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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
2015-10-07
Tunable damping, saturation magnetization, and exchange stiffness of half-Heusler NiMnSb thin films
The half-metallic half-Heusler alloy NiMnSb is a promising candidate for applications in spintronic devices due to its low magnetic damping and its rich anisotropies. Here we use ferromagnetic resonance (FMR) measurements and calculations from first principles to investigate how the composition of the epitaxially grown NiMnSb influences the magnetodynamic properties of saturation magnetization $M_S$, Gilbert damping $\alpha$, and exchange stiffness $A$. $M_S$ and $A$ are shown to have a maximum for stoichiometric composition, while the Gilbert damping is minimum. We find excellent quantitative agreement between theory and experiment for $M_S$ and $\alpha$. The calculated $A$ shows the same trend as the experimental data, but has a larger magnitude. Additionally to the unique in-plane anisotropy of the material, these tunabilities of the magnetodynamic properties can be taken advantage of when employing NiMnSb films in magnonic devices.
1510.01894v1
2017-08-07
Chiral damping, chiral gyromagnetism and current-induced torques in textured one-dimensional Rashba ferromagnets
We investigate Gilbert damping, spectroscopic gyromagnetic ratio and current-induced torques in the one-dimensional Rashba model with an additional noncollinear magnetic exchange field. We find that the Gilbert damping differs between left-handed and right-handed N\'eel-type magnetic domain walls due to the combination of spatial inversion asymmetry and spin-orbit interaction (SOI), consistent with recent experimental observations of chiral damping. Additionally, we find that also the spectroscopic $g$ factor differs between left-handed and right-handed N\'eel-type domain walls, which we call chiral gyromagnetism. We also investigate the gyromagnetic ratio in the Rashba model with collinear magnetization, where we find that scattering corrections to the $g$ factor vanish for zero SOI, become important for finite spin-orbit coupling, and tend to stabilize the gyromagnetic ratio close to its nonrelativistic value.
1708.02008v2
2017-09-14
Intrinsic Damping Phenomena from Quantum to Classical Magnets:An ab-initio Study of Gilbert Damping in Pt/Co Bilayer
A fully quantum mechanical description of the precessional damping of Pt/Co bilayer is presented in the framework of the Keldysh Green function approach using {\it ab initio} electronic structure calculations. In contrast to previous calculations of classical Gilbert damping ($\alpha_{GD}$), we demonstrate that $\alpha_{GD}$ in the quantum case does not diverge in the ballistic regime due to the finite size of the total spin, $S$. In the limit of $S\rightarrow\infty$ we show that the formalism recovers the torque correlation expression for $\alpha_{GD}$ which we decompose into spin-pumping and spin-orbital torque correlation contributions. The formalism is generalized to take into account a self consistently determined dephasing mechanism which preserves the conservation laws and allows the investigation of the effect of disorder. The dependence of $\alpha_{GD}$ on Pt thickness and disorder strength is calculated and the spin diffusion length of Pt and spin mixing conductance of the bilayer are determined and compared with experiments.
1709.04911v2
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
2006-02-03
Microscopic description of Landau-Lifshitz-Gilbert type equation based on the s-d model
A Landau-Lifshitz-Gilbert type equation has been derived by using s-d model in which the s-electron system is regarded as an environment coupled weakly with the localized spins. Based on the irreducible linear response theory, we show that the relaxation function of the s-electron spin leads to the Gilbert type damping term which corresponds to the retarded resistance function in the generalized Langevin equation. The Ohmic form of the Gilbert term stems from the fact that the imaginary part of the response function (spin susceptibility) of the itinerant electron system is proportional to the frequency (omega) in the low omega region. It is confirmed that the Caldeira-Leggett theory based on the path-integral approach gives the same result.
0602075v2
2014-09-08
Self-similar solutions of the one-dimensional Landau-Lifshitz-Gilbert equation
We consider the one-dimensional Landau-Lifshitz-Gilbert (LLG) equation, a model describing the dynamics for the spin in ferromagnetic materials. Our main aim is the analytical study of the bi-parametric family of self-similar solutions of this model. In the presence of damping, our construction provides a family of global solutions of the LLG equation which are associated to a discontinuous initial data of infinite (total) energy, and which are smooth and have finite energy for all positive times. Special emphasis will be given to the behaviour of this family of solutions with respect to the Gilbert damping parameter. We would like to emphasize that our analysis also includes the study of self-similar solutions of the Schr\"odinger map and the heat flow for harmonic maps into the 2-sphere as special cases. In particular, the results presented here recover some of the previously known results in the setting of the 1d-Schr\"odinger map equation.
1409.2340v1
2017-09-12
Green's function formalism for spin transport in metal-insulator-metal heterostructures
We develop a Green's function formalism for spin transport through heterostructures that contain metallic leads and insulating ferromagnets. While this formalism in principle allows for the inclusion of various magnonic interactions, we focus on Gilbert damping. As an application, we consider ballistic spin transport by exchange magnons in a metal-insulator-metal heterostructure with and without disorder. For the former case, we show that the interplay between disorder and Gilbert damping leads to spin current fluctuations. For the case without disorder, we obtain the dependence of the transmitted spin current on the thickness of the ferromagnet. Moreover, we show that the results of the Green's function formalism agree in the clean and continuum limit with those obtained from the linearized stochastic Landau-Lifshitz-Gilbert equation. The developed Green's function formalism is a natural starting point for numerical studies of magnon transport in heterostructures that contain normal metals and magnetic insulators.
1709.03775v1
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
2010-02-17
Measurement of Gilbert damping parameters in nanoscale CPP-GMR spin-valves
In-situ, device level measurement of thermal mag-noise spectral linewidths in 60nm diameter CPP-GMR spin-valve stacks of IrMn/ref/Cu/free, with reference and free layer of similar CoFe/CoFeGe alloy, are used to simultaneously determine the intrinsic Gilbert damping for both magnetic layers. It is shown that careful alignment at a "magic-angle" between free and reference layer static equilibrium magnetization can allow direct measurement of the broadband intrinsic thermal spectra in the virtual absence of spin-torque effects which otherwise grossly distort the spectral line shapes and require linewidth extrapolations to zero current (which are nonetheless also shown to agree well with the direct method). The experimental magic-angle spectra are shown to be in good qualitative and quantitative agreement with both macrospin calculations and micromagnetic eigenmode analysis. Despite similar composition and thickness, it is repeatedly found that the IrMn exchange pinned reference layer has ten times larger intrinsic Gilbert damping (alpha ~ 0.1) than that of the free-layer (alpha ~ 0.01). It is argued that the large reference layer damping results from strong, off -resonant coupling to to lossy modes of an IrMn/ref couple, rather than commonly invoked two-magnon processes.
1002.3295v1
2018-09-28
Isotropic non-local Gilbert damping driven by spin currents in epitaxial Pd/Fe/MgO(001) films
Although both theoretical predications and experimental observations demonstrated that the damping factor is anisotropic at ferromagnet/semiconductor interface with robust interfacial spin-orbit coupling, it is not well understood whether non-local Gilbert damping driven by spin currents in heavy metal/ferromagnetic metal (HM/FM) bilayers is anisotropic or not. Here, we investigated the in-plane angular- and frequency- dependence of magnetic relaxation of epitaxial Fe/MgO(001) films with different capping layers of Pd and Cu. After disentangling the parasitic contributions, such as two-magnon scattering (TMS), mosaicity, and field-dragging effect, we unambiguously observed that both local and non-local Gilbert damping are isotropic in Fe(001) plane, suggesting that the pure spin currents absorption is independent of Fe magnetization orientation in the epitaxial Pd/Fe heterostructure. First principles calculation reveals that the effective spin mixing conductance of Pd/Fe interface is nearly invariant for different magnetization directions in good agreement with the experimental observations. These results offer a valuable insight into the transmission and absorption of pure spin currents, and facilitate us to utilize next-generation spintronic devices.
1809.11020v1
2004-09-24
Minimal field requirement in precessional magnetization switching
We investigate the minimal field strength in precessional magnetization switching using the Landau-Lifshitz-Gilbert equation in under-critically damped systems. It is shown that precessional switching occurs when localized trajectories in phase space become unlocalized upon application of field pulses. By studying the evolution of the phase space, we obtain the analytical expression of the critical switching field in the limit of small damping for a magnetic object with biaxial anisotropy. We also calculate the switching times for the zero damping situation. We show that applying field along the medium axis is good for both small field and fast switching times.
0409671v1
2011-11-04
Tunable magnetization relaxation in spin valves
In spin values the damping parameters of the free layer are determined non-locally by the entire magnetic configuration. In a dual spin valve structure that comprises a free layer embedded between two pinned layers, the spin pumping mechanism, in combination with the angular momentum conservation, renders the tensor-like damping parameters tunable by varying the interfacial and diffusive properties. Simulations based on the Landau-Lifshitz-Gilbert phenomenology for a macrospin model are performed with the tensor-like damping and the relaxation time of the free layer magnetization is found to be largely dependent on while tunable through the magnetic configuration of the source-drain magnetization.
1111.1219v1
2012-05-25
Spin wave amplification driven by heat flow: the role of damping and exchange interaction
In this article we report on micromagnetic simulations performed on a permalloy nanostructure in presence of a uniform thermal gradient. Our numerical simulations show that heat flow is an effective mean to compensate the damping, and that the gradients at which spin-wave amplification is observed are experimentally accessible. In particular, we have studied the role of the Gilbert damping parameter on spin-wave amplification.
1205.5650v2
2015-04-23
Magnetization damping in noncollinear spin valves with antiferromagnetic interlayer couplings
We study the magnetic damping in the simplest of synthetic antiferromagnets, i.e. antiferromagnetically exchange-coupled spin valves in which applied magnetic fields tune the magnetic configuration to become noncollinear. We formulate the dynamic exchange of spin currents in a noncollinear texture based on the spindiffusion theory with quantum mechanical boundary conditions at the ferrromagnet|normal-metal interfaces and derive the Landau-Lifshitz-Gilbert equations coupled by the static interlayer non-local and the dynamic exchange interactions. We predict non-collinearity-induced additional damping that can be sensitively modulated by an applied magnetic field. The theoretical results compare favorably with published experiments.
1504.06042v1
2016-05-05
Theory of magnon motive force in chiral ferromagnets
We predict that magnon motive force can lead to temperature dependent, nonlinear chiral damping in both conducting and insulating ferromagnets. We estimate that this damping can significantly influence the motion of skyrmions and domain walls at finite temperatures. We also find that in systems with low Gilbert damping moving chiral magnetic textures and resulting magnon motive forces can induce large spin and energy currents in the transverse direction.
1605.01694v2
2018-04-19
Damping of magnetization dynamics by phonon pumping
We theoretically investigate pumping of phonons by the dynamics of a magnetic film into a non-magnetic contact. The enhanced damping due to the loss of energy and angular momentum shows interference patterns as a function of resonance frequency and magnetic film thickness that cannot be described by viscous ("Gilbert") damping. The phonon pumping depends on magnetization direction as well as geometrical and material parameters and is observable, e.g., in thin films of yttrium iron garnet on a thick dielectric substrate.
1804.07080v2
2024-01-22
Damping-Enhanced Magnon Transmission
The inevitable Gilbert damping in magnetization dynamics is usually regarded as detrimental to spin transport. Here we demonstrate in a ferromagnetic-insulator--normal-metal heterostructure that the strong momentum dependence and chirality of the eddy-current-induced damping causes also beneficial scattering properties. Here we show that a potential barrier that reflects magnon wave packets becomes transparent in the presence of a metallic cap layer, but only in one direction. We formulate the unidirectional transmission in terms of a generalized group velocity with an imaginary component and the magnon skin effect. This trick to turn presumably harmful dissipation into useful functionalities should be useful for future quantum magnonic devices.
2401.12022v1
2013-05-03
Co2 FeAl thin films grown on MgO substrates: Correlation between static, dynamic and structural properties
Co2FeAl (CFA) thin films with thickness varying from 10 nm to 115 nm have been deposited on MgO(001) substrates by magnetron sputtering and then capped by Ta or Cr layer. X-rays diffraction (XRD) revealed that the cubic $[001]$ CFA axis is normal to the substrate and that all the CFA films exhibit full epitaxial growth. The chemical order varies from the $B2$ phase to the $A2$ phase when decreasing the thickness. Magneto-optical Kerr effect (MOKE) and vibrating sample magnetometer measurements show that, depending on the field orientation, one or two-step switchings occur. Moreover, the films present a quadratic MOKE signal increasing with the CFA thickness, due to the increasing chemical order. Ferromagnetic resonance, MOKE transverse bias initial inverse susceptibility and torque (TBIIST) measurements reveal that the in-plane anisotropy results from the superposition of a uniaxial and of a fourfold symmetry term. The fourfold anisotropy is in accord with the crystal structure of the samples and is correlated to the biaxial strain and to the chemical order present in the films. In addition, a large negative perpendicular uniaxial anisotropy is observed. Frequency and angular dependences of the FMR linewidth show two magnon scattering and mosaicity contributions, which depend on the CFA thickness. A Gilbert damping coefficient as low as 0.0011 is found.
1305.0714v1
2016-08-29
Sub-micrometer yttrium iron garnet LPE films with low ferromagnetic resonance losses
Using liquid phase epitaxy (LPE) technique (111) yttrium iron garnet (YIG) films with thicknesses of ~100 nm and surface roughnesses as low as 0.3 nm have been grown as a basic material for spin-wave propagation experiments in microstructured waveguides. The continuously strained films exhibit nearly perfect crystallinity without significant mosaicity and with effective lattice misfits of delta a(perpendicular)/a(substrate) ~10-4 and below. The film/substrate interface is extremely sharp without broad interdiffusion layer formation. All LPE films exhibit a nearly bulk-like saturation magnetization of (1800+-20) Gs and an `easy cone' anisotropy type with extremely small in-plane coercive fields <0.2 Oe. There is a rather weak in-plane magnetic anisotropy with a pronounced six-fold symmetry observed for saturation field <1.5 Oe. No significant out-of-plane anisotropy is observed, but a weak dependence of the effective magnetization on the lattice misfit is detected. The narrowest ferromagnetic resonance linewidth is determined to be 1.4 Oe @ 6.5 GHz which is the lowest value reported so far for YIG films of 100 nm thicknesses and below. The Gilbert damping coefficient for investigated LPE films is estimated to be close to 1 x 10-4.
1608.08043v1
2019-09-12
Spin Transport in Thick Insulating Antiferromagnetic Films
Spin transport of magnonic excitations in uniaxial insulating antiferromagnets (AFs) is investigated. In linear response to spin biasing and a temperature gradient, the spin transport properties of normal-metal--insulating antiferromagnet--normal-metal heterostructures are calculated. We focus on the thick-film regime, where the AF is thicker than the magnon equilibration length. This regime allows the use of a drift-diffusion approach, which is opposed to the thin-film limit considered by Bender {\it et al.} 2017, where a stochastic approach is justified. We obtain the temperature- and thickness-dependence of the structural spin Seebeck coefficient $\mathcal{S}$ and magnon conductance $\mathcal{G}$. In their evaluation we incorporate effects from field- and temperature-dependent spin conserving inter-magnon scattering processes. Furthermore, the interfacial spin transport is studied by evaluating the contact magnon conductances in a microscopic model that accounts for the sub-lattice symmetry breaking at the interface. We find that while inter-magnon scattering does slightly suppress the spin Seebeck effect, transport is generally unaffected, with the relevant spin decay length being determined by non-magnon-conserving processes such as Gilbert damping. In addition, we find that while the structural spin conductance may be enhanced near the spin flip transition, it does not diverge due to spin impedance at the normal metal|magnet interfaces.
1909.05881v2
2020-09-22
Magnon-mediated spin currents in Tm3Fe5O12/Pt with perpendicular magnetic anisotropy
The control of pure spin currents carried by magnons in magnetic insulator (MI) garnet films with a robust perpendicular magnetic anisotropy (PMA) is of great interest to spintronic technology as they can be used to carry, transport and process information. Garnet films with PMA present labyrinth domain magnetic structures that enrich the magnetization dynamics, and could be employed in more efficient wave-based logic and memory computing devices. In MI/NM bilayers, where NM being a normal metal providing a strong spin-orbit coupling, the PMA benefits the spin-orbit torque (SOT) driven magnetization's switching by lowering the needed current and rendering the process faster, crucial for developing magnetic random-access memories (SOT-MRAM). In this work, we investigated the magnetic anisotropies in thulium iron garnet (TIG) films with PMA via ferromagnetic resonance measurements, followed by the excitation and detection of magnon-mediated pure spin currents in TIG/Pt driven by microwaves and heat currents. TIG films presented a Gilbert damping constant {\alpha}~0.01, with resonance fields above 3.5 kOe and half linewidths broader than 60 Oe, at 300 K and 9.5 GHz. The spin-to-charge current conversion through TIG/Pt was observed as a micro-voltage generated at the edges of the Pt film. The obtained spin Seebeck coefficient was 0.54 {\mu}V/K, confirming also the high interfacial spin transparency.
2009.10299v1
2021-03-08
Emerging magnetic nutation
Nutation has been recognized as of great significance for spintronics; but justifying its presence has proven to be a hard problem. In this paper we show that nutation can be understood as emerging from a systematic expansion of a kernel that describes the history of the interaction of a magnetic moment with a bath of colored noise. The parameter of the expansion is the ratio of the colored noise timescale to the precession period. In the process we obtain the Gilbert damping from the same expansion. We recover the known results, when the coefficients of the two terms are proportional to one another, in the white noise limit; and show how colored noise leads to situations where this simple relation breaks down, but what replaces it can be understood by the appropriate generalization of the fluctuation--dissipation theorem. Numerical simulations of the stochastic equations support the analytic approach. In particular we find that the equilibration time is about an order of magnitude longer than the timescale set by the colored noise for a wide range of values of the latter and we can identify the presence of nutation in the non-uniform way the magnetization approaches equilibrium.
2103.04787v3
2008-11-04
Amplitude-Phase Coupling in a Spin-Torque Nano-Oscillator
The spin-torque nano-oscillator in the presence of thermal fluctuation is described by the normal form of the Hopf bifurcation with an additive white noise. By the application of the reduction method, the amplitude-phase coupling factor, which has a significant effect on the power spectrum of the spin-torque nano-oscillator, is calculated from the Landau-Lifshitz-Gilbert-Slonczewski equation with the nonlinear Gilbert damping. The amplitude-phase coupling factor exhibits a large variation depending on in-plane anisotropy under the practical external fields.
0811.0425v1
2013-09-28
High-efficiency GHz frequency doubling without power threshold in thin-film Ni81Fe19
We demonstrate efficient second-harmonic generation at moderate input power for thin film Ni81Fe19 undergoing ferromagnetic resonance (FMR). Powers of the generated second-harmonic are shown to be quadratic in input power, with an upconversion ratio three orders of magnitude higher than that demonstrated in ferrite. The second harmonic signal generated exhibits a significantly lower linewidth than that predicted by low-power Gilbert damping, and is excited without threshold. Results are in good agreement with an analytic, approximate expansion of the Landau-Lifshitz-Gilbert (LLG) equation.
1309.7483v1
2016-06-30
Skyrmion dynamics in a chiral magnet driven by periodically varying spin currents
In this work, we investigated the spin dynamics in a slab of chiral magnets induced by an alternating (ac) spin current. Periodic trajectories of the skyrmion in real space are discovered under the ac current as a result of the Magnus and viscous forces, which originate from the Gilbert damping, the spin transfer torque, and the $ \beta $-nonadiabatic torque effects. The results are obtained by numerically solving the Landau-Lifshitz-Gilbert equation and can be explained by the Thiele equation characterizing the skyrmion core motion.
1606.09326v2
2018-03-19
Dynamics of a Magnetic Needle Magnetometer: Sensitivity to Landau-Lifshitz-Gilbert Damping
An analysis of a single-domain magnetic needle in the presence of an external magnetic field ${\bf B}$ is carried out with the aim of achieving a high precision magnetometer. We determine the uncertainty $\Delta B$ of such a device due to Gilbert dissipation and the associated internal magnetic field fluctuations that gives rise to diffusion of the magnetic needle axis direction ${\bf n}$ and the needle orbital angular momentum. The levitation of the magnetic needle in a magnetic trap and its stability are also analyzed.
1803.10064v2
2020-08-27
Nutation Resonance in Ferromagnets
The inertial dynamics of magnetization in a ferromagnet is investigated theoretically. The analytically derived dynamic response upon microwave excitation shows two peaks: ferromagnetic and nutation resonances. The exact analytical expressions of frequency and linewidth of the magnetic nutation resonance are deduced from the frequency dependent susceptibility determined by the inertial Landau-Lifshitz-Gilbert equation. The study shows that the dependence of nutation linewidth on the Gilbert precession damping has a minimum, which becomes more expressive with increase of the applied magnetic field.
2008.12221v3
2009-08-05
Persistence effects in deterministic diffusion
In systems which exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random walk models. Provided the decay of correlations is fast enough, one can ignore memory effects and approximate the diffusion coefficient according to dimensional arguments. By successively including the effects of one and two steps of memory on this approximation, we examine the effects of ``persistence'' on the diffusion coefficients of extended two-dimensional billiard tables and show how to properly account for these effects, using walks in which a particle undergoes jumps in different directions with probabilities that depend on where they came from.
0908.0600v1
2009-08-10
Diffusion coefficients for multi-step persistent random walks on lattices
We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with two-step memory on different classes of one-, two- and higher-dimensional lattices.
0908.1271v1
2007-02-01
Adiabatic Domain Wall Motion and Landau-Lifshitz Damping
Recent theory and measurements of the velocity of current-driven domain walls in magnetic nanowires have re-opened the unresolved question of whether Landau-Lifshitz damping or Gilbert damping provides the more natural description of dissipative magnetization dynamics. In this paper, we argue that (as in the past) experiment cannot distinguish the two, but that Landau-Lifshitz damping nevertheless provides the most physically sensible interpretation of the equation of motion. From this perspective, (i) adiabatic spin-transfer torque dominates the dynamics with small corrections from non-adiabatic effects; (ii) the damping always decreases the magnetic free energy, and (iii) microscopic calculations of damping become consistent with general statistical and thermodynamic considerations.
0702020v3
2009-04-09
Evaluating the locality of intrinsic precession damping in transition metals
The Landau-Lifshitz-Gilbert damping parameter is typically assumed to be a local quantity, independent of magnetic configuration. To test the validity of this assumption we calculate the precession damping rate of small amplitude non-uniform mode magnons in iron, cobalt, and nickel. At scattering rates expected near and above room temperature, little change in the damping rate is found as the magnon wavelength is decreased from infinity to a length shorter than features probed in recent experiments. This result indicates that non-local effects due to the presence of weakly non-uniform modes, expected in real devices, should not appreciably affect the dynamic response of the element at typical operating temperatures. Conversely, at scattering rates expected in very pure samples around cryogenic temperatures, non-local effects result in an order of magnitude decrease in damping rates for magnons with wavelengths commensurate with domain wall widths. While this low temperature result is likely of little practical importance, it provides an experimentally testable prediction of the non-local contribution of the spin-orbit torque-correlation model of precession damping. None of these results exhibit strong dependence on the magnon propagation direction.
0904.1455v1
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
2004-05-02
Spin Dynamics and Multiple Reflections in Ferromagnetic Film in Contact with Normal Metal Layers
Spin dynamics of a metallic ferromagnetic film imbedded between normal metal layers is studied using the spin-pumping theory of Tserkovnyak et al. [Phys. Rev. Lett. 88, 117601 (2002)]. The scattering matrix for this structure is obtained using a spin-dependent potential with quantum well in the ferromagnetic region. Owing to multiple reflections in the well, the excess Gilbert damping and the gyromagnetic ratio exhibit quantum oscillations as a function of the thickness of the ferromagnetic film. The wavelength of the oscillations is given by the depth of the quantum well. For iron film imbedded between gold layers, the amplitude of the oscillations of the Gilbert damping is in an order of magnitude agreement with the damping observed by Urban et al. [Phys. Rev. Lett. 87, 217204 (2001)]. The results are compared with the linear response theory of Mills [Phys. Rev. B 68, 0144419 (2003)].
0405020v1
2004-06-18
Spin pumping and magnetization dynamics in ferromagnet-Luttinger liquid junctions
We study spin transport between a ferromagnet with time-dependent magnetization and a conducting carbon nanotube or quantum wire, modeled as a Luttinger liquid. The precession of the magnetization vector of the ferromagnet due for instance to an outside applied magnetic field causes spin pumping into an adjacent conductor. Conversely, the spin injection causes increased magnetization damping in the ferromagnet. We find that, if the conductor adjacent to the ferromagnet is a Luttinger liquid, spin pumping/damping is suppressed by interactions, and the suppression has clear Luttinger liquid power law temperature dependence. We apply our result to a few particular setups. First we study the effective Landau-Lifshitz-Gilbert (LLG) coupled equations for the magnetization vectors of the two ferromagnets in a FM-LL-FM junction. Also, we compute the Gilbert damping for a FM-LL and a FM-LL-metal junction.
0406437v1
2004-10-30
Dynamics of Domain Wall in a Biaxial Ferromagnet With Spin-torque
The dynamics of the domain wall (DW) in a biaxial ferromagnet interacting with a spin-polarized current are described by sine-gordon (SG) equation coupled with Gilbert damping term in this paper. Within our frame-work of this model, we obtain a threshold of the current in the motion of a single DW with the perturbation theory on kink soliton solution to the corresponding ferromagnetic system, and the threshold is shown to be dependent on the Gilbert damping term. Also, the motion properties of the DW are discussed for the zero- and nonzero-damping cases, which shows that our theory to describe the dynamics of the DW are self-consistent.
0411005v3
2005-10-31
Time-Resolved Spin Torque Switching and Enhanced Damping in Py/Cu/Py Spin-Valve Nanopillars
We report time-resolved measurements of current-induced reversal of a free magnetic layer in Py/Cu/Py elliptical nanopillars at temperatures T = 4.2 K to 160 K. Comparison of the data to Landau-Lifshitz-Gilbert macrospin simulations of the free layer switching yields numerical values for the spin torque and the Gilbert damping parameters as functions of T. The damping is strongly T-dependent, which we attribute to the antiferromagnetic pinning behavior of a thin permalloy oxide layer around the perimeter of the free layer. This adventitious antiferromagnetic pinning layer can have a major impact on spin torque phenomena.
0510798v2
2006-09-18
General Form of Magnetization Damping: Magnetization dynamics of a spin system evolving nonadiabatically and out of equilibrium
Using an effective Hamiltonian including the Zeeman and internal interactions, we describe the quantum theory of magnetization dynamics when the spin system evolves non-adiabatically and out of equilibrium. The Lewis-Riesenfeld dynamical invariant method is employed along with the Liouville-von Neumann equation for the density matrix. We derive a dynamical equation for magnetization defined with respect to the density operator with a general form of magnetization damping that involves the non-equilibrium contribution in addition to the Landau-Lifshitz-Gilbert equation. Two special cases of the radiation-spin interaction and the spin-spin exchange interaction are considered. For the radiation-spin interaction, the damping term is shown to be of the Gilbert type, while in the spin-spin exchange interaction case the results depend on a coupled chain of correlation functions.
0609431v2
2010-12-25
Screw-pitch effect and velocity oscillation of domain-wall in ferromagnetic nanowire driven by spin-polarized current
We investigate the dynamics of domain wall in ferromagnetic nanowire with spin-transfer torque. The critical current condition is obtained analytically. Below the critical current, we get the static domain wall solution which shows that the spin-polarized current can't drive domain wall moving continuously. In this case, the spin-transfer torque plays both the anti-precession and anti-damping roles, which counteracts not only the spin-precession driven by the effective field but also Gilbert damping to the moment. Above the critical value, the dynamics of domain wall exhibits the novel screw-pitch effect characterized by the temporal oscillation of domain wall velocity and width, respectively. Both the theoretical analysis and numerical simulation demonstrate that this novel phenomenon arise from the conjunctive action of Gilbert-damping and spin-transfer torque. We also find that the roles of spin-transfer torque are entirely contrary for the cases of below and above the critical current.
1012.5473v1
2014-06-24
Interface enhancement of Gilbert damping from first-principles
The enhancement of Gilbert damping observed for Ni80Fe20 (Py) films in contact with the non-magnetic metals Cu, Pd, Ta and Pt, is quantitatively reproduced using first-principles scattering theory. The "spin-pumping" theory that qualitatively explains its dependence on the Py thickness is generalized to include a number of factors known to be important for spin transport through interfaces. Determining the parameters in this theory from first-principles shows that interface spin-flipping makes an essential contribution to the damping enhancement. Without it, a much shorter spin-flip diffusion length for Pt would be needed than the value we calculate independently.
1406.6225v2
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
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
2016-10-21
Spin transport and dynamics in all-oxide perovskite La$_{2/3}$Sr$_{1/3}$MnO$_3$/SrRuO$_3$ bilayers probed by ferromagnetic resonance
Thin films of perovskite oxides offer the possibility of combining emerging concepts of strongly correlated electron phenomena and spin current in magnetic devices. However, spin transport and magnetization dynamics in these complex oxide materials are not well understood. Here, we experimentally quantify spin transport parameters and magnetization damping in epitaxial perovskite ferromagnet/paramagnet bilayers of La$_{2/3}$Sr$_{1/3}$MnO$_3$/SrRuO$_3$ (LSMO/SRO) by broadband ferromagnetic resonance spectroscopy. From the SRO thickness dependence of Gilbert damping, we estimate a short spin diffusion length of $\lesssim$1 nm in SRO and an interfacial spin-mixing conductance comparable to other ferromagnet/paramagnetic-metal bilayers. Moreover, we find that anisotropic non-Gilbert damping due to two-magnon scattering also increases with the addition of SRO. Our results demonstrate LSMO/SRO as a spin-source/spin-sink system that may be a foundation for examining spin-current transport in various perovskite heterostructures.
1610.06661v1
2019-02-12
Ultra-low damping in lift-off structured yttrium iron garnet thin films
We show that using maskless photolithography and the lift-off technique, patterned yttrium iron garnet thin films possessing ultra-low Gilbert damping can be accomplished. The films of 70 nm thickness were grown on (001)-oriented gadolinium gallium garnet by means of pulsed laser deposition, and they exhibit high crystalline quality, low surface roughness, and the effective magnetization of 127 emu/cm3. The Gilbert damping parameter is as low as 5x10-4. The obtained structures have well-defined sharp edges which along with good structural and magnetic film properties pave a path in the fabrication of high-quality magnonic circuits and oxide-based spintronic devices.
1902.04605v1
2019-02-20
CoFeB/MgO/CoFeB structures with orthogonal easy axes: perpendicular anisotropy and damping
We report on the Gilbert damping parameter $\alpha$, the effective magnetization $4\pi M_{eff}$, and the asymmetry of the $g$-factor in bottom-CoFeB(0.93~nm)/MgO(0.90--1.25~nm)/CoFeB(1.31~nm)-top as-deposited systems. Magnetization of CoFeB layers exhibits a specific noncollinear configuration with orthogonal easy axes and with $4\pi M_{eff}$ values of $+2.2$ kG and $-2.3$ kG for the bottom and top layers, respectively. We show that $4\pi M_{eff}$ depends on the asymmetry $g_\perp - g_\parallel$ of the $g$-factor measured in the perpendicular and the in-plane directions revealing a highly nonlinear relationship. In contrast, the Gilbert damping is practically the same for both layers. Annealing of the films results in collinear easy axes perpendicular to the plane for both layers. However, the linewidth is strongly increased due to enhanced inhomogeneous broadening.
1902.07563v1
2021-06-28
Stability of a Magnetically Levitated Nanomagnet in Vacuum: Effects of Gas and Magnetization Damping
In the absence of dissipation a non-rotating magnetic nanoparticle can be stably levitated in a static magnetic field as a consequence of the spin origin of its magnetization. Here we study the effects of dissipation on the stability of the system, considering the interaction with the background gas and the intrinsic Gilbert damping of magnetization dynamics. At large applied magnetic fields we identify magnetization switching induced by Gilbert damping as the key limiting factor for stable levitation. At low applied magnetic fields and for small particle dimensions magnetization switching is prevented due to the strong coupling of rotation and magnetization dynamics, and the stability is mainly limited by the gas-induced dissipation. In the latter case, high vacuum should be sufficient to extend stable levitation over experimentally relevant timescales. Our results demonstrate the possibility to experimentally observe the phenomenon of quantum spin stabilized magnetic levitation.
2106.14858v3
2021-10-31
Thermally induced all-optical ferromagnetic resonance in thin YIG films
All-optical ferromagnetic resonance (AO-FMR) is a powerful tool for local detection of micromagnetic parameters, such as magnetic anisotropy, Gilbert damping or spin stiffness. In this work we demonstrate that the AO-FMR method can be used in thin films of Yttrium Iron Garnet (YIG) if a metallic capping layer (Au, Pt) is deposited on top of the film. Magnetization precession is triggered by heating of the metallic layer with femtosecond laser pulses. The heating modifies the magneto-crystalline anisotropy of the YIG film and shifts the quasi-equilibrium orientation of magnetization, which results in precessional magnetization dynamics. The laser-induced magnetization precession corresponds to a uniform (Kittel) magnon mode, with the precession frequency determined by the magnetic anisotropy of the material as well as the external magnetic field, and the damping time set by a Gilbert damping parameter. The AO-FMR method thus enables measuring local magnetic properties, with spatial resolution given only by the laser spot size.
2111.00586v1
2024-01-01
Calculation of Gilbert damping and magnetic moment of inertia using torque-torque correlation model within ab initio Wannier framework
Magnetization dynamics in magnetic materials are well described by the modified semiclassical Landau-Lifshitz-Gilbert (LLG) equation, which includes the magnetic damping $\alpha$ and the magnetic moment of inertia $\mathrm{I}$ tensors as key parameters. Both parameters are material-specific and physically represent the time scales of damping of precession and nutation in magnetization dynamics. $\alpha$ and $\mathrm{I}$ can be calculated quantum mechanically within the framework of the torque-torque correlation model. The quantities required for the calculation are torque matrix elements, the real and imaginary parts of the Green's function and its derivatives. Here, we calculate these parameters for the elemental magnets such as Fe, Co and Ni in an ab initio framework using density functional theory and Wannier functions. We also propose a method to calculate the torque matrix elements within the Wannier framework. We demonstrate the effectiveness of the method by comparing it with the experiments and the previous ab initio and empirical studies and show its potential to improve our understanding of spin dynamics and to facilitate the design of spintronic devices.
2401.00714v1
2023-08-18
Large thermo-spin effects in Heusler alloy based spin-gapless semiconductor thin films
Recently, Heusler alloys-based spin gapless semiconductors (SGSs) with high Curie temperature (TC) and sizeable spin polarization have emerged as potential candidates for tunable spintronic applications. We report comprehensive investigation of the temperature dependent ANE and intrinsic longitudinal spin Seebeck effect (LSSE) in CoFeCrGa thin films grown on MgO substrates. Our findings show the anomalous Nernst coefficient for the MgO/CoFeCrGa (95 nm) film is $\cong 1.86$ micro V/K at room temperature which is nearly two orders of magnitude higher than that of the bulk polycrystalline sample of CoFeCrGa (= 0.018 micro V/K) but comparable to that of the magnetic Weyl semimetal Co2MnGa thin film (2-3 micro V/K). Furthermore, the LSSE coefficient for our MgO/CoFeCrGa(95nm)/Pt(5nm) heterostructure is $\cong 20.5$ $\mu$V/K/$\Omega$ at room temperature which is twice larger than that of the half-metallic ferromagnetic La$_{0.7}$Sr$_{0.3}$MnO$_3$ thin films ($\cong$ 20.5 $\mu$V/K/$\Omega$). We show that both ANE and LSSE coefficients follow identical temperature dependences and exhibit a maximum at $\cong$ 225 K which is understood as the combined effects of inelastic magnon scatterings and reduced magnon population at low temperatures. Our analyses not only indicate that the extrinsic skew scattering is the dominating mechanism for ANE in these films but also provide critical insights into the functional form of the observed temperature dependent LSSE at low temperatures. Furthermore, by employing radio frequency transverse susceptibility and broadband ferromagnetic resonance in combination with the LSSE measurements, we establish a correlation among the observed LSSE signal, magnetic anisotropy and Gilbert damping of the CoFeCrGa thin films, which will be beneficial for fabricating tunable and highly efficient Heusler alloys based spincaloritronic nanodevices.
2308.09843v1
2017-12-20
Unifying ultrafast demagnetization and intrinsic Gilbert damping in Co/Ni bilayers with electronic relaxation near the Fermi surface
The ability to controllably manipulate the laser-induced ultrafast magnetic dynamics is a prerequisite for future high speed spintronic devices. The optimization of devices requires the controllability of the ultrafast demagnetization time, , and intrinsic Gilbert damping, . In previous attempts to establish the relationship between and , the rare-earth doping of a permalloy film with two different demagnetization mechanism is not a suitable candidate. Here, we choose Co/Ni bilayers to investigate the relations between and by means of time-resolved magneto-optical Kerr effect (TRMOKE) via adjusting the thickness of the Ni layers, and obtain an approximately proportional relation between these two parameters. The remarkable agreement between TRMOKE experiment and the prediction of breathing Fermi-surface model confirms that a large Elliott-Yafet spin-mixing parameter is relevant to the strong spin-orbital coupling at the Co/Ni interface. More importantly, a proportional relation between and in such metallic films or heterostructures with electronic relaxation near Fermi surface suggests the local spin-flip scattering domains the mechanism of ultrafast demagnetization, otherwise the spin-current mechanism domains. It is an effective method to distinguish the dominant contributions to ultrafast magnetic quenching in metallic heterostructures by investigating both the ultrafast demagnetization time and Gilbert damping simultaneously. Our work can open a novel avenue to manipulate the magnitude and efficiency of Terahertz emission in metallic heterostructures such as the perpendicular magnetic anisotropic Ta/Pt/Co/Ni/Pt/Ta multilayers, and then it has an immediate implication of the design of high frequency spintronic devices.
1712.07323v1
2015-06-16
Fast energy decay for wave equations with variable damping coefficients in the 1-D half line
We derive fast decay estimates of the total energy for wave equations with localized variable damping coefficients, which are dealt with in the one dimensional half line $(0,\infty)$. The variable damping coefficient vanishes near the boundary $x = 0$, and is effective critically near spatial infinity $x = \infty$.
1506.04851v1
2008-05-22
Intrinsic and non-local Gilbert damping in polycrystalline nickel studied by Ti:Sapphire laser fs spectroscopy
The use of femtosecond laser pulses generated by a Ti:Sapphire laser system allows us to gain an insight into the magnetization dynamics on time scales from sub-picosecond up to 1 ns directly in the time domain. This experimental technique is used to excite a polycrystalline nickel (Ni) film optically and probe the dynamics afterwards. Different spin wave modes (the Kittel mode, perpendicular standing spin-wave modes (PSSW) and dipolar spin-wave modes (Damon-Eshbach modes)) are identified as the Ni thickness is increased. The Kittel mode allows determination of the Gilbert damping parameter alpha extracted from the magnetization relaxation time tau_alpha. The non-local damping by spin currents emitted into a non-magnetic metallic layer of vanadium (V), palladium (Pd) and the rare earth dysprosium (Dy) are studied for wedge-shaped Ni films 1 nm-30 nm. The damping parameter increases from alpha=0.045 intrinsic for nickel to alpha>0.10 for the heavy materials, such as Pd and Dy, for the thinnest Ni films below 10 nm thickness. Also, for the thinnest reference Ni film thickness, an increased magnetic damping below 4 nm is observed. The origin of this increase is discussed within the framework of line broadening by locally different precessional frequencies within the laser spot region.
0805.3495v1
2015-06-18
The absence of intraband scattering in a consistent theory of Gilbert damping in metallic ferromagnets
Damping of magnetization dynamics in a ferromagnetic metal is usually characterized by the Gilbert parameter alpha. Recent calculations of this quantity, using a formula due to Kambersky, find that it is infinite for a perfect crystal owing to an intraband scattering term which is of third order in the spin-orbit parameter xi This surprising result conflicts with recent work by Costa and Muniz who study damping numerically by direct calculation of the dynamical transverse spin susceptibility in the presence of spin-orbit coupling. We resolve this inconsistency by following the Costa-Muniz approach for a slightly simplified model where it is possible to calculate alpha analytically. We show that to second order in the spin-orbit parameter xi one retrieves the Kambersky result for alpha, but to higher order one does not obtain any divergent intraband terms. The present work goes beyond that of Costa and Muniz by pointing out the necessity of including the effect of long-range Coulomb interaction in calculating damping for large xi. A direct derivation of the Kambersky formula is given which shows clearly the restriction of its validity to second order in xi so that no intraband scattering terms appear. This restriction has an important effect on the damping over a substantial range of impurity content and temperature. The experimental situation is discussed.
1506.05622v2
2020-02-07
Engineering Co$_2$MnAl$_x$Si$_{1-x}$ Heusler compounds as a model system to correlate spin polarization, intrinsic Gilbert damping and ultrafast demagnetization
Engineering of magnetic materials for developing better spintronic applications relies on the control of two key parameters: the spin polarization and the Gilbert damping responsible for the spin angular momentum dissipation. Both of them are expected to affect the ultrafast magnetization dynamics occurring on the femtosecond time scale. Here, we use engineered Co2MnAlxSi1-x Heusler compounds to adjust the degree of spin polarization P from 60 to 100% and investigate how it correlates with the damping. We demonstrate experimentally that the damping decreases when increasing the spin polarization from 1.1 10-3 for Co2MnAl with 63% spin polarization to an ultra-low value of 4.10-4 for the half-metal magnet Co2MnSi. This allows us investigating the relation between these two parameters and the ultrafast demagnetization time characterizing the loss of magnetization occurring after femtosecond laser pulse excitation. The demagnetization time is observed to be inversely proportional to 1-P and as a consequence to the magnetic damping, which can be attributed to the similarity of the spin angular momentum dissipation processes responsible for these two effects. Altogether, our high quality Heusler compounds allow controlling the band structure and therefore the channel for spin angular momentum dissipation.
2002.02686v1
2006-08-22
Simulation of stress-impedance effects in low magnetostrictive films
A theoretical study of stress-impedance effect based on the solution of Landau-Lifsitz-Gilbert equation has been carried out. The results show that stress impedance effects depend largely on several extrinsic (external bias field, external frequency) and intrinsic (orientation and magnitude of uniaxial anisotropy, damping) parameters.
0608488v1
2017-03-09
Material developments and domain wall based nanosecond-scale switching process in perpendicularly magnetized STT-MRAM cells
We investigate the Gilbert damping and the magnetization switching of perpendicularly magnetized FeCoB-based free layers embedded in tunnel junctions adequate for spin-torque operated memories. We study the influence of the boron content in MgO / FeCoB /Ta systems alloys on their Gilbert damping after crystallization annealing. Increasing the boron content from 20 to 30\% increases the crystallization temperature, thereby postponing the onset of elemental diffusion within the free layer. This reduction of the interdiffusion of the Ta atoms helps maintaining the Gilbert damping at a low level of 0.009 without any penalty on the anisotropy and the magneto-transport properties up to the 400$^\circ$C annealing required in CMOS back-end of line processing. In addition, we show that dual MgO free layers of composition MgO/FeCoB/Ta/FeCoB/MgO have a substantially lower damping than their MgO/FeCoB/Ta counterparts, reaching damping parameters as low as 0.0039 for a 3 \r{A} thick Tantalum spacer. This confirms that the dominant channel of damping is the presence of Ta impurities within the FeCoB alloy. On optimized tunnel junctions, we then study the duration of the switching events induced by spin-transfer-torque. We focus on the sub-threshold thermally activated switching in optimal applied field conditions. From the electrical signatures of the switching, we infer that once the nucleation has occurred, the reversal proceeds by a domain wall sweeping though the device at a few 10 m/s. The smaller the device, the faster its switching. We present an analytical model to account for our findings. The domain wall velocity is predicted to scale linearly with the current for devices much larger than the wall width. The wall velocity depends on the Bloch domain wall width, such that the devices with the lowest exchange stiffness will be the ones that host the domain walls with the slowest mobilities.
1703.03198v3
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
2002-07-30
Microscopic relaxation mechanisms and linear magnetization dynamics
Linear magnetization dynamics in the presense of a thermal bath is analyzed for two general classes of microscopic damping mechanisms. The resulting stochastic differential equations are always in the form of a damped harmonic oscillator driven by a thermal field. The damping term contains both the interaction mechanisms and the symmetry of the magnetic system. Back transformation from the oscillator coordinates to the magnetization variables results in a macroscopic tensor form of damping that reflects the system anisotropy. Scalar Landau-Lifshitz-Gilbert damping term is valid only for systems with axial symmetry. Analysis of FMR linewith measurements versus frequency, temperature, and film thickness in NiFe films shows good agreement with a combination of slow-relaxing impurity and magnon-electron confluence processes.
0207721v1
2014-05-09
Magnetization dynamics and damping due to electron-phonon scattering in a ferrimagnetic exchange model
We present a microscopic calculation of magnetization damping for a magnetic "toy model." The magnetic system consists of itinerant carriers coupled antiferromagnetically to a dispersionless band of localized spins, and the magnetization damping is due to coupling of the itinerant carriers to a phonon bath in the presence of spin-orbit coupling. Using a mean-field approximation for the kinetic exchange model and assuming the spin-orbit coupling to be of the Rashba form, we derive Boltzmann scattering integrals for the distributions and spin coherences in the case of an antiferromagnetic exchange splitting, including a careful analysis of the connection between lifetime broadening and the magnetic gap. For the Elliott-Yafet type itinerant spin dynamics we extract dephasing and magnetization times T_1 and T_2 from initial conditions corresponding to a tilt of the magnetization vector, and draw a comparison to phenomenological equations such as the Landau-Lifshitz or the Gilbert damping. We also analyze magnetization precession and damping for this system including an anisotropy field and find a carrier mediated dephasing of the localized spin via the mean-field coupling.
1405.2347v1
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
2022-10-16
Magnetic damping anisotropy in the two-dimensional van der Waals material Fe$_3$GeTe$_2$ from first principles
Magnetization relaxation in the two-dimensional itinerant ferromagnetic van der Waals material Fe$_3$GeTe$_2$, below the Curie temperature, is fundamentally important for applications to low-dimensional spintronics devices. We use first-principles scattering theory to calculate the temperature-dependent Gilbert damping for bulk and single-layer Fe$_3$GeTe$_2$. The calculated damping frequency of bulk Fe$_3$GeTe$_2$ increases monotonically with temperature because of the dominance of resistivitylike behavior. By contrast, a very weak temperature dependence is found for the damping frequency of a single layer, which is attributed to strong surface scattering in this highly confined geometry. A systematic study of the damping anisotropy reveals that orientational anisotropy is present in both bulk and single-layer Fe3GeTe2. Rotational anisotropy is significant at low temperatures for both the bulk and a single layer and is gradually diminished by temperature-induced disorder. The rotational anisotropy can be significantly enhanced by up to 430% in gated single-layer Fe$_3$GeTe$_2$.
2210.08429v1
2016-09-26
Relativistic theory of spin relaxation mechanisms in the Landau-Lifshitz-Gilbert equation of spin dynamics
Starting from the Dirac-Kohn-Sham equation we derive the relativistic equation of motion of spin angular momentum in a magnetic solid under an external electromagnetic field. This equation of motion can be written in the form of the well-known Landau-Lifshitz-Gilbert equation for a harmonic external magnetic field, and leads to a more general magnetization dynamics equation for a general time-dependent magnetic field. In both cases with an electronic spin-relaxation term which stems from the spin-orbit interaction. We thus rigorously derive, from fundamental principles, a general expression for the anisotropic damping tensor which is shown to contain an isotropic Gilbert contribution as well as an anisotropic Ising-like and a chiral, Dzyaloshinskii-Moriya-like contribution. The expression for the spin relaxation tensor comprises furthermore both electronic interband and intraband transitions. We also show that when the externally applied electromagnetic field possesses spin angular momentum, this will lead to an optical spin torque exerted on the spin moment.
1609.07901v1
2023-08-07
$\textit{In situ}$ electric-field control of ferromagnetic resonance in the low-loss organic-based ferrimagnet V[TCNE]$_{x\sim 2}$
We demonstrate indirect electric-field control of ferromagnetic resonance (FMR) in devices that integrate the low-loss, molecule-based, room-temperature ferrimagnet vanadium tetracyanoethylene (V[TCNE]$_{x \sim 2}$) mechanically coupled to PMN-PT piezoelectric transducers. Upon straining the V[TCNE]$_x$ films, the FMR frequency is tuned by more than 6 times the resonant linewidth with no change in Gilbert damping for samples with $\alpha = 6.5 \times 10^{-5}$. We show this tuning effect is due to a strain-dependent magnetic anisotropy in the films and find the magnetoelastic coefficient $|\lambda_S| \sim (1 - 4.4)$ ppm, backed by theoretical predictions from DFT calculations and magnetoelastic theory. Noting the rapidly expanding application space for strain-tuned FMR, we define a new metric for magnetostrictive materials, $\textit{magnetostrictive agility}$, given by the ratio of the magnetoelastic coefficient to the FMR linewidth. This agility allows for a direct comparison between magnetostrictive materials in terms of their comparative efficacy for magnetoelectric applications requiring ultra-low loss magnetic resonance modulated by strain. With this metric, we show V[TCNE]$_x$ is competitive with other magnetostrictive materials including YIG and Terfenol-D. This combination of ultra-narrow linewidth and magnetostriction in a system that can be directly integrated into functional devices without requiring heterogeneous integration in a thin-film geometry promises unprecedented functionality for electric-field tuned microwave devices ranging from low-power, compact filters and circulators to emerging applications in quantum information science and technology.
2308.03353v1
2002-11-22
Nonlinear microscopic relaxation of uniform magnetization precession
Dynamic relaxation for nonlinear magnetization excitation is analyzed. For direct processes, such as magnon-electron scattering and two-magnon scattering, the relaxation rate is determined from the linear case simply by utilizing the magnetization oscillation frequency for nonlinear excitation. For an indirect process, such as slow-relaxing impurities, the analysis gives an additional relaxation term proportional to the excitation level. In all cases the effective magnetization damping is increased compared to Landau-Lifshitz-Gilbert damping.
0211499v1
2005-10-11
Non-damping magnetization oscillations in a single-domain ferromagnet
Non-damped oscillations of the magnetization vector of a ferromagnetic system subject to a spin polarized current and an external magnetic field are studied theoretically by solving the Landau-Lifshitz-Gilbert equation. It is shown that the frequency and amplitude of such oscillations can be controlled by means of an applied magnetic field and a spin current. The possibility of injection of the oscillating spin current into a non-magnetic system is also discussed.
0510280v1
2007-03-27
Gauge Field Formulation of Adiabatic Spin Torques
Previous calculation of spin torques for small-amplitude magnetization dynamics around a uniformly magnetized state [J. Phys. Soc. Jpn. {\bf 75} (2006) 113706] is extended here to the case of finite-amplitude dynamics. This is achieved by introducing an `` adiabatic'' spin frame for conduction electrons, and the associated SU(2) gauge field. In particular, the Gilbert damping is shown to arise from the time variation of the spin-relaxation source terms in this new frame, giving a new physical picture of the damping. The present method will allow a `` first-principle'' derivation of spin torques without any assumptions such as rotational symmetry in spin space.
0703705v1
2008-05-09
Spin dynamics in (III,Mn)V ferromagnetic semiconductors: the role of correlations
We address the role of correlations between spin and charge degrees of freedom on the dynamical properties of ferromagnetic systems governed by the magnetic exchange interaction between itinerant and localized spins. For this we introduce a general theory that treats quantum fluctuations beyond the Random Phase Approximation based on a correlation expansion of the Green's function equations of motion. We calculate the spin susceptibility, spin--wave excitation spectrum, and magnetization precession damping. We find that correlations strongly affect the magnitude and carrier concentration dependence of the spin stiffness and magnetization Gilbert damping.
0805.1320v2
2010-01-16
Resonance Damping in Ferromagnets and Ferroelectrics
The phenomenological equations of motion for the relaxation of ordered phases of magnetized and polarized crystal phases can be developed in close analogy with one another. For the case of magnetized systems, the driving magnetic field intensity toward relaxation was developed by Gilbert. For the case of polarized systems, the driving electric field intensity toward relaxation was developed by Khalatnikov. The transport times for relaxation into thermal equilibrium can be attributed to viscous sound wave damping via magnetostriction for the magnetic case and electrostriction for the polarization case.
1001.2845v1
2016-05-15
Propagation of Thermally Induced Magnonic Spin Currents
The propagation of magnons in temperature gradients is investigated within the framework of an atomistic spin model with the stochastic Landau-Lifshitz-Gilbert equation as underlying equation of motion. We analyze the magnon accumulation, the magnon temperature profile as well as the propagation length of the excited magnons. The frequency distribution of the generated magnons is investigated in order to derive an expression for the influence of the anisotropy and the damping parameter on the magnon propagation length. For soft ferromagnetic insulators with low damping a propagation length in the range of some $\mu$m can be expected for exchange driven magnons.
1605.04543v1
2021-03-05
Universal spin wave damping in magnetic Weyl semimetals
We analyze the decay of spin waves into Stoner excitations in magnetic Weyl semimetals. The lifetime of a mode is found to have a universal dependence on its frequency and momentum, and on a few parameters that characterize the relativistic Weyl spectrum. At the same time, Gilbert damping by Weyl electrons is absent. The decay rate of spin waves is calculated perturbatively using the s-d model of itinerant Weyl or Dirac electrons coupled to local moments. We show that many details of the Weyl spectrum, such as the momentum-space locations, dispersions and sizes of the Weyl Fermi pockets, can be deduced indirectly by probing the spin waves of local moments using inelastic neutron scattering.
2103.03885v1
2023-02-17
Control of magnon-photon coupling by spin torque
We demonstrate the influence of damping and field-like torques in the magnon-photon coupling process by classically integrating the generalized Landau-Lifshitz-Gilbert equation with RLC equation in which a phase correlation between dynamic magnetization and microwave current through combined Amp\`ere and Faraday effects are considered. We show that the gap between two hybridized modes can be controlled in samples with damping parameter in the order of $10^{-3}$ by changing the direction of the dc current density $J$ if a certain threshold is reached. Our results suggest that an experimental realization of the proposed magnon-photon coupling control mechanism is feasible in yttrium iron garnet/Pt hybrid structures.
2302.08910v1
2017-03-21
Using rf voltage induced ferromagnetic resonance to study the spin-wave density of states and the Gilbert damping in perpendicularly magnetized disks
We study how the shape of the spinwave resonance lines in rf-voltage induced FMR can be used to extract the spinwave density of states and the damping within the precessing layer in nanoscale tunnel junctions that possess perpendicular anisotropy. We work with a field applied along the easy axis to preserve the uniaxial symmetry of the system. We describe the set-up to study the susceptibility contributions of the spin waves in the field-frequency space. We then identify the maximum device size above which the spinwaves can no longer be studied in isolation as the linewidths of their responses make them overlap. The rf-voltage induced signal is the sum of two voltages that have comparable magnitudes: a first voltage that originates from the transverse susceptibility and rectification by magnetoresistance and a second voltage that arises from the non-linear longitudinal susceptibility and the resultant time-averaged change of the micromagnetic configuration. The transverse and longitudinal susceptibility signals have different dc bias dependences such that they can be separated by measuring how the device rectifies the rf voltage at different dc bias voltages. The transverse and longitudinal susceptibility signals have different lineshapes; their joint studies can yield the Gilbert damping of the free layer of the device with a degree of confidence that compares well with standard FMR. Our method is illustrated on FeCoB-based free layers in which the individual spin-waves can be sufficiently resolved only for disk diameters below 200 nm. The resonance line shapes on devices with 90 nm diameters are consistent with a Gilbert damping of 0.011. This damping of 0.011 exceeds the value of 0.008 measured on the unpatterned films, which indicates that device-level measurements are needed for a correct evaluation of dissipation.
1703.07310v2
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
2019-08-19
Spectral determinant for the damped wave equation on an interval
We evaluate the spectral determinant for the damped wave equation on an interval of length $T$ with Dirichlet boundary conditions, proving that it does not depend on the damping. This is achieved by analysing the square of the damped wave operator using the general result by Burghelea, Friedlander, and Kappeler on the determinant for a differential operator with matrix coefficients.
1908.06862v1
2020-10-12
Decays rates for Kelvin-Voigt damped wave equations II: the geometric control condition
We study in this article decay rates for Kelvin-Voigt damped wave equations under a geometric control condition. We prove that when the damping coefficient is sufficiently smooth ($C^1$ vanishing nicely) we show that exponential decay follows from geometric control conditions (see~\cite{BuCh, Te12} for similar results under stronger assumptions on the damping function).
2010.05614v2
2019-06-21
Unique determination of the damping coefficient in the wave equation using point source and receiver data
In this article, we consider the inverse problems of determining the damping coefficient appearing in the wave equation. We prove the unique determination of the coefficient from the data coming from a single coincident source-receiver pair. Since our problem is under-determined, so some extra assumption on the coefficient is required to prove the uniqueness.
1906.08987v1
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
2002-08-06
Spin pumping and magnetization dynamics in metallic multilayers
We study the magnetization dynamics in thin ferromagnetic films and small ferromagnetic particles in contact with paramagnetic conductors. A moving magnetization vector causes \textquotedblleft pumping\textquotedblright of spins into adjacent nonmagnetic layers. This spin transfer affects the magnetization dynamics similar to the Landau-Lifshitz-Gilbert phenomenology. The additional Gilbert damping is significant for small ferromagnets, when the nonmagnetic layers efficiently relax the injected spins, but the effect is reduced when a spin accumulation build-up in the normal metal opposes the spin pumping. The damping enhancement is governed by (and, in turn, can be used to measure) the mixing conductance or spin-torque parameter of the ferromagnet--normal-metal interface. Our theoretical findings are confirmed by agreement with recent experiments in a variety of multilayer systems.
0208091v2
2005-12-29
Current-induced magnetization dynamics in disordered itinerant ferromagnets
Current-driven magnetization dynamics in ferromagnetic metals are studied in a self-consistent adiabatic local-density approximation in the presence of spin-conserving and spin-dephasing impurity scattering. Based on a quantum kinetic equation, we derive Gilbert damping and spin-transfer torques entering the Landau-Lifshitz equation to linear order in frequency and wave vector. Gilbert damping and a current-driven dissipative torque scale identically and compete, with the result that a steady current-driven domain-wall motion is insensitive to spin dephasing in the limit of weak ferromagnetism. A uniform magnetization is found to be much more stable against spin torques in the itinerant than in the \textit{s}-\textit{d} model for ferromagnetism. A dynamic spin-transfer torque reminiscent of the spin pumping in multilayers is identified and shown to govern the current-induced domain-wall distortion.
0512715v4
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
2007-08-03
Strong spin-orbit induced Gilbert damping and g-shift in iron-platinum nanoparticles
The shape of ferromagnetic resonance spectra of highly dispersed, chemically disordered Fe_{0.2}Pt_{0.8} nanospheres is perfectly described by the solution of the Landau-Lifshitz-Gilbert (LLG) equation excluding effects by crystalline anisotropy and superparamagnetic fluctuations. Upon decreasing temperature, the LLG damping $\alpha(T)$ and a negative g-shift, g(T)-g_0, increase proportional to the particle magnetic moments determined from the Langevin analysis of the magnetization isotherms. These novel features are explained by the scattering of the $q \to 0$ magnon from an electron-hole (e/h) pair mediated by the spin-orbit coupling, while the sd-exchange can be ruled out. The large saturation values, $\alpha(0)=0.76$ and $g(0)/g_0-1=-0.37$, indicate the dominance of an overdamped 1 meV e/h-pair which seems to originate from the discrete levels of the itinerant electrons in the d_p=3 nm nanoparticles.
0708.0463v1
2008-05-01
Chaotic Spin Dynamics of a Long Nanomagnet Driven by a Current
We study the spin dynamics of a long nanomagnet driven by an electrical current. In the case of only DC current, the spin dynamics has a sophisticated bifurcation diagram of attractors. One type of attractors is a weak chaos. On the other hand, in the case of only AC current, the spin dynamics has a rather simple bifurcation diagram of attractors. That is, for small Gilbert damping, when the AC current is below a critical value, the attractor is a limit cycle; above the critical value, the attractor is chaotic (turbulent). For normal Gilbert damping, the attractor is always a limit cycle in the physically interesting range of the AC current. We also developed a Melnikov integral theory for a theoretical prediction on the occurrence of chaos. Our Melnikov prediction seems performing quite well in the DC case. In the AC case, our Melnikov prediction seems predicting transient chaos. The sustained chaotic attractor seems to have extra support from parametric resonance leading to a turbulent state.
0805.0147v1
2010-10-08
A unified first-principles study of Gilbert damping, spin-flip diffusion and resistivity in transition metal alloys
Using a formulation of first-principles scattering theory that includes disorder and spin-orbit coupling on an equal footing, we calculate the resistivity $\rho$, spin flip diffusion length $l_{sf}$ and the Gilbert damping parameter $\alpha$ for Ni$_{1-x}$Fe$_x$ substitutional alloys as a function of $x$. For the technologically important Ni$_{80}$Fe$_{20}$ alloy, permalloy, we calculate values of $\rho = 3.5 \pm 0.15$ $\mu$Ohm-cm, $l_{sf}=5.5 \pm 0.3$ nm, and $\alpha= 0.0046 \pm 0.0001$ compared to experimental low-temperature values in the range $4.2-4.8$ $\mu$Ohm-cm for $\rho$, $5.0-6.0$ nm for $l_{sf}$, and $0.004-0.013$ for $\alpha$ indicating that the theoretical formalism captures the most important contributions to these parameters.
1010.1626v3
2011-02-22
Ab-initio calculation of the Gilbert damping parameter via linear response formalism
A Kubo-Greenwood-like equation for the Gilbert damping parameter $\alpha$ is presented that is based on the linear response formalism. Its implementation using the fully relativistic Korringa-Kohn-Rostoker (KKR) band structure method in combination with Coherent Potential Approximation (CPA) alloy theory allows it to be applied to a wide range of situations. This is demonstrated with results obtained for the bcc alloy system Fe$_x$Co$_{1-x}$ as well as for a series of alloys of permalloy with 5d transition metals. To account for the thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. The corresponding calculations for Ni correctly describe the rapid change of $\alpha$ when small amounts of substitutional Cu are introduced.
1102.4551v1
2012-08-07
Observation of Coherent Helimagnons and Gilbert damping in an Itinerant Magnet
We study the magnetic excitations of itinerant helimagnets by applying time-resolved optical spectroscopy to Fe0.8Co0.2Si. Optically excited oscillations of the magnetization in the helical state are found to disperse to lower frequency as the applied magnetic field is increased; the fingerprint of collective modes unique to helimagnets, known as helimagnons. The use of time-resolved spectroscopy allows us to address the fundamental magnetic relaxation processes by directly measuring the Gilbert damping, revealing the versatility of spin dynamics in chiral magnets. (*These authors contributed equally to this work)
1208.1462v1
2012-11-02
Dynamic Spin Injection into Chemical Vapor Deposited Graphene
We demonstrate dynamic spin injection into chemical vapor deposition (CVD) grown graphene by spin pumping from permalloy (Py) layers. Ferromagnetic resonance measurements at room temperature reveal a strong enhancement of the Gilbert damping at the Py/graphene interface, exceeding that observed in even Py/platinum interfaces. Similar results are also shown on Co/graphene layers. This enhancement in the Gilbert damping is understood as the consequence of spin pumping at the interface driven by magnetization dynamics. Our observations suggest a strong enhancement of spin-orbit coupling in CVD graphene, in agreement with earlier spin valve measurements.
1211.0492v1
2013-01-10
First-principles calculation of the Gilbert damping parameter via the linear response formalism with application to magnetic transition-metals and alloys
A method for the calculations of the Gilbert damping parameter $\alpha$ is presented, which based on the linear response formalism, has been implemented within the fully relativistic Korringa-Kohn-Rostoker band structure method in combination with the coherent potential approximation alloy theory. To account for thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. This allows the determination of $\alpha$ for various types of materials, such as elemental magnetic systems and ordered magnetic compounds at finite temperature, as well as for disordered magnetic alloys at $T = 0$ K and above. The effects of spin-orbit coupling, chemical and temperature induced structural disorder are analyzed. Calculations have been performed for the 3$d$ transition-metals bcc Fe, hcp Co, and fcc Ni, their binary alloys bcc Fe$_{1-x}$Co$_{x}$, fcc Ni$_{1-x}$Fe$_x$, fcc Ni$_{1-x}$Co$_x$ and bcc Fe$_{1-x}$V$_{x}$, and for 5d impurities in transition-metal alloys. All results are in satisfying agreement with experiment.
1301.2114v1
2014-01-24
Wavenumber-dependent Gilbert damping in metallic ferromagnets
New terms to the dynamical equation of magnetization motion, associated with spin transport, have been reported over the past several years. Each newly identified term is thought to possess both a real and an imaginary effective field leading to fieldlike and dampinglike torques on magnetization. Here we show that three metallic ferromagnets possess an imaginary effective-field term which mirrors the well-known real effective-field term associated with exchange in spin waves. Using perpendicular standing spin wave resonance between 2-26 GHz, we evaluate the magnitude of the finite-wavenumber ($k$) dependent Gilbert damping $\alpha$ in three typical device ferromagnets, Ni$_{79}$Fe$_{21}$, Co, and Co$_{40}$Fe$_{40}$B$_{20}$, and demonstrate for the first time the presence of a $k^2$ term as $\Delta\alpha=\Delta\alpha_0+A_{k}\cdot k^2$ in all three metals. We interpret the new term as the continuum analog of spin pumping, predicted recently, and show that its magnitude, $A_{k}$=0.07-0.1 nm$^2$, is consistent with transverse spin relaxation lengths as measured by conventional (interlayer) spin pumping.
1401.6467v2
2014-12-11
Deviation From the Landau-Lifshitz-Gilbert equation in the Inertial regime of the Magnetization
We investigate in details the inertial dynamics of a uniform magnetization in the ferromagnetic resonance (FMR) context. Analytical predictions and numerical simulations of the complete equations within the Inertial Landau-Lifshitz-Gilbert (ILLG) model are presented. In addition to the usual precession resonance, the inertial model gives a second resonance peak associated to the nutation dynamics provided that the damping is not too large. The analytical resolution of the equations of motion yields both the precession and nutation angular frequencies. They are function of the inertial dynamics characteristic time $\tau$, the dimensionless damping $\alpha$ and the static magnetic field $H$. A scaling function with respect to $\alpha\tau\gamma H$ is found for the nutation angular frequency, also valid for the precession angular frequency when $\alpha\tau\gamma H\gg 1$. Beyond the direct measurement of the nutation resonance peak, we show that the inertial dynamics of the magnetization has measurable effects on both the width and the angular frequency of the precession resonance peak when varying the applied static field. These predictions could be used to experimentally identify the inertial dynamics of the magnetization proposed in the ILLG model.
1412.3783v1
2015-08-04
A Critical Analysis of the Feasibility of Pure Strain-Actuated Giant Magnetostrictive Nanoscale Memories
Concepts for memories based on the manipulation of giant magnetostrictive nanomagnets by stress pulses have garnered recent attention due to their potential for ultra-low energy operation in the high storage density limit. Here we discuss the feasibility of making such memories in light of the fact that the Gilbert damping of such materials is typically quite high. We report the results of numerical simulations for several classes of toggle precessional and non-toggle dissipative magnetoelastic switching modes. Material candidates for each of the several classes are analyzed and forms for the anisotropy energy density and ranges of material parameters appropriate for each material class are employed. Our study indicates that the Gilbert damping as well as the anisotropy and demagnetization energies are all crucial for determining the feasibility of magnetoelastic toggle-mode precessional switching schemes. The roles of thermal stability and thermal fluctuations for stress-pulse switching of giant magnetostrictive nanomagnets are also discussed in detail and are shown to be important in the viability, design, and footprint of magnetostrictive switching schemes.
1508.00629v2
2015-12-16
Parity-time symmetry breaking in magnetic systems
The understanding of out-of-equilibrium physics, especially dynamic instabilities and dynamic phase transitions, is one of the major challenges of contemporary science, spanning the broadest wealth of research areas that range from quantum optics to living organisms. Focusing on nonequilibrium dynamics of an open dissipative spin system, we introduce a non-Hermitian Hamiltonian approach, in which non-Hermiticity reflects dissipation and deviation from equilibrium. The imaginary part of the proposed spin Hamiltonian describes the effects of Gilbert damping and applied Slonczewski spin-transfer torque. In the classical limit, our approach reproduces Landau-Lifshitz-Gilbert-Slonczewski dynamics of a large macrospin. We reveal the spin-transfer torque-driven parity-time symmetry-breaking phase transition corresponding to a transition from precessional to exponentially damped spin dynamics. Micromagnetic simulations for nanoscale ferromagnetic disks demonstrate the predicted effect. Our findings can pave the way to a general quantitative description of out-of-equilibrium phase transitions driven by spontaneous parity-time symmetry breaking.
1512.05408v2
2017-01-11
The Cauchy problem for the Landau-Lifshitz-Gilbert equation in BMO and self-similar solutions
We prove a global well-posedness result for the Landau-Lifshitz equation with Gilbert damping provided that the BMO semi-norm of the initial data is small. As a consequence, we deduce the existence of self-similar solutions in any dimension. In the one-dimensional case, we characterize the self-similar solutions associated with an initial data given by some ($\mathbb{S}^2$-valued) step function and establish their stability. We also show the existence of multiple solutions if the damping is strong enough. Our arguments rely on the study of a dissipative quasilinear Schr\"odinger obtained via the stereographic projection and techniques introduced by Koch and Tataru.
1701.03083v2
2017-01-27
Structural scale $q-$derivative and the LLG-Equation in a scenario with fractionality
In the present contribution, we study the Landau-Lifshitz-Gilbert equation with two versions of structural derivatives recently proposed: the scale $q-$derivative in the non-extensive statistical mechanics and the axiomatic metric derivative, which presents Mittag-Leffler functions as eigenfunctions. The use of structural derivatives aims to take into account long-range forces, possible non-manifest or hidden interactions and the dimensionality of space. Having this purpose in mind, we build up an evolution operator and a deformed version of the LLG equation. Damping in the oscillations naturally show up without an explicit Gilbert damping term.
1701.08076v2
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
2019-03-07
Current-induced motion of twisted skyrmions
Twisted skyrmions, whose helicity angles are different from that of Bloch skyrmions and N\'eel skyrmions, have already been demonstrated in experiments recently. In this work, we first contrast the magnetic structure and origin of the twisted skyrmion with other three types of skyrmion including Bloch skyrmion, N\'eel skyrmion and antiskyrmion. Following, we investigate the dynamics of twisted skyrmions driven by the spin transfer toque (STT) and the spin Hall effect (SHE) by using micromagnetic simulations. It is found that the spin Hall angle of the twisted skyrmion is related to the dissipative force tensor and the Gilbert damping both for the motions induced by the STT and the SHE, especially for the SHE induced motion, the skyrmion Hall angle depends substantially on the skyrmion helicity. At last, we demonstrate that the trajectory of the twisted skyrmion can be controlled in a two dimensional plane with a Gilbert damping gradient. Our results provide the understanding of current-induced motion of twisted skyrmions, which may contribute to the applications of skyrmion-based racetrack memories.
1903.02812v1
2019-07-03
Anisotropy of spin-transfer torques and Gilbert damping induced by Rashba coupling
Spin-transfer torques (STT), Gilbert damping (GD), and effective spin renormalization (ESR) are investigated microscopically in a 2D Rashba ferromagnet with spin-independent Gaussian white-noise disorder. Rashba spin-orbit coupling induced anisotropy of these phenomena is thoroughly analysed. For the case of two partly filled spin subbands, a remarkable relation between the anisotropic STT, GD, and ESR is established. In the absence of magnetic field and other torques on magnetization, this relation corresponds to a current-induced motion of a magnetic texture with the classical drift velocity of conduction electrons. Finally, we compute spin susceptibility of the system and generalize the notion of spin-polarized current.
1907.02041v3
2021-11-05
Giant oscillatory Gilbert damping in superconductor/ferromagnet/superconductor junctions
Interfaces between materials with differently ordered phases present unique opportunities for exotic physical properties, especially the interplay between ferromagnetism and superconductivity in the ferromagnet/superconductor heterostructures. The investigation of zero- and pi-junctions has been of particular interest for both fundamental physical science and emerging technologies. Here, we report the experimental observation of giant oscillatory Gilbert damping in the superconducting Nb/NiFe/Nb junctions with respect to the NiFe thickness. This observation suggests an unconventional spin pumping and relaxation via zero-energy Andreev bound states that exist only in the Nb/NiFe/Nb pi-junctions, but not in the Nb/NiFe/Nb zero-junctions. Our findings could be important for further exploring the exotic physical properties of ferromagnet/superconductor heterostructures, and potential applications of ferromagnet pi-junctions in quantum computing, such as half-quantum flux qubits.
2111.03233v1
2022-11-14
Magnetization Dynamics in Synthetic Antiferromagnets with Perpendicular Magnetic Anisotropy
Understanding the rich physics of magnetization dynamics in perpendicular synthetic antiferromagnets (p-SAFs) is crucial for developing next-generation spintronic devices. In this work, we systematically investigate the magnetization dynamics in p-SAFs combining time-resolved magneto-optical Kerr effect (TR-MOKE) measurements with theoretical modeling. These model analyses, based on a Landau-Lifshitz-Gilbert approach incorporating exchange coupling, provide details about the magnetization dynamic characteristics including the amplitudes, directions, and phases of the precession of p-SAFs under varying magnetic fields. These model-predicted characteristics are in excellent quantitative agreement with TR-MOKE measurements on an asymmetric p-SAF. We further reveal the damping mechanisms of two procession modes co-existing in the p-SAF and successfully identify individual contributions from different sources, including Gilbert damping of each ferromagnetic layer, spin pumping, and inhomogeneous broadening. Such a comprehensive understanding of magnetization dynamics in p-SAFs, obtained by integrating high-fidelity TR-MOKE measurements and theoretical modeling, can guide the design of p-SAF-based architectures for spintronic applications.
2211.07744v2
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