Anderson model and time-dependent density functional theory in magnetic adatoms and dimers deposited on Au(111) surface.
2202.06154v1
2022-11-23
The fractional Landau-Lifshitz-Gilbert equation
The dynamics of a magnetic moment or spin are of high interest to applications in technology. Dissipation in these systems is therefore of importance for improvement of efficiency of devices, such as the ones proposed in spintronics. A large spin in a magnetic field is widely assumed to be described by the Landau-Lifshitz-Gilbert (LLG) equation, which includes a phenomenological Gilbert damping. Here, we couple a large spin to a bath and derive a generic (non-)Ohmic damping term for the low-frequency range using a Caldeira-Leggett model. This leads to a fractional LLG equation, where the first-order derivative Gilbert damping is replaced by a fractional derivative of order $s \ge 0$. We show that the parameter $s$ can be determined from a ferromagnetic resonance experiment, where the resonance frequency and linewidth no longer scale linearly with the effective field strength.
2211.12889v1
2018-05-04
Effective damping enhancement in noncollinear spin structures
Damping mechanisms in magnetic systems determine the lifetime, diffusion and transport properties of magnons, domain walls, magnetic vortices, and skyrmions. Based on the phenomenological Landau-Lifshitz-Gilbert equation, here the effective damping parameter in noncollinear magnetic systems is determined describing the linewidth in resonance experiments or the decay parameter in time-resolved measurements. It is shown how the effective damping can be calculated from the elliptic polarization of magnons, arising due to the noncollinear spin arrangement. It is concluded that the effective damping is larger than the Gilbert damping, and it may significantly differ between excitation modes. Numerical results for the effective damping are presented for the localized magnons in isolated skyrmions, with parameters based on the Pd/Fe/Ir(111) model-type system.
1805.01815v2
2017-01-12
Dynamic coupling of ferromagnets via spin Hall magnetoresistance
The synchronized magnetization dynamics in ferromagnets on a nonmagnetic heavy metal caused by the spin Hall effect is investigated theoretically. The direct and inverse spin Hall effects near the ferromagnetic/nonmagnetic interface generate longitudinal and transverse electric currents. The phenomenon is known as the spin Hall magnetoresistance effect, whose magnitude depends on the magnetization direction in the ferromagnet due to the spin transfer effect. When another ferromagnet is placed onto the same nonmagnet, these currents are again converted to the spin current by the spin Hall effect and excite the spin torque to this additional ferromagnet, resulting in the excitation of the coupled motions of the magnetizations. The in-phase or antiphase synchronization of the magnetization oscillations, depending on the value of the Gilbert damping constant and the field-like torque strength, is found in the transverse geometry by solving the Landau-Lifshitz-Gilbert equation numerically. On the other hand, in addition to these synchronizations, the synchronization having a phase difference of a quarter of a period is also found in the longitudinal geometry. The analytical theory clarifying the relation among the current, frequency, and phase difference is also developed, where it is shown that the phase differences observed in the numerical simulations correspond to that giving the fixed points of the energy supplied by the coupling torque.
1701.03201v2
2023-12-14
Nonlocal damping of spin waves in a magnetic insulator induced by normal, heavy, or altermagnetic metallic overlayer: a Schwinger-Keldysh field theory approach
Understanding spin wave (SW) damping, and how to control it to the point of being able to amplify SW-mediated signals, is one of the key requirements to bring the envisaged magnonic technologies to fruition. Even widely used magnetic insulators with low magnetization damping in their bulk, such as yttrium iron garnet, exhibit 100-fold increase in SW damping due to inevitable contact with metallic layers in magnonic circuits, as observed in very recent experiments [I. Bertelli et al., Adv. Quantum Technol. 4, 2100094 (2021)] mapping SW damping in spatially-resolved fashion. Here, we provide microscopic and rigorous understanding of wavevector-dependent SW damping using extended Landau-Lifshitz-Gilbert equation with nonlocal damping tensor, instead of conventional local scalar Gilbert damping, as derived from Schwinger-Keldysh nonequilibrium quantum field theory. In this picture, the origin of nonlocal magnetization damping and thereby induced wavevector-dependent SW damping is interaction of localized magnetic moments of magnetic insulator with conduction electrons from the examined three different types of metallic overlayers -- normal, heavy, and altermagnetic. Due to spin-split energy-momentum dispersion of conduction electrons in the latter two cases, the nonlocal damping is anisotropic in spin and space, and it can be dramatically reduced by changing the relative orientation of the two layers when compared to the usage of normal metal overlayer.
2312.09140v1
2006-04-21
Dynamic approach for micromagnetics close to the Curie temperature
In conventional micromagnetism magnetic domain configurations are calculated based on a continuum theory for the magnetization which is assumed to be of constant length in time and space. Dynamics is usually described with the Landau-Lifshitz-Gilbert (LLG) equation the stochastic variant of which includes finite temperatures. Using simulation techniques with atomistic resolution we show that this conventional micromagnetic approach fails for higher temperatures since we find two effects which cannot be described in terms of the LLG equation: i) an enhanced damping when approaching the Curie temperature and, ii) a magnetization magnitude that is not constant in time. We show, however, that both of these effects are naturally described by the Landau-Lifshitz-Bloch equation which links the LLG equation with the theory of critical phenomena and turns out to be a more realistic equation for magnetization dynamics at elevated temperatures.
0604508v1
2017-03-20
Relativistic theory of magnetic inertia in ultrafast spin dynamics
The influence of possible magnetic inertia effects has recently drawn attention in ultrafast magnetization dynamics and switching. Here we derive rigorously a description of inertia in the Landau-Lifshitz-Gilbert equation on the basis of the Dirac-Kohn-Sham framework. Using the Foldy-Wouthuysen transformation up to the order of $1/c^4$ gives the intrinsic inertia of a pure system through the 2$^{\rm nd}$ order time-derivative of magnetization in the dynamical equation of motion. Thus, the inertial damping $\mathcal{I}$ is a higher order spin-orbit coupling effect, $\sim 1/c^4$, as compared to the Gilbert damping $\Gamma$ that is of order $1/c^2$. Inertia is therefore expected to play a role only on ultrashort timescales (sub-picoseconds). We also show that the Gilbert damping and inertial damping are related to one another through the imaginary and real parts of the magnetic susceptibility tensor respectively.
1704.01559v1
2020-06-30
Negative Gilbert damping in cavity optomagnonics
Exceptional point (EP) associated with the parity-time (PT) symmetry breaking is receiving considerable recent attention by the broad physics community. By introducing balanced gain and loss, it has been realized in photonic, acoustic, and electronic structures. However, the observation of magnonic EP remains elusive. The major challenge is to experimentally generate the negative Gilbert damping, which was thought to be highly unlikely but is demanded by the PT symmetry. In this work, we study the magneto-optical interaction of circularly-polarized lasers with a submicron magnet placed in an optical cavity. We show that the off-resonant coupling between the driving laser and cavity photon in the far-blue detuning can induce the magnetic gain (or negative damping) exactly of the Gilbert type. A hyperbolic-tangent function ansatz is found to well describe the time-resolved spin switching as the intrinsic magnetization dissipation is overcome. When the optically pumped magnet interacts with a purely lossy one, we observe a phase transition from the imbalanced to passive PT symmetries by varying the detuning coeffcient. Our findings provide a feasible way to manipulate the sign of the magnetic damping parameter and to realize the EP in cavity optomagnonics.
2006.16510v1
2023-05-16
Non-Hermitian Casimir Effect of Magnons
There has been a growing interest in non-Hermitian quantum mechanics. The key concepts of quantum mechanics are quantum fluctuations. Quantum fluctuations of quantum fields confined in a finite-size system induce the zero-point energy shift. This quantum phenomenon, the Casimir effect, is one of the most striking phenomena of quantum mechanics in the sense that there are no classical analogs and has been attracting much attention beyond the hierarchy of energy scales, ranging from elementary particle physics to condensed matter physics, together with photonics. However, the non-Hermitian extension of the Casimir effect and the application to spintronics have not yet been investigated enough, although exploring energy sources and developing energy-efficient nanodevices are its central issues. Here we fill this gap. By developing a magnonic analog of the Casimir effect into non-Hermitian systems, we show that this non-Hermitian Casimir effect of magnons is enhanced as the Gilbert damping constant (i.e., the energy dissipation rate) increases. When the damping constant exceeds a critical value, the non-Hermitian Casimir effect of magnons exhibits an oscillating behavior, including a beating one, as a function of the film thickness and is characterized by the exceptional point. Our result suggests that energy dissipation serves as a key ingredient of Casimir engineering.
2305.09231v1
2014-04-05
Gilbert damping in noncollinear ferromagnets
The precession and damping of a collinear magnetization displaced from its equilibrium are described by the Landau-Lifshitz-Gilbert equation. For a noncollinear magnetization, it is not known how the damping should be described. We use first-principles scattering theory to investigate the damping in one-dimensional transverse domain walls (DWs) of the important ferromagnetic alloy Ni$_{80}$Fe$_{20}$ and interpret the results in terms of phenomenological models. The damping is found to depend not only on the magnetization texture but also on the specific dynamic modes of Bloch and N\'eel DWs. Even in the highly disordered Ni$_{80}$Fe$_{20}$ alloy, the damping is found to be remarkably nonlocal.
1404.1488v2
2023-08-14
Temperature Evolution of Magnon Propagation Length in Tm$_3$Fe$_5$O$_{12}$ Thin Films: Roles of Magnetic Anisotropy and Gilbert Damping
The magnon propagation length ($\langle\xi\rangle$) of a ferro/ferrimagnet (FM) is one of the key factors that controls the generation and propagation of thermally-driven spin current in FM/heavy metal (HM) bilayer based spincaloritronic devices. Theory predicts that for the FM layer, $\langle\xi\rangle$ is inversely proportional to the Gilbert damping ($\alpha$) and the square root of the effective magnetic anisotropy constant ($K_{\rm eff}$). However, direct experimental evidence of this relationship is lacking. To experimentally confirm this prediction, we employ a combination of longitudinal spin Seebeck effect (LSSE), transverse susceptibility, and ferromagnetic resonance experiments to investigate the temperature evolution of $\langle\xi\rangle$ and establish its correlation with the effective magnetic anisotropy field, $H_K^{\rm eff}$ ($\propto K_{\rm eff}$) and $\alpha$ in Tm$_3$Fe$_5$O$_{12}$ (TmIG)/Pt bilayers. We observe concurrent drops in the LSSE voltage and $\langle\xi\rangle$ below 200$^\circ$K in TmIG/Pt bilayers regardless of TmIG film thickness and substrate choice and attribute it to the noticeable increases in $H_K^{\rm eff}$ and $\alpha$ that occur within the same temperature range. From the TmIG thickness dependence of the LSSE voltage, we determined the temperature dependence of $\langle\xi\rangle$ and highlighted its correlation with the temperature-dependent $H_K^{\rm eff}$ and $\alpha$ in TmIG/Pt bilayers, which will be beneficial for the development of rare-earth iron garnet-based efficient spincaloritronic nanodevices.
2308.07236v3