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2017-06-14
Temperature-dependent Gilbert damping of Co2FeAl thin films with different degree of atomic order
Half-metallicity and low magnetic damping are perpetually sought for in spintronics materials and full Heusler alloys in this respect provide outstanding properties. However, it is challenging to obtain the well-ordered half-metallic phase in as-deposited full Heusler alloys thin films and theory has struggled to establish a fundamentals understanding of the temperature dependent Gilbert damping in these systems. Here we present a study of the temperature dependent Gilbert damping of differently ordered as-deposited Co2FeAl full Heusler alloy thin films. The sum of inter- and intraband electron scattering in conjunction with the finite electron lifetime in Bloch states govern the Gilbert damping for the well-ordered phase in contrast to the damping of partially-ordered and disordered phases which is governed by interband electronic scattering alone. These results, especially the ultralow room temperature intrinsic damping observed for the well-ordered phase provide new fundamental insights to the physical origin of the Gilbert damping in full Heusler alloy thin films.
1706.04670v2
2023-11-27
Gilbert damping in two-dimensional metallic anti-ferromagnets
A finite spin life-time of conduction electrons may dominate Gilbert damping of two-dimensional metallic anti-ferromagnets or anti-ferromagnet/metal heterostructures. We investigate the Gilbert damping tensor for a typical low-energy model of a metallic anti-ferromagnet system with honeycomb magnetic lattice and Rashba spin-orbit coupling for conduction electrons. We distinguish three regimes of spin relaxation: exchange-dominated relaxation for weak spin-orbit coupling strength, Elliot-Yafet relaxation for moderate spin-orbit coupling, and Dyakonov-Perel relaxation for strong spin-orbit coupling. We show, however, that the latter regime takes place only for the in-plane Gilbert damping component. We also show that anisotropy of Gilbert damping persists for any finite spin-orbit interaction strength provided we consider no spatial variation of the N\'eel vector. Isotropic Gilbert damping is restored only if the electron spin-orbit length is larger than the magnon wavelength. Our theory applies to MnPS3 monolayer on Pt or to similar systems.
2311.16268v2
2013-08-01
Inverse Spin Hall Effect in nanometer-thick YIG/Pt system
High quality nanometer-thick (20 nm, 7 nm and 4 nm) epitaxial YIG films have been grown on GGG substrates using pulsed laser deposition. The Gilbert damping coefficient for the 20 nm thick films is 2.3 x 10-4 which is the lowest value reported for sub-micrometric thick films. We demonstrate Inverse spin Hall effect (ISHE) detection of propagating spin waves using Pt. The amplitude and the lineshape of the ISHE voltage correlate well to the increase of the Gilbert damping when decreasing thickness of YIG. Spin Hall effect based loss-compensation experiments have been conducted but no change in the magnetization dynamics could be detected.
1308.0192v1
2020-08-14
Large enhancement of spin pumping due to the surface bound states in normal metal/superconductor structures
We show that the spin pumping from ferromagnetic insulator into the adjacent metallic spin sink can be strongly stimulated by the superconducting correlations. The key physical mechanism responsible for this effect is the presence of quasiparticle surface states at the ferromagnetic insulator/superconductor interface. We consider the minimal model when these states appear because of the suppressed pairing constant within the interfacial normal layer. For thin normal layers we obtain a strongly peaked temperature dependence of the Gilbert damping coefficient which has been recently observed in such systems. For thicker normal layers the Gilbert damping monotonically increases down to the temperatures much smaller than the critical one. The suggested model paves the way to controlling the temperature dependence of the spin pumping by fabricating hybrid normal metal/superconductor spin sinks.
2008.06253v1
2012-07-28
Ultrafast optical control of magnetization in EuO thin films
All-optical pump-probe detection of magnetization precession has been performed for ferromagnetic EuO thin films at 10 K. We demonstrate that the circularly-polarized light can be used to control the magnetization precession on an ultrafast time scale. This takes place within the 100 fs duration of a single laser pulse, through combined contribution from two nonthermal photomagnetic effects, i.e., enhancement of the magnetization and an inverse Faraday effect. From the magnetic field dependences of the frequency and the Gilbert damping parameter, the intrinsic Gilbert damping coefficient is evaluated to be {\alpha} \approx 3\times10^-3.
1207.6686v1
2015-01-02
Inertia, diffusion and dynamics of a driven skyrmion
Skyrmions recently discovered in chiral magnets are a promising candidate for magnetic storage devices because of their topological stability, small size ($\sim 3-100$nm), and ultra-low threshold current density ($\sim 10^{6}$A/m$^2$) to drive their motion. However, the time-dependent dynamics has hitherto been largely unexplored. Here we show, by combining the numerical solution of the Landau-Lifshitz-Gilbert equation and the analysis of a generalized Thiele's equation, that inertial effects are almost completely absent in skyrmion dynamics driven by a time-dependent current. In contrast, the response to time-dependent magnetic forces and thermal fluctuations depends strongly on frequency and is described by a large effective mass and a (anti-) damping depending on the acceleration of the skyrmion. Thermal diffusion is strongly suppressed by the cyclotron motion and is proportional to the Gilbert damping coefficient $\alpha$. This indicates that the skyrmion position is stable, and its motion responds to the time-dependent current without delay or retardation even if it is fast. These findings demonstrate the advantages of skyrmions as information carriers.
1501.00444v1
2008-07-31
Scattering Theory of Gilbert Damping
The magnetization dynamics of a single domain ferromagnet in contact with a thermal bath is studied by scattering theory. We recover the Landau-Liftshitz-Gilbert equation and express the effective fields and Gilbert damping tensor in terms of the scattering matrix. Dissipation of magnetic energy equals energy current pumped out of the system by the time-dependent magnetization, with separable spin-relaxation induced bulk and spin-pumping generated interface contributions. In linear response, our scattering theory for the Gilbert damping tensor is equivalent with the Kubo formalism.
0807.5009v1
2016-04-11
All-Optical Study of Tunable Ultrafast Spin Dynamics in [Co/Pd]-NiFe Systems: The Role of Spin-Twist Structure on Gilbert Damping
We investigate optically induced ultrafast magnetization dynamics in [Co(0.5 nm)/Pd(1 nm)]x5/NiFe(t) exchange-spring samples with tilted perpendicular magnetic anisotropy using a time-resolved magneto-optical Kerr effect magnetometer. The competition between the out-of-plane anisotropy of the hard layer, the in-plane anisotropy of the soft layer and the applied bias field reorganizes the spins in the soft layer, which are modified further with the variation in t. The spin-wave spectrum, the ultrafast demagnetization time, and the extracted damping coefficient all depend on the spin distribution in the soft layer, while the latter two also depend on the spin-orbit coupling between the Co and Pd layers. The spin-wave spectra change from multimode to single-mode as t increases. At the maximum field reached in this study, H=2.5 kOe, the damping shows a nonmonotonic dependence on t with a minimum at t=7.5 nm. For t<7.5 nm, intrinsic effects dominate, whereas for t>7.5 nm, extrinsic effects govern the damping mechanisms.
1604.02998v1
2024-01-18
Real-space nonlocal Gilbert damping from exchange torque correlation applied to bulk ferromagnets and their surfaces
In this work we present an ab initio scheme based on linear response theory of exchange torque correlation, implemented into the real-space Korringa-Kohn-Rostoker (RS-KKR) framework to calculate diagonal elements of the atomic-site-dependent intrinsic Gilbert damping tensor. The method is first applied to bcc iron and fcc cobalt bulk systems. Beside reproducing earlier results from the literature for those bulk magnets, the effect of the lattice compression is also studied for Fe bulk, and significant changes for the Gilbert damping are found. Furthermore, (001)-oriented surfaces of Fe and Co are also investigated. It is found that the on-site Gilbert damping increases in the surface atomic layer and decreases in the subsurface layer, and approaches the bulk value moving further inside the magnets. Realistic atomic relaxation of the surface layers enhances the identified effects. The first-neighbor damping parameters are extremely sensitive to the surface relaxation. Despite their inhomogeneity caused by the surface, the transverse Gilbert damping tensor components remain largely insensitive to the magnetization direction.
2401.09938v2
2007-06-12
Gilbert and Landau-Lifshitz damping in the presense of spin-torque
A recent article by Stiles et al. (cond-mat/0702020) argued in favor of the Landau-Lifshitz damping term in the micromagnetic equations of motion over that of the more commonly accepted Gilbert damping form. Much of their argument revolved around spin-torque driven domain wall motion in narrow magnetic wires, since the presence of spin-torques can more acutely draw a distinction between the two forms of damping. In this article, the author uses simple arguments and examples to offer an alternative point of view favoring Gilbert.
0706.1736v1
2015-06-02
Current-Driven Motion of Magnetic Domain Wall with Many Bloch Lines
The current-driven motion of a domain wall (DW) in a ferromagnet with many Bloch lines (BLs) via the spin transfer torque is studied theoretically. It is found that the motion of BLs changes the current-velocity ($j$-$v$) characteristic dramatically. Especially, the critical current density to overcome the pinning force is reduced by the factor of the Gilbert damping coefficient $\alpha$ even compared with that of a skyrmion. This is in sharp contrast to the case of magnetic field driven motion, where the existence of BLs reduces the mobility of the DW.
1506.00723v1
2023-03-13
Experimental investigation of the effect of topological insulator on the magnetization dynamics of ferromagnetic metal: $BiSbTe_{1.5}Se_{1.5}$ and $Ni_{80}Fe_{20}$ heterostructure
We have studied ferromagnetic metal/topological insulator bilayer system to understand magnetization dynamics of ferromagnetic metal (FM) in contact with a topological insulator (TI). At magnetic resonance condition, the precessing magnetization in the metallic ferromagnet ($Ni_{80}Fe_{20}$) injects spin current into the topological insulator ($BiSbTe_{1.5}Se_{1.5}$), a phenomenon known as spin-pumping. Due to the spin pumping effect, fast relaxation in the ferromagnet results in the broadening of ferromagnetic resonance linewidth ($\Delta H$). We evaluated the parameters like effective Gilbert damping coefficient ($\alpha_{eff}$), spin-mixing conductance ($g_{eff}^{\uparrow \downarrow}$) and spin current density ($j_S^0$) to confirm a successful spin injection due to spin-pumping into the $BiSbTe_{1.5}Se_{1.5}$ layer. TIs embody a spin-momentum locked surface state that span the bulk band-gap. It can act differently to the FM magnetization than the other normal metals. To probe the effect of topological surface state, a systematic low temperature study is crucial as surface state of TI dominates at lower temperatures. The exponential growth of $\Delta H$ for all different thickness combination of FM/TI bilayers and effective Gilbert damping coefficient ($\alpha_{eff}$) with lowering temperature confirms the prediction that spin chemical bias generated from spin-pumping induces surface current in TI due to spin-momentum locking. The hump-like feature of magnetic anisotropy field ($H_K$)of the bilayer around 60K suggests that the decrease of interfacial in-plane magnetic anisotropy can result from exchange coupling between the TI surface state and the local moments of FM layer.
2303.07025v2
2021-01-07
Mechanisms behind large Gilbert damping anisotropies
A method with which to calculate the Gilbert damping parameter from a real-space electronic structure method is reported here. The anisotropy of the Gilbert damping with respect to the magnetic moment direction and local chemical environment is calculated for bulk and surfaces of Fe$_{50}$Co$_{50}$ alloys from first principles electronic structure in a real space formulation. The size of the damping anisotropy for Fe$_{50}$Co$_{50}$ alloys is demonstrated to be significant. Depending on details of the simulations, it reaches a maximum-minimum damping ratio as high as 200%. Several microscopic origins of the strongly enhanced Gilbert damping anisotropy have been examined, where in particular interface/surface effects stand out, as do local distortions of the crystal structure. Although theory does not reproduce the experimentally reported high ratio of 400% [Phys. Rev. Lett. 122, 117203 (2019)], it nevertheless identifies microscopic mechanisms that can lead to huge damping anisotropies.
2101.02794v2
2018-08-13
Gilbert damping phenomenology for two-sublattice magnets
We present a systematic phenomenological description of Gilbert damping in two-sublattice magnets. Our theory covers the full range of materials from ferro- via ferri- to antiferromagnets. Following a Rayleigh dissipation functional approach within a Lagrangian classical field formulation, the theory captures intra- as well as cross-sublattice terms in the Gilbert damping, parameterized by a 2$\times$2 matrix. When spin-pumping into an adjacent conductor causes dissipation, we obtain the corresponding Gilbert damping matrix in terms of the interfacial spin-mixing conductances. Our model reproduces the experimentally observed enhancement of the ferromagnetic resonance linewidth in a ferrimagnet close to its compensation temperature without requiring an increased Gilbert parameter. It also predicts new contributions to damping in an antiferromagnet and suggests the resonance linewidths as a direct probe of the sublattice asymmetry, which may stem from boundary or bulk.
1808.04385v2
2021-07-02
Anomalous Gilbert Damping and Duffing Features of the SFS {\boldmath $\varphi_0$} Josephson Junction
We demonstrate unusual features of phase dynamics, IV-characteristics and magnetization dynamics of the $\varphi_0$ Josephson junction at small values of spin-orbit interaction, ratio of Josephson to magnetic energy and Gilbert damping. In particular, an anomalous shift of the ferromagnetic resonance frequency with an increase of Gilbert damping is found. The ferromagnetic resonance curves show the Duffing oscillator behaviour, reflecting the nonlinear nature of Landau-Lifshitz-Gilbert (LLG) equation. Based on the numerical analysis of each term in LLG equation we obtained an approximated equation demonstrated both damping effect and Duffing oscillator features. The resulting Duffing equation incorporates the Gilbert damping in a special way across the dissipative term and the restoring force. A resonance method for the determination of spin-orbit interaction in noncentrosymmetric materials which play the role of barrier in $\varphi_0$ junctions is proposed.
2107.00982v3
2023-03-07
Electrically tunable Gilbert damping in van der Waals heterostructures of two-dimensional ferromagnetic metals and ferroelectrics
Tuning the Gilbert damping of ferromagnetic (FM) metals via a nonvolatile way is of importance to exploit and design next-generation novel spintronic devices. Through systematical first-principles calculations, we study the magnetic properties of the van der Waals heterostructure of two-dimensional FM metal CrTe2 and ferroelectric (FE) In2Te3 monolayers. The ferromagnetism of CrTe2 is maintained in CrTe2/In2Te3 and its magnetic easy axis can be switched from in-plane to out-of-plane by reversing the FE polarization of In2Te3. Excitingly, we find that the Gilbert damping of CrTe2 is tunable when the FE polarization of In2Te3 is reversed from upward to downward. By analyzing the k-dependent contributions to the Gilbert damping, we unravel that such tunability results from the changed intersections between the bands of CrTe2 and Fermi level on the reversal of the FE polarizations of In2Te3 in CrTe2/In2Te3. Our work provides an appealing way to electrically tailor Gilbert dampings of two-dimensional FM metals by contacting them with ferroelectrics.
2303.03852v1
2015-08-28
The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space
We prove that in dimensions three and higher the Landau-Lifshitz- Gilbert equation with small initial data in the critical Besov space is globally wellposed in a uniform way with respect to the Gilbert damping parameter. Then we show that the global solution converges to that of the Schrodinger maps in the natural space as the Gilbert damping term vanishes. The proof is based on some studies on the derivative Ginzburg-Landau equations.
1508.07118v3
2023-09-20
Evaluating Gilbert Damping in Magnetic Insulators from First Principles
Magnetic damping has a significant impact on the performance of various magnetic and spintronic devices, making it a long-standing focus of research. The strength of magnetic damping is usually quantified by the Gilbert damping constant in the Landau-Lifshitz-Gilbert equation. Here we propose a first-principles based approach to evaluate the Gilbert damping constant contributed by spin-lattice coupling in magnetic insulators. The approach involves effective Hamiltonian models and spin-lattice dynamics simulations. As a case study, we applied our method to Y$_3$Fe$_5$O$_{12}$, MnFe$_2$O$_4$ and Cr$_2$O$_3$. Their damping constants were calculated to be $0.8\times10^{-4}$, $0.2\times10^{-4}$, $2.2\times 10^{-4}$, respectively at a low temperature. The results for Y$_3$Fe$_5$O$_{12}$ and Cr$_2$O$_3$ are in good agreement with experimental measurements, while the discrepancy in MnFe$_2$O$_4$ can be attributed to the inhomogeneity and small band gap in real samples. The stronger damping observed in Cr$_2$O$_3$, compared to Y$_3$Fe$_5$O$_{12}$, essentially results from its stronger spin-lattice coupling. In addition, we confirmed a proportional relationship between damping constants and the temperature difference of subsystems, which had been reported in previous studies. These successful applications suggest that our approach serves as a promising candidate for estimating the Gilbert damping constant in magnetic insulators.
2309.11152v1
2008-11-25
The quantum-mechanical basis of an extended Landau-Lifshitz-Gilbert equation for a current-carrying ferromagnetic wire
An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for a simple model which includes impurity scattering. This is done by comparing the energies and lifetimes of a spin wave calculated from the LLG equation and from the explicit model. Two terms are of particular importance since they describe non-adiabatic spin-transfer torque and damping processes which do not rely on spin-orbit coupling. It is shown that these terms may have a significant influence on the velocity of a current-driven domain wall and they become dominant in the case of a narrow wall.
0811.4118v1
2019-06-25
Conductivity-Like Gilbert Damping due to Intraband Scattering in Epitaxial Iron
Confirming the origin of Gilbert damping by experiment has remained a challenge for many decades, even for simple ferromagnetic metals. In this Letter, we experimentally identify Gilbert damping that increases with decreasing electronic scattering in epitaxial thin films of pure Fe. This observation of conductivity-like damping, which cannot be accounted for by classical eddy current loss, is in excellent quantitative agreement with theoretical predictions of Gilbert damping due to intraband scattering. Our results resolve the longstanding question about a fundamental damping mechanism and offer hints for engineering low-loss magnetic metals for cryogenic spintronics and quantum devices.
1906.10326v2
2008-08-28
Gilbert Damping in Conducting Ferromagnets II: Model Tests of the Torque-Correlation Formula
We report on a study of Gilbert damping due to particle-hole pair excitations in conducting ferromagnets. We focus on a toy two-band model and on a four-band spherical model which provides an approximate description of ferromagnetic (Ga,Mn)As. These models are sufficiently simple that disorder-ladder-sum vertex corrections to the long-wavelength spin-spin response function can be summed to all orders. An important objective of this study is to assess the reliability of practical approximate expressions which can be combined with electronic structure calculations to estimate Gilbert damping in more complex systems.
0808.3923v1
2010-01-26
Effect of spin-conserving scattering on Gilbert damping in ferromagnetic semiconductors
The Gilbert damping in ferromagnetic semiconductors is theoretically investigated based on the $s$-$d$ model. In contrast to the situation in metals, all the spin-conserving scattering in ferromagnetic semiconductors supplies an additional spin relaxation channel due to the momentum dependent effective magnetic field of the spin-orbit coupling, thereby modifies the Gilbert damping. In the presence of a pure spin current, we predict a new contribution due to the interplay of the anisotropic spin-orbit coupling and a pure spin current.
1001.4576v1
2011-05-20
Magnetization Dissipation in the Ferromagnetic Semiconductor (Ga,Mn)As
We compute the Gilbert damping in (Ga,Mn)As based on the scattering theory of magnetization relaxation. The disorder scattering is included non-perturbatively. In the clean limit, the spin-pumping from the localized d-electrons to the itinerant holes dominates the relaxation processes. In the diffusive regime, the breathing Fermi-surface effect is balanced by the effects of interband scattering, which cause the Gilbert damping constant to saturate at around 0.005. In small samples, the system shape induces a large anisotropy in the Gilbert damping.
1105.4148v2
2008-12-17
Origin of intrinsic Gilbert damping
The damping of magnetization, represented by the rate at which it relaxes to equilibrium, is successfully modeled as a phenomenological extension in the Landau-Lifschitz-Gilbert equation. This is the damping torque term known as Gilbert damping and its direction is given by the vector product of the magnetization and its time derivative. Here we derive the Gilbert term from first principles by a non-relativistic expansion of the Dirac equation. We find that the Gilbert term arises when one calculates the time evolution of the spin observable in the presence of the full spin-orbital coupling terms, while recognizing the relationship between the curl of the electric field and the time varying magnetic induction.
0812.3184v2
2019-07-01
Magnon decay theory of Gilbert damping in metallic antiferromagnets
Gilbert damping is a key property governing magnetization dynamics in ordered magnets. We present a theoretical study of intrinsic Gilbert damping induced by magnon decay in antiferromagnetic metals through $s$-$d$ exchange interaction. Our theory delineates the qualitative features of damping in metallic antiferromagnets owing to their bipartite nature, in addition to providing analytic expressions for the damping parameters. Magnon-induced intraband electron scattering is found to predominantly cause magnetization damping, whereas the N\'eel field is found to be damped via disorder. Depending on the conduction electron band structure, we predict that magnon-induced interband electron scattering around band crossings may be exploited to engineer a strong N\'eel field damping.
1907.01045v1
2022-11-24
Influence of non-local damping on magnon properties of ferromagnets
We study the influence of non-local damping on magnon properties of Fe, Co, Ni and Fe$_{1-x}$Co$_{x}$ ($x=30\%,50\%$) alloys. The Gilbert damping parameter is typically considered as a local scalar both in experiment and in theoretical modelling. However, recent works have revealed that Gilbert damping is a non-local quantity that allows for energy dissipation between atomic sites. With the Gilbert damping parameters calculated from a state-of-the-art real-space electronic structure method, magnon lifetimes are evaluated from spin dynamics and linear response, where a good agreement is found between these two methods. It is found that non-local damping affects the magnon lifetimes in different ways depending on the system. Specifically, we find that in Fe, Co, and Ni the non-local damping decreases the magnon lifetimes, while in $\rm Fe_{70}Co_{30}$ and Fe$_{50}$Co$_{50}$ an opposite, non-local damping effect is observed, and our data show that it is much stronger in the former.
2211.13486v1
2010-02-26
Correlation Effects in the Stochastic Landau-Lifshitz-Gilbert Equation
We analyze the Landau-Lifshitz-Gilbert equation when the precession motion of the magnetic moments is additionally subjected to an uniaxial anisotropy and is driven by a multiplicative coupled stochastic field with a finite correlation time $\tau$. The mean value for the spin wave components offers that the spin-wave dispersion relation and its damping is strongly influenced by the deterministic Gilbert damping parameter $\alpha$, the strength of the stochastic forces $D$ and its temporal range $\tau$. The spin-spin-correlation function can be calculated in the low correlation time limit by deriving an evolution equation for the joint probability function. The stability analysis enables us to find the phase diagram within the $\alpha-D$ plane for different values of $\tau$ where damped spin wave solutions are stable. Even for zero deterministic Gilbert damping the magnons offer a finite lifetime. We detect a parameter range where the deterministic and the stochastic damping mechanism are able to compensate each other leading to undamped spin-waves. The onset is characterized by a critical value of the correlation time. An enhancement of $\tau$ leads to an increase of the oscillations of the correlation function.
1002.4958v1
2019-02-26
Enhanced Gilbert Damping in Re doped FeCo Films: A Combined Experimental and Theoretical Study
The effects of rhenium doping in the range 0 to 10 atomic percent on the static and dynamic magnetic properties of Fe65Co35 thin films have been studied experimentally as well as with first principles electronic structure calculations focusing on the change of the saturation magnetization and the Gilbert damping parameter. Both experimental and theoretical results show that the saturation magnetization decreases with increasing Re doping level, while at the same time Gilbert damping parameter increases. The experimental low temperature saturation magnetic induction exhibits a 29 percent decrease, from 2.31 T to 1.64 T, in the investigated doping concentration range, which is more than predicted by the theoretical calculations. The room temperature value of the damping parameter obtained from ferromagnetic resonance measurements, correcting for extrinsic contributions to the damping, is for the undoped sample 0.0027, which is close to the theoretically calculated Gilbert damping parameter. With 10 atomic percent Re doping, the damping parameter increases to 0.0090, which is in good agreement with the theoretical value of 0.0073. The increase in damping parameter with Re doping is explained by the increase in density of states at Fermi level, mostly contributed by the spin-up channel of Re. Moreover, both experimental and theoretical values for the damping parameter are observed to be weakly decreasing with decreasing temperature.
1902.09896v1
2018-12-18
Thermal gradient driven domain wall dynamics
The issue of whether a thermal gradient acts like a magnetic field or an electric current in the domain wall (DW) dynamics is investigated. Broadly speaking, magnetization control knobs can be classified as energy-driving or angular-momentum driving forces. DW propagation driven by a static magnetic field is the best-known example of the former in which the DW speed is proportional to the energy dissipation rate, and the current-driven DW motion is an example of the latter. Here we show that DW propagation speed driven by a thermal gradient can be fully explained as the angular momentum transfer between thermally generated spin current and DW. We found DW-plane rotation speed increases as DW width decreases. Both DW propagation speed along the wire and DW-plane rotation speed around the wire decrease with the Gilbert damping. These facts are consistent with the angular momentum transfer mechanism, but are distinct from the energy dissipation mechanism. We further show that magnonic spin-transfer torque (STT) generated by a thermal gradient has both damping-like and field-like components. By analyzing DW propagation speed and DW-plane rotation speed, the coefficient ( \b{eta}) of the field-like STT arising from the non-adiabatic process, is obtained. It is found that \b{eta} does not depend on the thermal gradient; increases with uniaxial anisotropy K_(||) (thinner DW); and decreases with the damping, in agreement with the physical picture that a larger damping or a thicker DW leads to a better alignment between the spin-current polarization and the local magnetization, or a better adiabaticity.
1812.07244v2
2023-06-07
Helicity-dependent optical control of the magnetization state emerging from the Landau-Lifshitz-Gilbert equation
It is well known that the Gilbert relaxation time of a magnetic moment scales inversely with the magnitude of the externally applied field, H, and the Gilbert damping, {\alpha}. Therefore, in ultrashort optical pulses, where H can temporarily be extremely large, the Gilbert relaxation time can momentarily be extremely short, reaching even picosecond timescales. Here we show that for typical ultrashort pulses, the optical control of the magnetization emerges by merely considering the optical magnetic field in the Landau-Lifshitz-Gilbert (LLG) equation. Surprisingly, when circularly polarized optical pulses are introduced to the LLG equation, an optically induced helicity-dependent torque results. We find that the strength of the interaction is determined by {\eta}={\alpha}{\gamma}H/f_opt, where f_opt and {\gamma} are the optical frequency and gyromagnetic ratio. Our results illustrate the generality of the LLG equation to the optical limit and the pivotal role of the Gilbert damping in the general interaction between optical magnetic fields and spins in solids.
2306.04617v2
2018-04-03
Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms
The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term and the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy-Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.
1804.09242v1
2016-08-02
Ferromagnetic Damping/Anti-damping in a Periodic 2D Helical surface; A Non-Equilibrium Keldysh Green Function Approach
In this paper, we investigate theoretically the spin-orbit torque as well as the Gilbert damping for a two band model of a 2D helical surface state with a Ferromagnetic (FM) exchange coupling. We decompose the density matrix into the Fermi sea and Fermi surface components and obtain their contributions to the electronic transport as well as the spin-orbit torque (SOT). Furthermore, we obtain the expression for the Gilbert damping due to the surface state of a 3D Topological Insulator (TI) and predicted its dependence on the direction of the magnetization precession axis.
1608.00984v2
2016-02-19
A systematic study of magnetodynamic properties at finite temperatures in doped permalloy from first principles calculations
By means of first principles calculations, we have systematically investigated how the magnetodynamic properties Gilbert damping, magnetization and exchange stiffness are affected when permalloy (Py) (Fe$_{0.19}$Ni$_{0.81}$) is doped with 4d or 5d transition metal impurities. We find that the trends in the Gilbert damping can be understood from relatively few basic parameters such as the density of states at the Fermi level, the spin-orbit coupling and the impurity concentration. % The temperature dependence of the Gilbert damping is found to be very weak which we relate to the lack of intraband transitions in alloys. % Doping with $4d$ elements has no major impact on the studied Gilbert damping, apart from diluting the host. However, the $5d$ elements have a profound effect on the damping and allows it to be tuned over a large interval while maintaining the magnetization and exchange stiffness. % As regards spin stiffness, doping with early transition metals results in considerable softening, whereas late transition metals have a minor impact. % Our result agree well with earlier calculations where available. In comparison to experiments, the computed Gilbert damping appears slightly underestimated while the spin stiffness show good general agreement.
1602.06201v2
2002-11-01
Exploring dynamical magnetism with time-dependent density-functional theory: from spin fluctuations to Gilbert damping
We use time-dependent spin-density-functional theory to study dynamical magnetic phenomena. First, we recall that the local-spin-density approximation (LSDA) fails to account correctly for magnetic fluctuations in the paramagnetic state of iron and other itinerant ferromagnets. Next, we construct a gradient-dependent density functional that does not suffer from this problem of the LSDA. This functional is then used to derive, for the first time, the phenomenological Gilbert equation of micromagnetics directly from time-dependent density-functional theory. Limitations and extensions of Gilbert damping are discussed on this basis, and some comparisons with phenomenological theories and experiments are made.
0211021v1
2012-04-24
Nonlocal feedback in ferromagnetic resonance
Ferromagnetic resonance in thin films is analyzed under the influence of spatiotemporal feedback effects. The equation of motion for the magnetization dynamics is nonlocal in both space and time and includes isotropic, anisotropic and dipolar energy contributions as well as the conserved Gilbert- and the non-conserved Bloch-damping. We derive an analytical expression for the peak-to-peak linewidth. It consists of four separate parts originated by Gilbert damping, Bloch-damping, a mixed Gilbert-Bloch component and a contribution arising from retardation. In an intermediate frequency regime the results are comparable with the commonly used Landau-Lifshitz-Gilbert theory combined with two-magnon processes. Retardation effects together with Gilbert damping lead to a linewidth the frequency dependence of which becomes strongly nonlinear. The relevance and the applicability of our approach to ferromagnetic resonance experiments is discussed.
1204.5342v1
2017-04-24
Spin injection into silicon detected by broadband ferromagnetic resonance spectroscopy
We studied the spin injection in a NiFe(Py)/Si system using broadband ferromagnetic resonance spectroscopy. The Gilbert damping parameter of the Py layer on top of the Si channel was determined as a function of the Si doping concentration and Py layer thickness. For fixed Py thickness we observed an increase of the Gilbert damping parameter with decreasing resistivity of the Si channel. For a fixed Si doping concentration we measured an increasing Gilbert damping parameter for decreasing Py layer thickness. No increase of the Gilbert damping parameter was found Py/Si samples with an insulating interlayer. We attribute our observations to an enhanced spin injection into the low-resistivity Si by spin pumping.
1704.07006v1
2019-11-07
Quantum Oscillations of Gilbert Damping in Ferromagnetic/Graphene Bilayer Systems
We study the spin dynamics of a ferromagnetic insulator on which graphene is placed. We show that the Gilbert damping is enhanced by the proximity exchange coupling at the interface. The modulation of the Gilbert damping constant is proportional to the product of the spin-up and spin-down densities of states of graphene. Consequently, the Gilbert damping constant in a strong magnetic field oscillates as a function of the external magnetic field that originates from the Landau level structure of graphene. We find that a measurement of the oscillation period enables the strength of the exchange coupling constant to be determined. The results demonstrate in theory that the ferromagnetic resonance measurements may be used to detect the spin resolved electronic structure of the adjacent materials, which is critically important for future spin device evaluations.
1911.02775v2
2021-03-11
Magnetoelastic Gilbert damping in magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films
We report an enhanced magnetoelastic contribution to the Gilbert damping in highly magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films. This effect is mitigated for perpendicular-to-plane fields, leading to a large anisotropy of the Gilbert damping in all of the films (up to a factor of 10 at room temperature). These claims are supported by broadband measurements of the ferromagnetic resonance linewidths over a range of temperatures (5 to 400 K), which serve to elucidate the effect of both the magnetostriction and phonon relaxation on the magnetoelastic Gilbert damping.
2103.07008v1
2022-01-27
Effect of vertex corrections on the enhancement of Gilbert damping in spin pumping into a two-dimensional electron gas
We theoretically consider the effect of vertex correction on spin pumping from a ferromagnetic insulator (FI) into a two-dimensional electron gas (2DEG) in which the Rashba and Dresselhaus spin-orbit interactions coexist. The Gilbert damping in the FI is enhanced by elastic spin-flipping or magnon absorption. We show that the Gilbert damping due to elastic spin-flipping is strongly enhanced by the vertex correction when the ratio of the two spin-orbit interactions is near a special value at which the spin relaxation time diverges while that due to magnon absorption shows only small modification. We also show that the shift in the resonant frequency due to elastic spin-flipping is strongly enhanced in a similar way as the Gilbert damping.
2201.11498v3
2016-02-22
Effects of Landau-Lifshitz-Gilbert damping on domain growth
Domain patterns are simulated by the Landau-Lifshitz-Gilbert (LLG) equation with an easy-axis anisotropy. If the Gilbert damping is removed from the LLG equation, it merely describes the precession of magnetization with a ferromagnetic interaction. However, even without the damping, domains that look similar to those of scalar fields are formed, and they grow with time. It is demonstrated that the damping has no significant effects on domain growth laws and large-scale domain structure. In contrast, small-scale domain structure is affected by the damping. The difference in small-scale structure arises from energy dissipation due to the damping.
1602.06673v3
2018-06-13
Low magnetic damping of ferrimagnetic GdFeCo alloys
We investigate the Gilbert damping parameter for rare earth (RE)-transition metal (TM) ferrimagnets over a wide temperature range. Extracted from the field-driven magnetic domain-wall mobility, the Gilbert damping parameter was as low as 0.0072 and was almost constant across the angular momentum compensation temperature, starkly contrasting previous predictions that the Gilbert damping parameter should diverge at the angular momentum compensation temperature due to vanishing total angular momentum. Thus, magnetic damping of RE-TM ferrimagnets is not related to the total angular momentum but is dominated by electron scattering at the Fermi level where the TM has a dominant damping role.
1806.04881v1
2023-06-22
Gilbert damping in metallic ferromagnets from Schwinger-Keldysh field theory: Intrinsically nonlocal and nonuniform, and made anisotropic by spin-orbit coupling
Understanding the origin of damping mechanisms in magnetization dynamics of metallic ferromagnets is a fundamental problem for nonequilibrium many-body physics of systems where quantum conduction electrons interact with localized spins assumed to be governed by the classical Landau-Lifshitz-Gilbert (LLG) equation. It is also of critical importance for applications, as damping affects energy consumption and speed of spintronic and magnonic devices. Since the 1970s, a variety of linear-response and scattering theory approaches have been developed to produce widely used formulas for computation of spatially-independent Gilbert scalar parameter as the magnitude of the Gilbert damping term in the LLG equation. The largely unexploited for this purpose Schwinger-Keldysh field theory (SKFT) offers additional possibilities, such as to rigorously derive an extended LLG equation by integrating quantum electrons out. Here we derive such equation whose Gilbert damping for metallic ferromagnets is nonlocal, i.e., dependent on all localized spins at a given time, and nonuniform, even if all localized spins are collinear and spin-orbit coupling (SOC) is absent. This is in sharp contrast to standard lore, where nonlocal damping is considered to emerge only if localized spins are noncollinear; for such situations, direct comparison on the example of magnetic domain wall shows that SKFT-derived nonlocal damping is an order of magnitude larger than the previously considered one. Switching on SOC makes such nonlocal damping anisotropic, in contrast to standard lore where SOC is usually necessary to obtain nonzero Gilbert damping scalar parameter. Our analytical formulas, with their nonlocality being more prominent in low spatial dimensions, are fully corroborated by numerically exact quantum-classical simulations.
2306.13013v4
2018-07-20
Another view on Gilbert damping in two-dimensional ferromagnets
A keen interest towards technological implications of spin-orbit driven magnetization dynamics requests a proper theoretical description, especially in the context of a microscopic framework, to be developed. Indeed, magnetization dynamics is so far approached within Landau-Lifshitz-Gilbert equation which characterizes torques on magnetization on purely phenomenological grounds. Particularly, spin-orbit coupling does not respect spin conservation, leading thus to angular momentum transfer to lattice and damping as a result. This mechanism is accounted by the Gilbert damping torque which describes relaxation of the magnetization to equilibrium. In this study we work out a microscopic Kubo-St\v{r}eda formula for the components of the Gilbert damping tensor and apply the elaborated formalism to a two-dimensional Rashba ferromagnet in the weak disorder limit. We show that an exact analytical expression corresponding to the Gilbert damping parameter manifests linear dependence on the scattering rate and retains the constant value up to room temperature when no vibrational degrees of freedom are present in the system. We argue that the methodology developed in this paper can be safely applied to bilayers made of non- and ferromagnetic metals, e.g., CoPt.
1807.07897v2
2008-06-28
Theory of spin magnetohydrodynamics
We develop a phenomenological hydrodynamic theory of coherent magnetic precession coupled to electric currents. Exchange interaction between electron spin and collective magnetic texture produces two reciprocal effects: spin-transfer torque on the magnetic order parameter and the Berry-phase gauge field experienced by the itinerant electrons. The dissipative processes are governed by three coefficients: the ohmic resistance, Gilbert damping of the magnetization, and the "beta coefficient" describing viscous coupling between magnetic dynamics and electric current, which stems from spin mistracking of the magnetic order. We develop general magnetohydrodynamic equations and discuss the net dissipation produced by the coupled dynamics. The latter in particular allows us to determine a lower bound on the magnetic-texture resistivity.
0806.4656v2
2008-11-13
Intrinsic Coupling between Current and Domain Wall Motion in (Ga,Mn)As
We consider current-induced domain wall motion and, the reciprocal process, moving domain wall-induced current. The associated Onsager coefficients are expressed in terms of scattering matrices. Uncommonly, in (Ga,Mn)As, the effective Gilbert damping coefficient $\alpha_w$ and the effective out-of-plane spin transfer torque parameter $\beta_w$ are dominated by spin-orbit interaction in combination with scattering off the domain wall, and not scattering off extrinsic impurities. Numerical calculations give $\alpha_w \sim 0.01$ and $\beta_w \sim 1$ in dirty (Ga,Mn)As. The extraordinary large $\beta_w$ parameter allows experimental detection of current or voltage induced by domain wall motion in (Ga,Mn)As.
0811.2235v2
2009-05-01
Spin excitations in a monolayer scanned by a magnetic tip
Energy dissipation via spin excitations is investigated for a hard ferromagnetic tip scanning a soft magnetic monolayer. We use the classical Heisenberg model with Landau-Lifshitz-Gilbert (LLG)-dynamics including a stochastic field representing finite temperatures. The friction force depends linearly on the velocity (provided it is small enough) for all temperatures. For low temperatures, the corresponding friction coefficient is proportional to the phenomenological damping constant of the LLG equation. This dependence is lost at high temperatures, where the friction coefficient decreases exponentially. These findings can be explained by properties of the spin polarization cloud dragged along with the tip.
0905.0112v2
2016-05-21
Landau-Lifshitz theory of the magnon-drag thermopower
Metallic ferromagnets subjected to a temperature gradient exhibit a magnonic drag of the electric current. We address this problem by solving a stochastic Landau-Lifshitz equation to calculate the magnon-drag thermopower. The long-wavelength magnetic dynamics result in two contributions to the electromotive force acting on electrons: (1) An adiabatic Berry-phase force related to the solid angle subtended by the magnetic precession and (2) a dissipative correction thereof, which is rooted microscopically in the spin-dephasing scattering. The first contribution results in a net force pushing the electrons towards the hot side, while the second contribution drags electrons towards the cold side, i.e., in the direction of the magnonic drift. The ratio between the two forces is proportional to the ratio between the Gilbert damping coefficient $\alpha$ and the coefficient $\beta$ parametrizing the dissipative contribution to the electromotive force.
1605.06578v1
2019-06-17
Controlling acoustic waves using magnetoelastic Fano resonances
We propose and analyze theoretically a class of energy-efficient magneto-elastic devices for analogue signal processing. The signals are carried by transverse acoustic waves while the bias magnetic field controls their scattering from a magneto-elastic slab. By tuning the bias field, one can alter the resonant frequency at which the propagating acoustic waves hybridize with the magnetic modes, and thereby control transmission and reflection coefficients of the acoustic waves. The scattering coefficients exhibit Breit-Wigner/Fano resonant behaviour akin to inelastic scattering in atomic and nuclear physics. Employing oblique incidence geometry, one can effectively enhance the strength of magnetoelastic coupling, and thus countermand the magnetic losses due to the Gilbert damping. We apply our theory to discuss potential benefits and issues in realistic systems and suggest further routes to enhance performance of the proposed devices.
1906.07297v2
2017-05-21
Dynamical depinning of chiral domain walls
The domain wall depinning field represents the minimum magnetic field needed to move a domain wall, typically pinned by samples' disorder or patterned constrictions. Conventionally, such field is considered independent on the Gilbert damping since it is assumed to be the field at which the Zeeman energy equals the pinning energy barrier (both damping independent). Here, we analyse numerically the domain wall depinning field as function of the Gilbert damping in a system with perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction. Contrary to expectations, we find that the depinning field depends on the Gilbert damping and that it strongly decreases for small damping parameters. We explain this dependence with a simple one-dimensional model and we show that the reduction of the depinning field is related to the internal domain wall dynamics, proportional to the Dzyaloshinskii-Moriya interaction, and the finite size of the pinning barriers.
1705.07489v2
2019-01-07
Giant anisotropy of Gilbert damping in epitaxial CoFe films
Tailoring Gilbert damping of metallic ferromagnetic thin films is one of the central interests in spintronics applications. Here we report a giant Gilbert damping anisotropy in epitaxial Co$_{50}$Fe$_{50}$ thin film with a maximum-minimum damping ratio of 400 \%, determined by broadband spin-torque as well as inductive ferromagnetic resonance. We conclude that the origin of this damping anisotropy is the variation of the spin orbit coupling for different magnetization orientations in the cubic lattice, which is further corroborate from the magnitude of the anisotropic magnetoresistance in Co$_{50}$Fe$_{50}$.
1901.01941v1
2019-11-02
Tuning Non-Gilbert-type damping in FeGa films on MgO(001) via oblique deposition
The ability to tailor the damping factor is essential for spintronic and spin-torque applications. Here, we report an approach to manipulate the damping factor of FeGa/MgO(001) films by oblique deposition. Owing to the defects at the surface or interface in thin films, two-magnon scattering (TMS) acts as a non-Gilbert damping mechanism in magnetization relaxation. In this work, the contribution of TMS was characterized by in-plane angular dependent ferromagnetic resonance (FMR). It is demonstrated that the intrinsic Gilbert damping is isotropic and invariant, while the extrinsic mechanism related to TMS is anisotropic and can be tuned by oblique deposition. Furthermore, the two and fourfold TMS related to the uniaxial magnetic anisotropy (UMA) and magnetocrystalline anisotropy were discussed. Our results open an avenue to manipulate magnetization relaxation in spintronic devices.
1911.00728v1
2001-10-11
Enhanced Gilbert Damping in Thin Ferromagnetic Films
Using a scattering matrix approach, the precession of the magnetization of a ferromagnet is shown to transfer spins into adjacent normal metal layers. This ``pumping'' of spins slows down the precession corresponding to an enhanced Gilbert damping factor in the Landau-Lifshitz equation. The damping is expressed in terms of the scattering matrix of the ferromagnet-normal metal interface, which is accessible to model and first-principles calculations. Our estimates for permalloy thin films explain the trends observed in recent experiments.
0110247v2
2006-01-10
Voltage dependence of Landau-Lifshitz-Gilbert damping of a spin in a current driven tunnel junction
We present a theory of Landau-Lifshitz-Gilbert damping $\alpha$ for a localized spin ${\vec S}$ in the junction coupled to the conduction electrons in both leads under an applied volatege $V$. We find the voltage dependence of the damping term reflecting the energy dependence of the density of states. We find the effect is linear in the voltage and cotrolled by particle-hole asymmetry of the leads.
0601185v1
2015-02-06
Microscopic theory of Gilbert damping in metallic ferromagnets
We present a microscopic theory for magnetization relaxation in metallic ferromagnets of nanoscopic dimensions that is based on the dynamic spin response matrix in the presence of spin-orbit coupling. Our approach allows the calculation of the spin excitation damping rate even for perfectly crystalline systems, where existing microscopic approaches fail. We demonstrate that the relaxation properties are not completely determined by the transverse susceptibility alone, and that the damping rate has a non-negligible frequency dependence in experimentally relevant situations. Our results indicate that the standard Landau-Lifshitz-Gilbert phenomenology is not always appropriate to describe spin dynamics of metallic nanostructure in the presence of strong spin-orbit coupling.
1502.02068v1
2018-05-03
Exact Intrinsic Localized Excitation of an Anisotropic Ferromagnetic Spin Chain in External Magnetic Field with Gilbert Damping, Spin Current and PT-Symmetry
We obtain the exact one-spin intrinsic localized excitation in an anisotropic Heisenberg ferromagnetic spin chain in a constant/variable external magnetic field with Gilbert damping included. We also point out how an appropriate magnitude spin current term in a spin transfer nano-oscillator (STNO) can stabilize the tendency towards damping. Further, we show how this excitation can be sustained in a recently suggested PT-symmetric magnetic nanostructure. We also briefly consider more general spin excitations.
1805.01230v1
2011-04-08
Magnetization Dissipation in Ferromagnets from Scattering Theory
The magnetization dynamics of ferromagnets are often formulated in terms of the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation describes the response of the magnetization in terms of effective fields, whereas the dissipative part is parameterized by the Gilbert damping tensor. We formulate a scattering theory for the magnetization dynamics and map this description on the linearized LLG equation by attaching electric contacts to the ferromagnet. The reactive part can then be expressed in terms of the static scattering matrix. The dissipative contribution to the low-frequency magnetization dynamics can be described as an adiabatic energy pumping process to the electronic subsystem by the time-dependent magnetization. The Gilbert damping tensor depends on the time derivative of the scattering matrix as a function of the magnetization direction. By the fluctuation-dissipation theorem, the fluctuations of the effective fields can also be formulated in terms of the quasistatic scattering matrix. The theory is formulated for general magnetization textures and worked out for monodomain precessions and domain wall motions. We prove that the Gilbert damping from scattering theory is identical to the result obtained by the Kubo formalism.
1104.1625v1
2022-02-12
Generalization of the Landau-Lifshitz-Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets
We propose a systematic and sequential expansion of the Landau-Lifshitz-Gilbert equation utilizing the dependence of the Gilbert damping tensor on the angle between magnetic moments, which arises from multi-body scattering processes. The tensor consists of a damping-like term and a correction to the gyromagnetic ratio. Based on electronic structure theory, both terms are shown to depend on e.g. the scalar, anisotropic, vector-chiral and scalar-chiral products of magnetic moments: $\vec{e}_i\cdot\vec{e}_j$, $(\vec{n}_{ij}\cdot\vec{e}_i)(\vec{n}_{ij}\cdot\vec{e}_j)$, $\vec{n}_{ij}\cdot(\vec{e}_i\times\vec{e}_j)$, $(\vec{e}_i\cdot\vec{e}_j)^2$, $\vec{e}_i\cdot(\vec{e}_j\times\vec{e}_k)$..., where some terms are subjected to the spin-orbit field $\vec{n}_{ij}$ in first and second order. We explore the magnitude of the different contributions using both the Alexander-Anderson model and time-dependent density functional theory in magnetic adatoms and dimers deposited on Au(111) surface.
2202.06154v1
2022-11-23
The fractional Landau-Lifshitz-Gilbert equation
The dynamics of a magnetic moment or spin are of high interest to applications in technology. Dissipation in these systems is therefore of importance for improvement of efficiency of devices, such as the ones proposed in spintronics. A large spin in a magnetic field is widely assumed to be described by the Landau-Lifshitz-Gilbert (LLG) equation, which includes a phenomenological Gilbert damping. Here, we couple a large spin to a bath and derive a generic (non-)Ohmic damping term for the low-frequency range using a Caldeira-Leggett model. This leads to a fractional LLG equation, where the first-order derivative Gilbert damping is replaced by a fractional derivative of order $s \ge 0$. We show that the parameter $s$ can be determined from a ferromagnetic resonance experiment, where the resonance frequency and linewidth no longer scale linearly with the effective field strength.
2211.12889v1
2018-05-04
Effective damping enhancement in noncollinear spin structures
Damping mechanisms in magnetic systems determine the lifetime, diffusion and transport properties of magnons, domain walls, magnetic vortices, and skyrmions. Based on the phenomenological Landau-Lifshitz-Gilbert equation, here the effective damping parameter in noncollinear magnetic systems is determined describing the linewidth in resonance experiments or the decay parameter in time-resolved measurements. It is shown how the effective damping can be calculated from the elliptic polarization of magnons, arising due to the noncollinear spin arrangement. It is concluded that the effective damping is larger than the Gilbert damping, and it may significantly differ between excitation modes. Numerical results for the effective damping are presented for the localized magnons in isolated skyrmions, with parameters based on the Pd/Fe/Ir(111) model-type system.
1805.01815v2
2023-12-14
Nonlocal damping of spin waves in a magnetic insulator induced by normal, heavy, or altermagnetic metallic overlayer: a Schwinger-Keldysh field theory approach
Understanding spin wave (SW) damping, and how to control it to the point of being able to amplify SW-mediated signals, is one of the key requirements to bring the envisaged magnonic technologies to fruition. Even widely used magnetic insulators with low magnetization damping in their bulk, such as yttrium iron garnet, exhibit 100-fold increase in SW damping due to inevitable contact with metallic layers in magnonic circuits, as observed in very recent experiments [I. Bertelli et al., Adv. Quantum Technol. 4, 2100094 (2021)] mapping SW damping in spatially-resolved fashion. Here, we provide microscopic and rigorous understanding of wavevector-dependent SW damping using extended Landau-Lifshitz-Gilbert equation with nonlocal damping tensor, instead of conventional local scalar Gilbert damping, as derived from Schwinger-Keldysh nonequilibrium quantum field theory. In this picture, the origin of nonlocal magnetization damping and thereby induced wavevector-dependent SW damping is interaction of localized magnetic moments of magnetic insulator with conduction electrons from the examined three different types of metallic overlayers -- normal, heavy, and altermagnetic. Due to spin-split energy-momentum dispersion of conduction electrons in the latter two cases, the nonlocal damping is anisotropic in spin and space, and it can be dramatically reduced by changing the relative orientation of the two layers when compared to the usage of normal metal overlayer.
2312.09140v1
2017-03-20
Relativistic theory of magnetic inertia in ultrafast spin dynamics
The influence of possible magnetic inertia effects has recently drawn attention in ultrafast magnetization dynamics and switching. Here we derive rigorously a description of inertia in the Landau-Lifshitz-Gilbert equation on the basis of the Dirac-Kohn-Sham framework. Using the Foldy-Wouthuysen transformation up to the order of $1/c^4$ gives the intrinsic inertia of a pure system through the 2$^{\rm nd}$ order time-derivative of magnetization in the dynamical equation of motion. Thus, the inertial damping $\mathcal{I}$ is a higher order spin-orbit coupling effect, $\sim 1/c^4$, as compared to the Gilbert damping $\Gamma$ that is of order $1/c^2$. Inertia is therefore expected to play a role only on ultrashort timescales (sub-picoseconds). We also show that the Gilbert damping and inertial damping are related to one another through the imaginary and real parts of the magnetic susceptibility tensor respectively.
1704.01559v1
2019-07-10
The superior role of the Gilbert damping on the signal-to-noise ratio in heat-assisted magnetic recording
In magnetic recording the signal-to-noise ratio (SNR) is a good indicator for the quality of written bits. However, a priori it is not clear which parameters have the strongest influence on the SNR. In this work, we investigate the role of the Gilbert damping on the SNR. Grains consisting of FePt like hard magnetic material with two different grain sizes $d_1=5\,$nm and $d_2=7\,$nm are considered and simulations of heat-assisted magnetic recording (HAMR) are performed with the atomistic simulation program VAMPIRE. The simulations display that the SNR saturates for damping constants larger or equal than 0.1. Additionally, we can show that the Gilbert damping together with the bit length have a major effect on the SNR whereas other write head and material parameters only have a minor relevance on the SNR.
1907.04577v2
2019-10-24
Spin waves in ferromagnetic thin films
A spin wave is the disturbance of intrinsic spin order in magnetic materials. In this paper, a spin wave in the Landau-Lifshitz-Gilbert equation is obtained based on the assumption that the spin wave maintains its shape while it propagates at a constant velocity. Our main findings include: (1) in the absence of Gilbert damping, the spin wave propagates at a constant velocity with the increment proportional to the strength of the magnetic field; (2) in the absence of magnetic field, at a given time the spin wave converges exponentially fast to its initial profile as the damping parameter goes to zero and in the long time the relaxation dynamics of the spin wave converges exponentially fast to the easy-axis direction with the exponent proportional to the damping parameter; (3) in the presence of both Gilbert damping and magnetic field, the spin wave converges to the easy-axis direction exponentially fast at a small timescale while propagates at a constant velocity beyond that. These provides a comprehensive understanding of spin waves in ferromagnetic materials.
1910.11200v1
2020-06-30
Negative Gilbert damping in cavity optomagnonics
Exceptional point (EP) associated with the parity-time (PT) symmetry breaking is receiving considerable recent attention by the broad physics community. By introducing balanced gain and loss, it has been realized in photonic, acoustic, and electronic structures. However, the observation of magnonic EP remains elusive. The major challenge is to experimentally generate the negative Gilbert damping, which was thought to be highly unlikely but is demanded by the PT symmetry. In this work, we study the magneto-optical interaction of circularly-polarized lasers with a submicron magnet placed in an optical cavity. We show that the off-resonant coupling between the driving laser and cavity photon in the far-blue detuning can induce the magnetic gain (or negative damping) exactly of the Gilbert type. A hyperbolic-tangent function ansatz is found to well describe the time-resolved spin switching as the intrinsic magnetization dissipation is overcome. When the optically pumped magnet interacts with a purely lossy one, we observe a phase transition from the imbalanced to passive PT symmetries by varying the detuning coeffcient. Our findings provide a feasible way to manipulate the sign of the magnetic damping parameter and to realize the EP in cavity optomagnonics.
2006.16510v1
2017-11-20
Spin Pumping in Ion-beam Sputtered Co_{2}FeAl/Mo Bilayers:Interfacial Gilbert Damping
The spin pumping mechanism and associated interfacial Gilbert damping are demonstrated in ion-beam sputtered Co2FeAl (CFA) /Mo bilayer thin films employing ferromagnetic resonance spectroscopy. The dependence of the net spin current transportation on Mo layer thickness, 0 to 10 nm, and the enhancement of the net effective Gilbert damping are reported. The experimental data has been analyzed using spin pumping theory in terms of spin current pumped through the ferromagnet /nonmagnetic metal interface to deduce the effective spin mixing conductance and the spin-diffusion length, which are estimated to be 1.16(0.19)x10^19 m^-2 and 3.50(0.35)nm, respectively. The damping constant is found to be 8.4(0.3)x10^-3 in the Mo(3.5nm) capped CFA(8nm) sample corresponding to a ~42% enhancement of the original Gilbert damping (6.0(0.3)x10^-3) in the uncapped CFA layer. This is further confirmed by inserting a Cu dusting layer which reduces the spin transport across the CFA /Mo interface. The Mo layer thickness dependent net spin current density is found to lie in the range of 1-3 MAm^-2, which also provides additional quantitative evidence of spin pumping in this bilayer thin film system.
1711.07455v1
2008-05-21
Non-equilibrium thermodynamic study of magnetization dynamics in the presence of spin-transfer torque
The dynamics of magnetization in the presence of spin-transfer torque was studied. We derived the equation for the motion of magnetization in the presence of a spin current by using the local equilibrium assumption in non-equilibrium thermodynamics. We show that, in the resultant equation, the ratio of the Gilbert damping constant, $\alpha$, and the coefficient, $\beta$, of the current-induced torque, called non-adiabatic torque, depends on the relaxation time of the fluctuating field $\tau_{c}$. The equality $\alpha=\beta$ holds when $\tau_c$ is very short compared to the time scale of magnetization dynamics. We apply our theory to current-induced magnetization reversal in magnetic multilayers and show that the switching time is a decreasing function of $\tau_{c}$.
0805.3306v1
2010-08-03
Determination of the spin-flip time in ferromagnetic SrRuO3 from time-resolved Kerr measurements
We report time-resolved Kerr effect measurements of magnetization dynamics in ferromagnetic SrRuO3. We observe that the demagnetization time slows substantially at temperatures within 15K of the Curie temperature, which is ~ 150K. We analyze the data with a phenomenological model that relates the demagnetization time to the spin flip time. In agreement with our observations the model yields a demagnetization time that is inversely proportional to T-Tc. We also make a direct comparison of the spin flip rate and the Gilbert damping coefficient showing that their ratio very close to kBTc, indicating a common origin for these phenomena.
1008.0674v1
2015-03-26
Thermophoresis of an Antiferromagnetic Soliton
We study dynamics of an antiferromagnetic soliton under a temperature gradient. To this end, we start by phenomenologically constructing the stochastic Landau-Lifshitz-Gilbert equation for an antiferromagnet with the aid of the fluctuation-dissipation theorem. We then derive the Langevin equation for the soliton's center of mass by the collective coordinate approach. An antiferromagentic soliton behaves as a classical massive particle immersed in a viscous medium. By considering a thermodynamic ensemble of solitons, we obtain the Fokker-Planck equation, from which we extract the average drift velocity of a soliton. The diffusion coefficient is inversely proportional to a small damping constant $\alpha$, which can yield a drift velocity of tens of m/s under a temperature gradient of $1$ K/mm for a domain wall in an easy-axis antiferromagnetic wire with $\alpha \sim 10^{-4}$.
1503.07854v2
2016-04-24
Coupled Spin-Light dynamics in Cavity Optomagnonics
Experiments during the past two years have shown strong resonant photon-magnon coupling in microwave cavities, while coupling in the optical regime was demonstrated very recently for the first time. Unlike with microwaves, the coupling in optical cavities is parametric, akin to optomechanical systems. This line of research promises to evolve into a new field of optomagnonics, aimed at the coherent manipulation of elementary magnetic excitations by optical means. In this work we derive the microscopic optomagnonic Hamiltonian. In the linear regime the system reduces to the well-known optomechanical case, with remarkably large coupling. Going beyond that, we study the optically induced nonlinear classical dynamics of a macrospin. In the fast cavity regime we obtain an effective equation of motion for the spin and show that the light field induces a dissipative term reminiscent of Gilbert damping. The induced dissipation coefficient however can change sign on the Bloch sphere, giving rise to self-sustained oscillations. When the full dynamics of the system is considered, the system can enter a chaotic regime by successive period doubling of the oscillations.
1604.07053v3
2018-02-07
Breaking the current density threshold in spin-orbit-torque magnetic random access memory
Spin-orbit-torque magnetic random access memory (SOT-MRAM) is a promising technology for the next generation of data storage devices. The main bottleneck of this technology is the high reversal current density threshold. This outstanding problem of SOT-MRAM is now solved by using a current density of constant magnitude and varying flow direction that reduces the reversal current density threshold by a factor of more than the Gilbert damping coefficient. The Euler-Lagrange equation for the fastest magnetization reversal path and the optimal current pulse are derived for an arbitrary magnetic cell. The theoretical limit of minimal reversal current density and current density for a GHz switching rate of the new reversal strategy for CoFeB/Ta SOT-MRAMs are respectively of the order of $10^5$ A/cm$^2$ and $10^6$ A/cm$^2$ far below $10^7$ A/cm$^2$ and $10^8$ A/cm$^2$ in the conventional strategy. Furthermore, no external magnetic field is needed for a deterministic reversal in the new strategy.
1802.02415v1
2022-04-22
A short-circuited coplanar waveguide for low-temperature single-port ferromagnetic resonance spectroscopy set-up to probe the magnetic properties of ferromagnetic thin films
A coplanar waveguide shorted in one end is proposed, designed, and implemented successfully to measure the properties of magnetic thin films as a part of the vector network analyzer ferromagnetic resonance (VNA-FMR) spectroscopy set-up. Its simple structure, potential applications and easy installation inside the cryostat chamber made it advantageous especially for low-temperature measurements. It provides a wide band of frequencies in the gigahertz range essential for FMR measurements. Our spectroscopy set-up with short-circuited coplanar waveguide has been used to extract Gilbert damping coefficient and effective magnetization values for standard ferromagnetic thin films like Py and Co. The thickness and temperature dependent studies of those magnetic parameters have also been done here for the afore mentioned magnetic samples.
2204.10596v2
2014-04-05
Gilbert damping in noncollinear ferromagnets
The precession and damping of a collinear magnetization displaced from its equilibrium are described by the Landau-Lifshitz-Gilbert equation. For a noncollinear magnetization, it is not known how the damping should be described. We use first-principles scattering theory to investigate the damping in one-dimensional transverse domain walls (DWs) of the important ferromagnetic alloy Ni$_{80}$Fe$_{20}$ and interpret the results in terms of phenomenological models. The damping is found to depend not only on the magnetization texture but also on the specific dynamic modes of Bloch and N\'eel DWs. Even in the highly disordered Ni$_{80}$Fe$_{20}$ alloy, the damping is found to be remarkably nonlocal.
1404.1488v2
2019-11-21
Low damping and microstructural perfection of sub-40nm-thin yttrium iron garnet films grown by liquid phase epitaxy
The field of magnon spintronics is experiencing an increasing interest in the development of solutions for spin-wave-based data transport and processing technologies that are complementary or alternative to modern CMOS architectures. Nanometer-thin yttrium iron garnet (YIG) films have been the gold standard for insulator-based spintronics to date, but a potential process technology that can deliver perfect, homogeneous large-diameter films is still lacking. We report that liquid phase epitaxy (LPE) enables the deposition of nanometer-thin YIG films with low ferromagnetic resonance losses and consistently high magnetic quality down to a thickness of 20 nm. The obtained epitaxial films are characterized by an ideal stoichiometry and perfect film lattices, which show neither significant compositional strain nor geometric mosaicity, but sharp interfaces. Their magneto-static and dynamic behavior is similar to that of single crystalline bulk YIG. We found, that the Gilbert damping coefficient alpha is independent of the film thickness and close to 1 x 10-4, and that together with an inhomogeneous peak-to-peak linewidth broadening of delta H0|| = 0.4 G, these values are among the lowest ever reported for YIG films with a thickness smaller than 40 nm. These results suggest, that nanometer-thin LPE films can be used to fabricate nano- and micro-scaled circuits with the required quality for magnonic devices. The LPE technique is easily scalable to YIG sample diameters of several inches.
1911.09400v1
2003-04-04
Dynamic exchange coupling and Gilbert damping in magnetic multilayers
We theoretically study dynamic properties of thin ferromagnetic films in contact with normal metals. Moving magnetizations cause a flow of spins into adjacent conductors, which relax by spin flip, scatter back into the ferromagnet, or are absorbed by another ferromagnet. Relaxation of spins outside the moving magnetization enhances the overall damping of the magnetization dynamics in accordance with the Gilbert phenomenology. Transfer of spins between different ferromagnets by these nonequilibrium spin currents leads to a long-ranged dynamic exchange interaction and novel collective excitation modes. Our predictions agree well with recent ferromagnetic-resonance experiments on ultrathin magnetic films.
0304116v1
2012-03-03
Scaling of intrinsic Gilbert damping with spin-orbital coupling strength
We have experimentally and theoretically investigated the dependence of the intrinsic Gilbert damping parameter $\alpha_0$ on the spin-orbital coupling strength $\xi$ by using L1$_{\mathrm{0}}$ ordered FePd$_{\mathrm{1-x}}$Pt$_{\mathrm{x}}$ ternary alloy films with perpendicular magnetic anisotropy. With the time-resolved magneto-optical Kerr effect, $\alpha_0$ is found to increase by more than a factor of ten when $x$ varies from 0 to 1.0. Since changes of other leading parameters are found to be neglected, the $\alpha_0$ has for the first time been proven to be proportional to $\xi^2$.
1203.0607v1
2013-03-20
Spin-pumping and Enhanced Gilbert Damping in Thin Magnetic Insulator Films
Precessing magnetization in a thin film magnetic insulator pumps spins into adjacent metals; however, this phenomenon is not quantitatively understood. We present a theory for the dependence of spin-pumping on the transverse mode number and in-plane wave vector. For long-wavelength spin waves, the enhanced Gilbert damping for the transverse mode volume waves is twice that of the macrospin mode, and for surface modes, the enhancement can be ten or more times stronger. Spin-pumping is negligible for short-wavelength exchange spin waves. We corroborate our analytical theory with numerical calculations in agreement with recent experimental results.
1303.4922v1
2022-06-10
Spin Pumping into Anisotropic Dirac Electrons
We study spin pumping into an anisotropic Dirac electron system induced by microwave irradiation to an adjacent ferromagnetic insulator theoretically. We formulate the Gilbert damping enhancement due to the spin current flowing into the Dirac electron system using second-order perturbation with respect to the interfacial exchange coupling. As an illustration, we consider the anisotropic Dirac system realized in bismuth to show that the Gilbert damping varies according to the magnetization direction in the ferromagnetic insulator. Our results indicate that this setup can provide helpful information on the anisotropy of the Dirac electron system.
2206.04899v1
2023-03-02
Spin Pumping into Carbon Nanotubes
We theoretically study spin pumping from a ferromagnetic insulator (FI) into a carbon nanotube (CNT). By employing the bosonization method, we formulate the Gilbert damping induced by the FI/CNT junction, which can be measured by ferromagnetic resonance. We show that the increase in the Gilbert damping has a temperature dependence characteristic of a Luttinger liquid and is highly sensitive to the Luttinger parameter of the spin sector for a clean interface. We also discuss the experimental relevance of our findings based on numerical estimates, using realistic parameters.
2303.01343v2
2019-08-29
Enhancement of ultrafast demagnetization rate and Gilbert damping driven by femtosecond laser-induced spin currents in Fe81Ga19/Ir20Mn80 bilayers
In spintronics applications, ultrafast spin dynamics have to be controlled at femtosecond (fs) timescales via fs-laser radiation. At such ultrafast timescales, the effect of the Gilbert damping factor {\alpha} on ultrafast demagnetization time should be considered. In previous explorations for the relationship between these two parameters, it was found that the theoretical calculations based on the local spin-flip scattering model do not agree with the experimental results. Here, we find that in Fe81Ga19(FeGa)/Ir20Mn80(IrMn) bilayers, the unconventional IrMn thickness dependence of {\alpha} results from the competition between spin currents pumped from the ferromagnetic (FM) FeGa layer to the antiferromagnetic (AFM) IrMn layer and those pumped from the AFM layer to the FM layer. More importantly, we establish a proportional relationship between the change of the ultrafast demagnetization rate and the enhancement of Gilbert damping induced by the spin currents via interfacial spin chemical potential . Our work builds a bridge to connect the ultrafast demagnetization time and Gilbert damping in ultrafast photo-induced spin currents dominated systems, which not only explains the disagreement between experimental and theoretical results in the relation of {\tau}_M with {\alpha}, but provides further insight into ultrafast spin dynamics as well.
1908.11084v1
2021-09-08
Room-Temperature Intrinsic and Extrinsic Damping in Polycrystalline Fe Thin Films
We examine room-temperature magnetic relaxation in polycrystalline Fe films. Out-of-plane ferromagnetic resonance (FMR) measurements reveal Gilbert damping parameters of $\approx$ 0.0024 for Fe films with thicknesses of 4-25 nm, regardless of their microstructural properties. The remarkable invariance with film microstructure strongly suggests that intrinsic Gilbert damping in polycrystalline metals at room temperature is a local property of nanoscale crystal grains, with limited impact from grain boundaries and film roughness. By contrast, the in-plane FMR linewidths of the Fe films exhibit distinct nonlinear frequency dependences, indicating the presence of strong extrinsic damping. To fit our in-plane FMR data, we have used a grain-to-grain two-magnon scattering model with two types of correlation functions aimed at describing the spatial distribution of inhomogeneities in the film. However, neither of the two correlation functions is able to reproduce the experimental data quantitatively with physically reasonable parameters. Our findings advance the fundamental understanding of intrinsic Gilbert damping in structurally disordered films, while demonstrating the need for a deeper examination of how microstructural disorder governs extrinsic damping.
2109.03684v2
2006-06-09
Spin wave dynamics and the determination of intrinsic Gilbert damping in locally-excited Permalloy thin films
Time-resolved scanning Kerr effect microscopy has been used to study magnetization dynamics in Permalloy thin films excited by transient magnetic pulses generated by a micrometer-scale transmission line structure. The results are consistent with magnetostatic spin wave theory and are supported by micromagnetic simulations. Magnetostatic volume and surface spin waves are measured for the same specimen using different bias field orientations and can be accurately calculated by k-space integrations over all excited plane wave components. A single damping constant of Gilbert form is sufficient to describe both scenarios. The nonuniform pulsed field plays a key role in the spin wave dynamics, with its Fourier transform serving as a weighting function for the participating modes. The intrinsic Gilbert damping parameter $\alpha$ is most conveniently measured when the spin waves are effectively stationary.
0606235v3
2007-05-10
Effective temperature and Gilbert damping of a current-driven localized spin
Starting from a model that consists of a semiclassical spin coupled to two leads we present a microscopic derivation of the Langevin equation for the direction of the spin. For slowly-changing direction it takes on the form of the stochastic Landau-Lifschitz-Gilbert equation. We give expressions for the Gilbert damping parameter and the strength of the fluctuations, including their bias-voltage dependence. At nonzero bias-voltage the fluctuations and damping are not related by the fluctuation-dissipation theorem. We find, however, that in the low-frequency limit it is possible to introduce a voltage-dependent effective temperature that characterizes the fluctuations in the direction of the spin, and its transport-steady-state probability distribution function.
0705.1432v3
2014-12-05
Calculating linear response functions for finite temperatures on the basis of the alloy analogy model
A scheme is presented that is based on the alloy analogy model and allows to account for thermal lattice vibrations as well as spin fluctuations when calculating response quantities in solids. Various models to deal with spin fluctuations are discussed concerning their impact on the resulting temperature dependent magnetic moment, longitudinal conductivity and Gilbert damping parameter. It is demonstrated that using the Monte Carlo (MC) spin configuration as an input, the alloy analogy model is capable to reproduce results of MC simulations on the average magnetic moment within all spin fluctuation models under discussion. On the other hand, response quantities are much more sensitive to the spin fluctuation model. Separate calculations accounting for either the thermal effect due to lattice vibrations or spin fluctuations show their comparable contributions to the electrical conductivity and Gilbert damping. However, comparison to results accounting for both thermal effects demonstrate violation of Matthiessen's rule, showing the non-additive effect of lattice vibrations and spin fluctuations. The results obtained for bcc Fe and fcc Ni are compared with the experimental data, showing rather good agreement for the temperature dependent electrical conductivity and Gilbert damping parameter.
1412.1988v1
2015-10-13
Nonlocal torque operators in ab initio theory of the Gilbert damping in random ferromagnetic alloys
We present an ab initio theory of the Gilbert damping in substitutionally disordered ferromagnetic alloys. The theory rests on introduced nonlocal torques which replace traditional local torque operators in the well-known torque-correlation formula and which can be formulated within the atomic-sphere approximation. The formalism is sketched in a simple tight-binding model and worked out in detail in the relativistic tight-binding linear muffin-tin orbital (TB-LMTO) method and the coherent potential approximation (CPA). The resulting nonlocal torques are represented by nonrandom, non-site-diagonal and spin-independent matrices, which simplifies the configuration averaging. The CPA-vertex corrections play a crucial role for the internal consistency of the theory and for its exact equivalence to other first-principles approaches based on the random local torques. This equivalence is also illustrated by the calculated Gilbert damping parameters for binary NiFe and FeCo random alloys, for pure iron with a model atomic-level disorder, and for stoichiometric FePt alloys with a varying degree of L10 atomic long-range order.
1510.03571v2
2016-12-07
Gilbert damping of magnetostatic modes in a yttrium iron garnet sphere
The magnetostatic mode (MSM) spectrum of a 300$\mu$m diameter single crystalline sphere of yttrium iron garnet is investigated using broadband ferromagnetic resonance (FMR). The individual MSMs are identified via their characteristic dispersion relations and the corresponding mode number tuples $(nmr)$ are assigned. Taking FMR data over a broad frequency and magnetic field range allows to analyze both the Gilbert damping parameter~$\alpha$ and the inhomogeneous line broadening contribution to the total linewidth of the MSMs separately. The linewidth analysis shows that all MSMs share the same Gilbert damping parameter $\alpha=2.7(5) \times 10^{-5}$ irrespective of their mode index. In contrast, the inhomogeneous line broadening shows a pronounced mode dependence. This observation is modeled in terms of two-magnon scattering processes of the MSMs into the spin-wave manifold, mediated by surface and volume defects.
1612.02360v1
2018-05-29
Gilbert damping in non-collinear magnetic system
The modification of the magnetization dissipation or Gilbert damping caused by an inhomogeneous magnetic structure and expressed in terms of a wave vector dependent tensor $\underline{\alpha}(\vec{q})$ is investigated by means of linear response theory. A corresponding expression for $\underline{\alpha}(\vec{q})$ in terms of the electronic Green function has been developed giving in particular the leading contributions to the Gilbert damping linear and quadratic in $q$. Numerical results for realistic systems are presented that have been obtained by implementing the scheme within the framework of the fully relativistic KKR (Korringa-Kohn-Rostoker) band structure method. Using the multilayered system (Cu/Fe$_{1-x}$Co$_x$/Pt)$_n$ as an example for systems without inversion symmetry we demonstrate the occurrence of non-vanishing linear contributions. For the alloy system bcc Fe$_{1-x}$Co$_x$ having inversion symmetry, on the other hand, only the quadratic contribution is non-zero. As it is shown, this quadratic contribution does not vanish even if the spin-orbit coupling is suppressed, i.e.\ it is a direct consequence of the non-collinear spin configuration.
1805.11468v1
2018-10-15
Localized spin waves in isolated $kπ$ skyrmions
The localized magnon modes of isolated $k\pi$ skyrmions on a field-polarized background are analyzed based on the Landau-Lifshitz-Gilbert equation within the terms of an atomistic classical spin model, with system parameters based on the Pd/Fe biatomic layer on Ir(111). For increasing skyrmion order $k$ a higher number of excitation modes are found, including modes with nodes in the radial eigenfunctions. It is shown that at low fields $2\pi$ and $3\pi$ skyrmions are destroyed via a burst instability connected to a breathing mode, while $1\pi$ skyrmions undergo an elliptic instability. At high fields all $k\pi$ skyrmions collapse due to the instability of a breathing mode. The effective damping parameters of the spin waves are calculated in the low Gilbert damping limit, and they are found to diverge in the case of the lowest-lying modes at the burst and collapse instabilities, but not at the elliptic instability. It is shown that the breathing modes of $k\pi$ skyrmions may become overdamped at higher Gilbert damping values.
1810.06471v1
2018-10-24
Nearly isotropic spin-pumping related Gilbert damping in Pt/Ni$_{81}$Fe$_{19}$/Pt
A recent theory by Chen and Zhang [Phys. Rev. Lett. 114, 126602 (2015)] predicts strongly anisotropic damping due to interfacial spin-orbit coupling in ultrathin magnetic films. Interfacial Gilbert-type relaxation, due to the spin pumping effect, is predicted to be significantly larger for magnetization oriented parallel to compared with perpendicular to the film plane. Here, we have measured the anisotropy in the Pt/Ni$_{81}$Fe$_{19}$/Pt system via variable-frequency, swept-field ferromagnetic resonance (FMR). We find a very small anisotropy of enhanced Gilbert damping with sign opposite to the prediction from the Rashba effect at the FM/Pt interface. The results are contrary to the predicted anisotropy and suggest that a mechanism separate from Rashba spin-orbit coupling causes the rapid onset of spin-current absorption in Pt.
1810.10595v4
2019-11-08
Giant anisotropy of Gilbert damping in a Rashba honeycomb antiferromagnet
Giant Gilbert damping anisotropy is identified as a signature of strong Rashba spin-orbit coupling in a two-dimensional antiferromagnet on a honeycomb lattice. The phenomenon originates in spin-orbit induced splitting of conduction electron subbands that strongly suppresses certain spin-flip processes. As a result, the spin-orbit interaction is shown to support an undamped non-equilibrium dynamical mode that corresponds to an ultrafast in-plane N\'eel vector precession and a constant perpendicular-to-the-plane magnetization. The phenomenon is illustrated on the basis of a two dimensional $s$-$d$ like model. Spin-orbit torques and conductivity are also computed microscopically for this model. Unlike Gilbert damping these quantities are shown to reveal only a weak anisotropy that is limited to the semiconductor regime corresponding to the Fermi energy staying in a close vicinity of antiferromagnetic gap.
1911.03408v1
2005-05-10
Fluctuation-dissipation considerations and damping models for ferromagnetic materials
The role of fluctuation-dissipation relations (theorems) for the magnetization dynamics with Landau-Lifshitz-Gilbert and Bloch-Bloembergen damping terms are discussed. We demonstrate that the use of the Callen-Welton fluctuation-dissipation theorem that was proven for Hamiltonian systems can give an inconsistent result for magnetic systems with dissipation.
0505259v1
2018-07-13
Gilbert damping of high anisotropy Co/Pt multilayers
Using broadband ferromagnetic resonance, we measure the damping parameter of [Co(5 \r{A})/Pt(3 \r{A})]${\times 6}$ multilayers whose growth was optimized to maximize the perpendicular anisotropy. Structural characterizations indicate abrupt interfaces essentially free of intermixing despite the miscible character of Co and Pt. Gilbert damping parameters as low as 0.021 can be obtained despite a magneto-crystalline anisotropy as large as $10^6~\textrm{J/m}^3$. The inhomogeneous broadening accounts for part of the ferromagnetic resonance linewidth, indicating some structural disorder leading to a equivalent 20 mT of inhomogenity of the effective field. The unexpectedly relatively low damping factor indicates that the presence of the Pt heavy metal within the multilayer may not be detrimental to the damping provided that intermixing is avoided at the Co/Pt interfaces.
1807.04977v1
2019-08-23
Damping enhancement in coherent ferrite/insulating-paramagnet bilayers
High-quality epitaxial ferrites, such as low-damping MgAl-ferrite (MAFO), are promising nanoscale building blocks for all-oxide heterostructures driven by pure spin current. However, the impact of oxide interfaces on spin dynamics in such heterostructures remains an open question. Here, we investigate the spin dynamics and chemical and magnetic depth profiles of 15-nm-thick MAFO coherently interfaced with an isostructural $\approx$1-8-nm-thick overlayer of paramagnetic CoCr$_2$O$_4$ (CCO) as an all-oxide model system. Compared to MAFO without an overlayer, effective Gilbert damping in MAFO/CCO is enhanced by a factor of $>$3, irrespective of the CCO overlayer thickness. We attribute this damping enhancement to spin scattering at the $\sim$1-nm-thick chemically disordered layer at the MAFO/CCO interface, rather than spin pumping or proximity-induced magnetism. Our results indicate that damping in ferrite-based heterostructures is strongly influenced by interfacial chemical disorder, even if the thickness of the disordered layer is a small fraction of the ferrite thickness.
1908.08629v2
2006-11-23
Analytical solutions for two-level systems with damping
A method is proposed to transform any analytic solution of the Bloch equation into an analytic solution of the Landau-Lifshitz-Gilbert equation. This allows for the analytical description of the dynamics of a two level system with damping. This method shows that damping turns the linear Schr\"{o}dinger equation of a two-level system into a nonlinear Schr\"{o}dinger equation. As applications, it is shown that damping has a relatively mild influence on self-induced transparency but destroys dynamical localization.
0611238v1
2023-04-19
Thickness-dependent magnetic properties in Pt[CoNi]n multilayers with perpendicular magnetic anisotropy
We systematically investigated the Ni and Co thickness-dependent perpendicular magnetic anisotropy (PMA) coefficient, magnetic domain structures, and magnetization dynamics of Pt(5 nm)/[Co(t_Co nm)/Ni(t_Ni nm)]5/Pt(1 nm) multilayers by combining the four standard magnetic characterization techniques. The magnetic-related hysteresis loops obtained from the field-dependent magnetization M and anomalous Hall resistivity (AHR) \r{ho}_xy found that the two serial multilayers with t_Co = 0.2 and 0.3 nm have the optimum PMA coefficient K_U well as the highest coercivity H_C at the Ni thickness t_Ni = 0.6 nm. Additionally, the magnetic domain structures obtained by Magneto-optic Kerr effect (MOKE) microscopy also significantly depend on the thickness and K_U of the films. Furthermore, the thickness-dependent linewidth of ferromagnetic resonance is inversely proportional to K_U and H_C, indicating that inhomogeneous magnetic properties dominate the linewidth. However, the intrinsic Gilbert damping constant determined by a linear fitting of frequency-dependent linewidth does not depend on Ni thickness and K_U. Our results could help promote the PMA [Co/Ni] multilayer applications in various spintronic and spin-orbitronic devices.
2304.09366v1
2017-01-10
Magnetic properties in ultra-thin 3d transition metal alloys II: Experimental verification of quantitative theories of damping and spin-pumping
A systematic experimental study of Gilbert damping is performed via ferromagnetic resonance for the disordered crystalline binary 3d transition metal alloys Ni-Co, Ni-Fe and Co-Fe over the full range of alloy compositions. After accounting for inhomogeneous linewidth broadening, the damping shows clear evidence of both interfacial damping enhancement (by spin pumping) and radiative damping. We quantify these two extrinsic contributions and thereby determine the intrinsic damping. The comparison of the intrinsic damping to multiple theoretical calculations yields good qualitative and quantitative agreement in most cases. Furthermore, the values of the damping obtained in this study are in good agreement with a wide range of published experimental and theoretical values. Additionally, we find a compositional dependence of the spin mixing conductance.
1701.02475v1
2004-12-18
Fluctuations of the Magnetization in Thin Films due to Conduction Electrons
A detailed analysis of damping and noise due to a {\it sd}-interaction in a thin ferromagnetic film sandwiched between two large normal metal layers is carried out. The magnetization is shown to obey in general a non-local equation of motion which differs from the the Gilbert equation and is extended to the non-adiabatic regime. To lowest order in the exchange interaction and in the limit where the Gilbert equation applies, we show that the damping term is enhanced due to interfacial effects but it also shows oscillations as a function of the film thickness. The noise calculation is however carried out to all orders in the exchange coupling constant. The ellipticity of the precession of the magnetization is taken into account. The damping is shown to have a Gilbert form only in the adiabatic limit while the relaxation time becomes strongly dependent on the geometry of the thin film. It is also shown that the induced noise characteristic of sd-exchange is inherently colored in character and depends on the symmetry of the Hamiltonian of the magnetization in the film. We show that the sd-noise can be represented in terms of an external stochastic field which is white only in the adiabatic regime. The temperature is also renormalized by the spin accumulation in the system. For large intra-atomic exchange interactions, the Gilbert-Brown equation is no longer valid.
0412510v1
2014-07-02
Spin Waves in Ferromagnetic Insulators Coupled via a Normal Metal
Herein, we study the spin-wave dispersion and dissipation in a ferromagnetic insulator--normal metal--ferromagnetic insulator system. Long-range dynamic coupling because of spin pumping and spin transfer lead to collective magnetic excitations in the two thin-film ferromagnets. In addition, the dynamic dipolar field contributes to the interlayer coupling. By solving the Landau-Lifshitz-Gilbert-Slonczewski equation for macrospin excitations and the exchange-dipole volume as well as surface spin waves, we compute the effect of the dynamic coupling on the resonance frequencies and linewidths of the various modes. The long-wavelength modes may couple acoustically or optically. In the absence of spin-memory loss in the normal metal, the spin-pumping-induced Gilbert damping enhancement of the acoustic mode vanishes, whereas the optical mode acquires a significant Gilbert damping enhancement, comparable to that of a system attached to a perfect spin sink. The dynamic coupling is reduced for short-wavelength spin waves, and there is no synchronization. For intermediate wavelengths, the coupling can be increased by the dipolar field such that the modes in the two ferromagnetic insulators can couple despite possible small frequency asymmetries. The surface waves induced by an easy-axis surface anisotropy exhibit much greater Gilbert damping enhancement. These modes also may acoustically or optically couple, but they are unaffected by thickness asymmetries.
1407.0635v1
2015-05-15
Reliable Damping of Free Surface Waves in Numerical Simulations
This paper generalizes existing approaches for free-surface wave damping via momentum sinks for flow simulations based on the Navier-Stokes equations. It is shown in 2D flow simulations that, to obtain reliable wave damping, the coefficients in the damping functions must be adjusted to the wave parameters. A scaling law for selecting these damping coefficients is presented, which enables similarity of the damping in model- and full-scale. The influence of the thickness of the damping layer, the wave steepness, the mesh fineness and the choice of the damping coefficients are examined. An efficient approach for estimating the optimal damping setup is presented. Results of 3D ship resistance computations show that the scaling laws apply to such simulations as well, so the damping coefficients should be adjusted for every simulation to ensure convergence of the solution in both model and full scale. Finally, practical recommendations for the setup of reliable damping in flow simulations with regular and irregular free surface waves are given.
1505.04087v2
2010-12-20
Global attractors for the one dimensional wave equation with displacement dependent damping
We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a global attractor.
1012.4455v1
2009-04-21
Tensor damping in metallic magnetic multilayers
The mechanism of spin-pumping, described by Tserkovnyak et al., is formally analyzed in the general case of a magnetic multilayer consisting of two or more metallic ferromagnetic (FM) films separated by normal metal (NM) layers. It is shown that the spin-pumping-induced dynamic coupling between FM layers modifies the linearized Gilbert equations in a way that replaces the scalar Gilbert damping constant with a nonlocal matrix of Cartesian damping tensors. The latter are shown to be methodically calculable from a matrix algebra solution of the Valet-Fert transport equations. As an example, explicit analytical results are obtained for a 5-layer (spin-valve) of form NM/FM/NM'/FM/NM. Comparisons with earlier well known results of Tserkovnyak et al. for the related 3-layer FM/NM/FM indicate that the latter inadvertently hid the tensor character of the damping, and instead singled out the diagonal element of the local damping tensor along the axis normal to the plane of the two magnetization vectors. For spin-valve devices of technological interest, the influence of the tensor components of the damping on thermal noise or spin-torque critical currents are strongly weighted by the relative magnitude of the elements of the nonlocal, anisotropic stiffness-field tensor-matrix, and for in-plane magnetized spin-valves are generally more sensitive to the in-plane element of the damping tensor.
0904.3150v2