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2004-10-30
Dynamics of Domain Wall in a Biaxial Ferromagnet With Spin-torque
The dynamics of the domain wall (DW) in a biaxial ferromagnet interacting with a spin-polarized current are described by sine-gordon (SG) equation coupled with Gilbert damping term in this paper. Within our frame-work of this model, we obtain a threshold of the current in the motion of a single DW with the perturbation theory on kink soliton solution to the corresponding ferromagnetic system, and the threshold is shown to be dependent on the Gilbert damping term. Also, the motion properties of the DW are discussed for the zero- and nonzero-damping cases, which shows that our theory to describe the dynamics of the DW are self-consistent.
0411005v3
2005-10-31
Time-Resolved Spin Torque Switching and Enhanced Damping in Py/Cu/Py Spin-Valve Nanopillars
We report time-resolved measurements of current-induced reversal of a free magnetic layer in Py/Cu/Py elliptical nanopillars at temperatures T = 4.2 K to 160 K. Comparison of the data to Landau-Lifshitz-Gilbert macrospin simulations of the free layer switching yields numerical values for the spin torque and the Gilbert damping parameters as functions of T. The damping is strongly T-dependent, which we attribute to the antiferromagnetic pinning behavior of a thin permalloy oxide layer around the perimeter of the free layer. This adventitious antiferromagnetic pinning layer can have a major impact on spin torque phenomena.
0510798v2
2006-09-18
General Form of Magnetization Damping: Magnetization dynamics of a spin system evolving nonadiabatically and out of equilibrium
Using an effective Hamiltonian including the Zeeman and internal interactions, we describe the quantum theory of magnetization dynamics when the spin system evolves non-adiabatically and out of equilibrium. The Lewis-Riesenfeld dynamical invariant method is employed along with the Liouville-von Neumann equation for the density matrix. We derive a dynamical equation for magnetization defined with respect to the density operator with a general form of magnetization damping that involves the non-equilibrium contribution in addition to the Landau-Lifshitz-Gilbert equation. Two special cases of the radiation-spin interaction and the spin-spin exchange interaction are considered. For the radiation-spin interaction, the damping term is shown to be of the Gilbert type, while in the spin-spin exchange interaction case the results depend on a coupled chain of correlation functions.
0609431v2
2010-12-25
Screw-pitch effect and velocity oscillation of domain-wall in ferromagnetic nanowire driven by spin-polarized current
We investigate the dynamics of domain wall in ferromagnetic nanowire with spin-transfer torque. The critical current condition is obtained analytically. Below the critical current, we get the static domain wall solution which shows that the spin-polarized current can't drive domain wall moving continuously. In this case, the spin-transfer torque plays both the anti-precession and anti-damping roles, which counteracts not only the spin-precession driven by the effective field but also Gilbert damping to the moment. Above the critical value, the dynamics of domain wall exhibits the novel screw-pitch effect characterized by the temporal oscillation of domain wall velocity and width, respectively. Both the theoretical analysis and numerical simulation demonstrate that this novel phenomenon arise from the conjunctive action of Gilbert-damping and spin-transfer torque. We also find that the roles of spin-transfer torque are entirely contrary for the cases of below and above the critical current.
1012.5473v1
2014-06-24
Interface enhancement of Gilbert damping from first-principles
The enhancement of Gilbert damping observed for Ni80Fe20 (Py) films in contact with the non-magnetic metals Cu, Pd, Ta and Pt, is quantitatively reproduced using first-principles scattering theory. The "spin-pumping" theory that qualitatively explains its dependence on the Py thickness is generalized to include a number of factors known to be important for spin transport through interfaces. Determining the parameters in this theory from first-principles shows that interface spin-flipping makes an essential contribution to the damping enhancement. Without it, a much shorter spin-flip diffusion length for Pt would be needed than the value we calculate independently.
1406.6225v2
2015-09-06
Study of spin dynamics and damping on the magnetic nanowire arrays with various nanowire widths
We investigate the spin dynamics including Gilbert damping in the ferromagnetic nanowire arrays. We have measured the ferromagnetic resonance of ferromagnetic nanowire arrays using vector-network analyzer ferromagnetic resonance (VNA-FMR) and analyzed the results with the micromagnetic simulations. We find excellent agreement between the experimental VNA-FMR spectra and micromagnetic simulations result for various applied magnetic fields. We find that the demagnetization factor for longitudinal conditions, Nz (Ny) increases (decreases) as decreasing the nanowire width in the micromagnetic simulations. For the transverse magnetic field, Nz (Ny) increases (decreases) as increasing the nanowire width. We also find that the Gilbert damping constant increases from 0.018 to 0.051 as the increasing nanowire width for the transverse case, while it is almost constant as 0.021 for the longitudinal case.
1509.01807v1
2016-03-25
Large spin pumping effect in antisymmetric precession of Ni$_{79}$Fe$_{21}$/Ru/Ni$_{79}$Fe$_{21}$
In magnetic trilayer structures, a contribution to the Gilbert damping of ferromagnetic resonance arises from spin currents pumped from one layer to another. This contribution has been demonstrated for layers with weakly coupled, separated resonances, where magnetization dynamics are excited predominantly in one layer and the other layer acts as a spin sink. Here we show that trilayer structures in which magnetizations are excited simultaneously, antisymmetrically, show a spin-pumping effect roughly twice as large. The antisymmetric (optical) mode of antiferromagnetically coupled Ni$_{79}$Fe$_{21}$(8nm)/Ru/Ni$_{79}$Fe$_{21}$(8nm) trilayers shows a Gilbert damping constant greater than that of the symmetric (acoustic) mode by an amount as large as the intrinsic damping of Py ($\Delta \alpha\simeq\textrm{0.006}$). The effect is shown equally in field-normal and field-parallel to film plane geometries over 3-25 GHz. The results confirm a prediction of the spin pumping model and have implications for the use of synthetic antiferromagnets (SAF)-structures in GHz devices.
1603.07977v1
2016-07-18
Magnetic Skyrmion Transport in a Nanotrack With Spatially Varying Damping and Non-adiabatic Torque
Reliable transport of magnetic skyrmions is required for any future skyrmion-based information processing devices. Here we present a micromagnetic study of the in-plane current-driven motion of a skyrmion in a ferromagnetic nanotrack with spatially sinusoidally varying Gilbert damping and/or non-adiabatic spin-transfer torque coefficients. It is found that the skyrmion moves in a sinusoidal pattern as a result of the spatially varying Gilbert damping and/or non-adiabatic spin-transfer torque in the nanotrack, which could prevent the destruction of the skyrmion caused by the skyrmion Hall effect. The results provide a guide for designing and developing the skyrmion transport channel in skyrmion-based spintronic applications.
1607.04983v3
2016-10-21
Spin transport and dynamics in all-oxide perovskite La$_{2/3}$Sr$_{1/3}$MnO$_3$/SrRuO$_3$ bilayers probed by ferromagnetic resonance
Thin films of perovskite oxides offer the possibility of combining emerging concepts of strongly correlated electron phenomena and spin current in magnetic devices. However, spin transport and magnetization dynamics in these complex oxide materials are not well understood. Here, we experimentally quantify spin transport parameters and magnetization damping in epitaxial perovskite ferromagnet/paramagnet bilayers of La$_{2/3}$Sr$_{1/3}$MnO$_3$/SrRuO$_3$ (LSMO/SRO) by broadband ferromagnetic resonance spectroscopy. From the SRO thickness dependence of Gilbert damping, we estimate a short spin diffusion length of $\lesssim$1 nm in SRO and an interfacial spin-mixing conductance comparable to other ferromagnet/paramagnetic-metal bilayers. Moreover, we find that anisotropic non-Gilbert damping due to two-magnon scattering also increases with the addition of SRO. Our results demonstrate LSMO/SRO as a spin-source/spin-sink system that may be a foundation for examining spin-current transport in various perovskite heterostructures.
1610.06661v1
2019-02-12
Ultra-low damping in lift-off structured yttrium iron garnet thin films
We show that using maskless photolithography and the lift-off technique, patterned yttrium iron garnet thin films possessing ultra-low Gilbert damping can be accomplished. The films of 70 nm thickness were grown on (001)-oriented gadolinium gallium garnet by means of pulsed laser deposition, and they exhibit high crystalline quality, low surface roughness, and the effective magnetization of 127 emu/cm3. The Gilbert damping parameter is as low as 5x10-4. The obtained structures have well-defined sharp edges which along with good structural and magnetic film properties pave a path in the fabrication of high-quality magnonic circuits and oxide-based spintronic devices.
1902.04605v1
2019-02-20
CoFeB/MgO/CoFeB structures with orthogonal easy axes: perpendicular anisotropy and damping
We report on the Gilbert damping parameter $\alpha$, the effective magnetization $4\pi M_{eff}$, and the asymmetry of the $g$-factor in bottom-CoFeB(0.93~nm)/MgO(0.90--1.25~nm)/CoFeB(1.31~nm)-top as-deposited systems. Magnetization of CoFeB layers exhibits a specific noncollinear configuration with orthogonal easy axes and with $4\pi M_{eff}$ values of $+2.2$ kG and $-2.3$ kG for the bottom and top layers, respectively. We show that $4\pi M_{eff}$ depends on the asymmetry $g_\perp - g_\parallel$ of the $g$-factor measured in the perpendicular and the in-plane directions revealing a highly nonlinear relationship. In contrast, the Gilbert damping is practically the same for both layers. Annealing of the films results in collinear easy axes perpendicular to the plane for both layers. However, the linewidth is strongly increased due to enhanced inhomogeneous broadening.
1902.07563v1
2021-06-28
Stability of a Magnetically Levitated Nanomagnet in Vacuum: Effects of Gas and Magnetization Damping
In the absence of dissipation a non-rotating magnetic nanoparticle can be stably levitated in a static magnetic field as a consequence of the spin origin of its magnetization. Here we study the effects of dissipation on the stability of the system, considering the interaction with the background gas and the intrinsic Gilbert damping of magnetization dynamics. At large applied magnetic fields we identify magnetization switching induced by Gilbert damping as the key limiting factor for stable levitation. At low applied magnetic fields and for small particle dimensions magnetization switching is prevented due to the strong coupling of rotation and magnetization dynamics, and the stability is mainly limited by the gas-induced dissipation. In the latter case, high vacuum should be sufficient to extend stable levitation over experimentally relevant timescales. Our results demonstrate the possibility to experimentally observe the phenomenon of quantum spin stabilized magnetic levitation.
2106.14858v3
2021-10-31
Thermally induced all-optical ferromagnetic resonance in thin YIG films
All-optical ferromagnetic resonance (AO-FMR) is a powerful tool for local detection of micromagnetic parameters, such as magnetic anisotropy, Gilbert damping or spin stiffness. In this work we demonstrate that the AO-FMR method can be used in thin films of Yttrium Iron Garnet (YIG) if a metallic capping layer (Au, Pt) is deposited on top of the film. Magnetization precession is triggered by heating of the metallic layer with femtosecond laser pulses. The heating modifies the magneto-crystalline anisotropy of the YIG film and shifts the quasi-equilibrium orientation of magnetization, which results in precessional magnetization dynamics. The laser-induced magnetization precession corresponds to a uniform (Kittel) magnon mode, with the precession frequency determined by the magnetic anisotropy of the material as well as the external magnetic field, and the damping time set by a Gilbert damping parameter. The AO-FMR method thus enables measuring local magnetic properties, with spatial resolution given only by the laser spot size.
2111.00586v1
2024-01-01
Calculation of Gilbert damping and magnetic moment of inertia using torque-torque correlation model within ab initio Wannier framework
Magnetization dynamics in magnetic materials are well described by the modified semiclassical Landau-Lifshitz-Gilbert (LLG) equation, which includes the magnetic damping $\alpha$ and the magnetic moment of inertia $\mathrm{I}$ tensors as key parameters. Both parameters are material-specific and physically represent the time scales of damping of precession and nutation in magnetization dynamics. $\alpha$ and $\mathrm{I}$ can be calculated quantum mechanically within the framework of the torque-torque correlation model. The quantities required for the calculation are torque matrix elements, the real and imaginary parts of the Green's function and its derivatives. Here, we calculate these parameters for the elemental magnets such as Fe, Co and Ni in an ab initio framework using density functional theory and Wannier functions. We also propose a method to calculate the torque matrix elements within the Wannier framework. We demonstrate the effectiveness of the method by comparing it with the experiments and the previous ab initio and empirical studies and show its potential to improve our understanding of spin dynamics and to facilitate the design of spintronic devices.
2401.00714v1
2017-12-20
Unifying ultrafast demagnetization and intrinsic Gilbert damping in Co/Ni bilayers with electronic relaxation near the Fermi surface
The ability to controllably manipulate the laser-induced ultrafast magnetic dynamics is a prerequisite for future high speed spintronic devices. The optimization of devices requires the controllability of the ultrafast demagnetization time, , and intrinsic Gilbert damping, . In previous attempts to establish the relationship between and , the rare-earth doping of a permalloy film with two different demagnetization mechanism is not a suitable candidate. Here, we choose Co/Ni bilayers to investigate the relations between and by means of time-resolved magneto-optical Kerr effect (TRMOKE) via adjusting the thickness of the Ni layers, and obtain an approximately proportional relation between these two parameters. The remarkable agreement between TRMOKE experiment and the prediction of breathing Fermi-surface model confirms that a large Elliott-Yafet spin-mixing parameter is relevant to the strong spin-orbital coupling at the Co/Ni interface. More importantly, a proportional relation between and in such metallic films or heterostructures with electronic relaxation near Fermi surface suggests the local spin-flip scattering domains the mechanism of ultrafast demagnetization, otherwise the spin-current mechanism domains. It is an effective method to distinguish the dominant contributions to ultrafast magnetic quenching in metallic heterostructures by investigating both the ultrafast demagnetization time and Gilbert damping simultaneously. Our work can open a novel avenue to manipulate the magnitude and efficiency of Terahertz emission in metallic heterostructures such as the perpendicular magnetic anisotropic Ta/Pt/Co/Ni/Pt/Ta multilayers, and then it has an immediate implication of the design of high frequency spintronic devices.
1712.07323v1
2008-05-22
Intrinsic and non-local Gilbert damping in polycrystalline nickel studied by Ti:Sapphire laser fs spectroscopy
The use of femtosecond laser pulses generated by a Ti:Sapphire laser system allows us to gain an insight into the magnetization dynamics on time scales from sub-picosecond up to 1 ns directly in the time domain. This experimental technique is used to excite a polycrystalline nickel (Ni) film optically and probe the dynamics afterwards. Different spin wave modes (the Kittel mode, perpendicular standing spin-wave modes (PSSW) and dipolar spin-wave modes (Damon-Eshbach modes)) are identified as the Ni thickness is increased. The Kittel mode allows determination of the Gilbert damping parameter alpha extracted from the magnetization relaxation time tau_alpha. The non-local damping by spin currents emitted into a non-magnetic metallic layer of vanadium (V), palladium (Pd) and the rare earth dysprosium (Dy) are studied for wedge-shaped Ni films 1 nm-30 nm. The damping parameter increases from alpha=0.045 intrinsic for nickel to alpha>0.10 for the heavy materials, such as Pd and Dy, for the thinnest Ni films below 10 nm thickness. Also, for the thinnest reference Ni film thickness, an increased magnetic damping below 4 nm is observed. The origin of this increase is discussed within the framework of line broadening by locally different precessional frequencies within the laser spot region.
0805.3495v1
2015-06-18
The absence of intraband scattering in a consistent theory of Gilbert damping in metallic ferromagnets
Damping of magnetization dynamics in a ferromagnetic metal is usually characterized by the Gilbert parameter alpha. Recent calculations of this quantity, using a formula due to Kambersky, find that it is infinite for a perfect crystal owing to an intraband scattering term which is of third order in the spin-orbit parameter xi This surprising result conflicts with recent work by Costa and Muniz who study damping numerically by direct calculation of the dynamical transverse spin susceptibility in the presence of spin-orbit coupling. We resolve this inconsistency by following the Costa-Muniz approach for a slightly simplified model where it is possible to calculate alpha analytically. We show that to second order in the spin-orbit parameter xi one retrieves the Kambersky result for alpha, but to higher order one does not obtain any divergent intraband terms. The present work goes beyond that of Costa and Muniz by pointing out the necessity of including the effect of long-range Coulomb interaction in calculating damping for large xi. A direct derivation of the Kambersky formula is given which shows clearly the restriction of its validity to second order in xi so that no intraband scattering terms appear. This restriction has an important effect on the damping over a substantial range of impurity content and temperature. The experimental situation is discussed.
1506.05622v2
2020-02-07
Engineering Co$_2$MnAl$_x$Si$_{1-x}$ Heusler compounds as a model system to correlate spin polarization, intrinsic Gilbert damping and ultrafast demagnetization
Engineering of magnetic materials for developing better spintronic applications relies on the control of two key parameters: the spin polarization and the Gilbert damping responsible for the spin angular momentum dissipation. Both of them are expected to affect the ultrafast magnetization dynamics occurring on the femtosecond time scale. Here, we use engineered Co2MnAlxSi1-x Heusler compounds to adjust the degree of spin polarization P from 60 to 100% and investigate how it correlates with the damping. We demonstrate experimentally that the damping decreases when increasing the spin polarization from 1.1 10-3 for Co2MnAl with 63% spin polarization to an ultra-low value of 4.10-4 for the half-metal magnet Co2MnSi. This allows us investigating the relation between these two parameters and the ultrafast demagnetization time characterizing the loss of magnetization occurring after femtosecond laser pulse excitation. The demagnetization time is observed to be inversely proportional to 1-P and as a consequence to the magnetic damping, which can be attributed to the similarity of the spin angular momentum dissipation processes responsible for these two effects. Altogether, our high quality Heusler compounds allow controlling the band structure and therefore the channel for spin angular momentum dissipation.
2002.02686v1
2006-08-22
Simulation of stress-impedance effects in low magnetostrictive films
A theoretical study of stress-impedance effect based on the solution of Landau-Lifsitz-Gilbert equation has been carried out. The results show that stress impedance effects depend largely on several extrinsic (external bias field, external frequency) and intrinsic (orientation and magnitude of uniaxial anisotropy, damping) parameters.
0608488v1
2017-03-09
Material developments and domain wall based nanosecond-scale switching process in perpendicularly magnetized STT-MRAM cells
We investigate the Gilbert damping and the magnetization switching of perpendicularly magnetized FeCoB-based free layers embedded in tunnel junctions adequate for spin-torque operated memories. We study the influence of the boron content in MgO / FeCoB /Ta systems alloys on their Gilbert damping after crystallization annealing. Increasing the boron content from 20 to 30\% increases the crystallization temperature, thereby postponing the onset of elemental diffusion within the free layer. This reduction of the interdiffusion of the Ta atoms helps maintaining the Gilbert damping at a low level of 0.009 without any penalty on the anisotropy and the magneto-transport properties up to the 400$^\circ$C annealing required in CMOS back-end of line processing. In addition, we show that dual MgO free layers of composition MgO/FeCoB/Ta/FeCoB/MgO have a substantially lower damping than their MgO/FeCoB/Ta counterparts, reaching damping parameters as low as 0.0039 for a 3 \r{A} thick Tantalum spacer. This confirms that the dominant channel of damping is the presence of Ta impurities within the FeCoB alloy. On optimized tunnel junctions, we then study the duration of the switching events induced by spin-transfer-torque. We focus on the sub-threshold thermally activated switching in optimal applied field conditions. From the electrical signatures of the switching, we infer that once the nucleation has occurred, the reversal proceeds by a domain wall sweeping though the device at a few 10 m/s. The smaller the device, the faster its switching. We present an analytical model to account for our findings. The domain wall velocity is predicted to scale linearly with the current for devices much larger than the wall width. The wall velocity depends on the Bloch domain wall width, such that the devices with the lowest exchange stiffness will be the ones that host the domain walls with the slowest mobilities.
1703.03198v3
2018-07-31
Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences
Relaxation effects are of primary importance in the description of magnetic excitations, leading to a myriad of methods addressing the phenomenological damping parameters. In this work, we consider several well-established forms of calculating the intrinsic Gilbert damping within a unified theoretical framework, mapping out their connections and the approximations required to derive each formula. This scheme enables a direct comparison of the different methods on the same footing and a consistent evaluation of their range of validity. Most methods lead to very similar results for the bulk ferromagnets Fe, Co and Ni, due to the low spin-orbit interaction strength and the absence of the spin pumping mechanism. The effects of inhomogeneities, temperature and other sources of finite electronic lifetime are often accounted for by an empirical broadening of the electronic energy levels. We show that the contribution to the damping introduced by this broadening is additive, and so can be extracted by comparing the results of the calculations performed with and without spin-orbit interaction. Starting from simulated ferromagnetic resonance spectra based on the underlying electronic structure, we unambiguously demonstrate that the damping parameter obtained within the constant broadening approximation diverges for three-dimensional bulk magnets in the clean limit, while it remains finite for monolayers. Our work puts into perspective the several methods available to describe and compute the Gilbert damping, building a solid foundation for future investigations of magnetic relaxation effects in any kind of material.
1807.11808v3
2002-07-30
Microscopic relaxation mechanisms and linear magnetization dynamics
Linear magnetization dynamics in the presense of a thermal bath is analyzed for two general classes of microscopic damping mechanisms. The resulting stochastic differential equations are always in the form of a damped harmonic oscillator driven by a thermal field. The damping term contains both the interaction mechanisms and the symmetry of the magnetic system. Back transformation from the oscillator coordinates to the magnetization variables results in a macroscopic tensor form of damping that reflects the system anisotropy. Scalar Landau-Lifshitz-Gilbert damping term is valid only for systems with axial symmetry. Analysis of FMR linewith measurements versus frequency, temperature, and film thickness in NiFe films shows good agreement with a combination of slow-relaxing impurity and magnon-electron confluence processes.
0207721v1
2006-10-10
Spin-transfer in an open ferromagnetic layer: from negative damping to effective temperature
Spin-transfer is a typical spintronics effect that allows a ferromagnetic layer to be switched by spin-injection. Most of the experimental results about spin transfer are described on the basis of the Landau-Lifshitz-Gilbert equation of the magnetization, in which additional current-dependent damping factors are added, and can be positive or negative. The origin of the damping can be investigated further by performing stochastic experiments, like one shot relaxation experiments under spin-injection in the activation regime of the magnetization. In this regime, the N\'eel-Brown activation law is observed which leads to the introduction of a current-dependent effective temperature. In order to justify the introduction of these counterintuitive parameters (effective temperature and negative damping), a detailed thermokinetic analysis of the different sub-systems involved is performed. We propose a thermokinetic description of the different forms of energy exchanged between the electric and the ferromagnetic sub-systems at a Normal/Ferromagnetic junction. The corresponding Fokker Planck equations, including relaxations, are derived. The damping coefficients are studied in terms of Onsager-Casimir transport coefficients, with the help of the reciprocity relations. The effective temperature is deduced in the activation regime.
0610264v1
2014-05-09
Magnetization dynamics and damping due to electron-phonon scattering in a ferrimagnetic exchange model
We present a microscopic calculation of magnetization damping for a magnetic "toy model." The magnetic system consists of itinerant carriers coupled antiferromagnetically to a dispersionless band of localized spins, and the magnetization damping is due to coupling of the itinerant carriers to a phonon bath in the presence of spin-orbit coupling. Using a mean-field approximation for the kinetic exchange model and assuming the spin-orbit coupling to be of the Rashba form, we derive Boltzmann scattering integrals for the distributions and spin coherences in the case of an antiferromagnetic exchange splitting, including a careful analysis of the connection between lifetime broadening and the magnetic gap. For the Elliott-Yafet type itinerant spin dynamics we extract dephasing and magnetization times T_1 and T_2 from initial conditions corresponding to a tilt of the magnetization vector, and draw a comparison to phenomenological equations such as the Landau-Lifshitz or the Gilbert damping. We also analyze magnetization precession and damping for this system including an anisotropy field and find a carrier mediated dephasing of the localized spin via the mean-field coupling.
1405.2347v1
2015-11-13
Magnified Damping under Rashba Spin Orbit Coupling
The spin orbit coupling spin torque consists of the field-like [REF: S.G. Tan et al., arXiv:0705.3502, (2007).] and the damping-like terms [REF: H. Kurebayashi et al., Nature Nanotechnology 9, 211 (2014).] that have been widely studied for applications in magnetic memory. We focus, in this article, not on the spin orbit effect producing the above spin torques, but on its magnifying the damping constant of all field like spin torques. As first order precession leads to second order damping, the Rashba constant is naturally co-opted, producing a magnified field-like damping effect. The Landau-Liftshitz-Gilbert equations are written separately for the local magnetization and the itinerant spin, allowing the progression of magnetization to be self-consistently locked to the spin.
1511.04227v1
2022-05-13
Precession dynamics of a small magnet with non-Markovian damping: Theoretical proposal for an experiment to determine the correlation time
Recent advances in experimental techniques have made it possible to manipulate and measure the magnetization dynamics on the femtosecond time scale which is the same order as the correlation time of the bath degrees of freedom. In the equations of motion of magnetization, the correlation of the bath is represented by the non-Markovian damping. For development of the science and technologies based on the ultrafast magnetization dynamics it is important to understand how the magnetization dynamics depend on the correlation time. It is also important to determine the correlation time experimentally. Here we study the precession dynamics of a small magnet with the non-Markovian damping. Extending the theoretical analysis of Miyazaki and Seki [J. Chem. Phys. 108, 7052 (1998)] we obtain analytical expressions of the precession angular velocity and the effective damping constant for any values of the correlation time under assumption of small Gilbert damping constant. We also propose a possible experiment for determination of the correlation time.
2205.06399v1
2022-10-16
Magnetic damping anisotropy in the two-dimensional van der Waals material Fe$_3$GeTe$_2$ from first principles
Magnetization relaxation in the two-dimensional itinerant ferromagnetic van der Waals material Fe$_3$GeTe$_2$, below the Curie temperature, is fundamentally important for applications to low-dimensional spintronics devices. We use first-principles scattering theory to calculate the temperature-dependent Gilbert damping for bulk and single-layer Fe$_3$GeTe$_2$. The calculated damping frequency of bulk Fe$_3$GeTe$_2$ increases monotonically with temperature because of the dominance of resistivitylike behavior. By contrast, a very weak temperature dependence is found for the damping frequency of a single layer, which is attributed to strong surface scattering in this highly confined geometry. A systematic study of the damping anisotropy reveals that orientational anisotropy is present in both bulk and single-layer Fe3GeTe2. Rotational anisotropy is significant at low temperatures for both the bulk and a single layer and is gradually diminished by temperature-induced disorder. The rotational anisotropy can be significantly enhanced by up to 430% in gated single-layer Fe$_3$GeTe$_2$.
2210.08429v1
2016-09-26
Relativistic theory of spin relaxation mechanisms in the Landau-Lifshitz-Gilbert equation of spin dynamics
Starting from the Dirac-Kohn-Sham equation we derive the relativistic equation of motion of spin angular momentum in a magnetic solid under an external electromagnetic field. This equation of motion can be written in the form of the well-known Landau-Lifshitz-Gilbert equation for a harmonic external magnetic field, and leads to a more general magnetization dynamics equation for a general time-dependent magnetic field. In both cases with an electronic spin-relaxation term which stems from the spin-orbit interaction. We thus rigorously derive, from fundamental principles, a general expression for the anisotropic damping tensor which is shown to contain an isotropic Gilbert contribution as well as an anisotropic Ising-like and a chiral, Dzyaloshinskii-Moriya-like contribution. The expression for the spin relaxation tensor comprises furthermore both electronic interband and intraband transitions. We also show that when the externally applied electromagnetic field possesses spin angular momentum, this will lead to an optical spin torque exerted on the spin moment.
1609.07901v1
2002-11-22
Nonlinear microscopic relaxation of uniform magnetization precession
Dynamic relaxation for nonlinear magnetization excitation is analyzed. For direct processes, such as magnon-electron scattering and two-magnon scattering, the relaxation rate is determined from the linear case simply by utilizing the magnetization oscillation frequency for nonlinear excitation. For an indirect process, such as slow-relaxing impurities, the analysis gives an additional relaxation term proportional to the excitation level. In all cases the effective magnetization damping is increased compared to Landau-Lifshitz-Gilbert damping.
0211499v1
2005-10-11
Non-damping magnetization oscillations in a single-domain ferromagnet
Non-damped oscillations of the magnetization vector of a ferromagnetic system subject to a spin polarized current and an external magnetic field are studied theoretically by solving the Landau-Lifshitz-Gilbert equation. It is shown that the frequency and amplitude of such oscillations can be controlled by means of an applied magnetic field and a spin current. The possibility of injection of the oscillating spin current into a non-magnetic system is also discussed.
0510280v1
2007-03-27
Gauge Field Formulation of Adiabatic Spin Torques
Previous calculation of spin torques for small-amplitude magnetization dynamics around a uniformly magnetized state [J. Phys. Soc. Jpn. {\bf 75} (2006) 113706] is extended here to the case of finite-amplitude dynamics. This is achieved by introducing an `` adiabatic'' spin frame for conduction electrons, and the associated SU(2) gauge field. In particular, the Gilbert damping is shown to arise from the time variation of the spin-relaxation source terms in this new frame, giving a new physical picture of the damping. The present method will allow a `` first-principle'' derivation of spin torques without any assumptions such as rotational symmetry in spin space.
0703705v1
2008-05-09
Spin dynamics in (III,Mn)V ferromagnetic semiconductors: the role of correlations
We address the role of correlations between spin and charge degrees of freedom on the dynamical properties of ferromagnetic systems governed by the magnetic exchange interaction between itinerant and localized spins. For this we introduce a general theory that treats quantum fluctuations beyond the Random Phase Approximation based on a correlation expansion of the Green's function equations of motion. We calculate the spin susceptibility, spin--wave excitation spectrum, and magnetization precession damping. We find that correlations strongly affect the magnitude and carrier concentration dependence of the spin stiffness and magnetization Gilbert damping.
0805.1320v2
2010-01-16
Resonance Damping in Ferromagnets and Ferroelectrics
The phenomenological equations of motion for the relaxation of ordered phases of magnetized and polarized crystal phases can be developed in close analogy with one another. For the case of magnetized systems, the driving magnetic field intensity toward relaxation was developed by Gilbert. For the case of polarized systems, the driving electric field intensity toward relaxation was developed by Khalatnikov. The transport times for relaxation into thermal equilibrium can be attributed to viscous sound wave damping via magnetostriction for the magnetic case and electrostriction for the polarization case.
1001.2845v1
2016-05-15
Propagation of Thermally Induced Magnonic Spin Currents
The propagation of magnons in temperature gradients is investigated within the framework of an atomistic spin model with the stochastic Landau-Lifshitz-Gilbert equation as underlying equation of motion. We analyze the magnon accumulation, the magnon temperature profile as well as the propagation length of the excited magnons. The frequency distribution of the generated magnons is investigated in order to derive an expression for the influence of the anisotropy and the damping parameter on the magnon propagation length. For soft ferromagnetic insulators with low damping a propagation length in the range of some $\mu$m can be expected for exchange driven magnons.
1605.04543v1
2021-03-05
Universal spin wave damping in magnetic Weyl semimetals
We analyze the decay of spin waves into Stoner excitations in magnetic Weyl semimetals. The lifetime of a mode is found to have a universal dependence on its frequency and momentum, and on a few parameters that characterize the relativistic Weyl spectrum. At the same time, Gilbert damping by Weyl electrons is absent. The decay rate of spin waves is calculated perturbatively using the s-d model of itinerant Weyl or Dirac electrons coupled to local moments. We show that many details of the Weyl spectrum, such as the momentum-space locations, dispersions and sizes of the Weyl Fermi pockets, can be deduced indirectly by probing the spin waves of local moments using inelastic neutron scattering.
2103.03885v1
2023-02-17
Control of magnon-photon coupling by spin torque
We demonstrate the influence of damping and field-like torques in the magnon-photon coupling process by classically integrating the generalized Landau-Lifshitz-Gilbert equation with RLC equation in which a phase correlation between dynamic magnetization and microwave current through combined Amp\`ere and Faraday effects are considered. We show that the gap between two hybridized modes can be controlled in samples with damping parameter in the order of $10^{-3}$ by changing the direction of the dc current density $J$ if a certain threshold is reached. Our results suggest that an experimental realization of the proposed magnon-photon coupling control mechanism is feasible in yttrium iron garnet/Pt hybrid structures.
2302.08910v1
2017-03-21
Using rf voltage induced ferromagnetic resonance to study the spin-wave density of states and the Gilbert damping in perpendicularly magnetized disks
We study how the shape of the spinwave resonance lines in rf-voltage induced FMR can be used to extract the spinwave density of states and the damping within the precessing layer in nanoscale tunnel junctions that possess perpendicular anisotropy. We work with a field applied along the easy axis to preserve the uniaxial symmetry of the system. We describe the set-up to study the susceptibility contributions of the spin waves in the field-frequency space. We then identify the maximum device size above which the spinwaves can no longer be studied in isolation as the linewidths of their responses make them overlap. The rf-voltage induced signal is the sum of two voltages that have comparable magnitudes: a first voltage that originates from the transverse susceptibility and rectification by magnetoresistance and a second voltage that arises from the non-linear longitudinal susceptibility and the resultant time-averaged change of the micromagnetic configuration. The transverse and longitudinal susceptibility signals have different dc bias dependences such that they can be separated by measuring how the device rectifies the rf voltage at different dc bias voltages. The transverse and longitudinal susceptibility signals have different lineshapes; their joint studies can yield the Gilbert damping of the free layer of the device with a degree of confidence that compares well with standard FMR. Our method is illustrated on FeCoB-based free layers in which the individual spin-waves can be sufficiently resolved only for disk diameters below 200 nm. The resonance line shapes on devices with 90 nm diameters are consistent with a Gilbert damping of 0.011. This damping of 0.011 exceeds the value of 0.008 measured on the unpatterned films, which indicates that device-level measurements are needed for a correct evaluation of dissipation.
1703.07310v2
2015-11-16
Determination of intrinsic damping of perpendicularly magnetized ultrathin films from time resolved precessional magnetization measurements
Magnetization dynamics are strongly influenced by damping. An effective damping constant {\alpha}eff is often determined experimentally from the spectral linewidth of the free induction decay of the magnetization after the system is excited to its non-equilibrium state. Such an {\alpha}eff, however, reflects both intrinsic damping as well as inhomogeneous broadening. In this paper we compare measurements of the magnetization dynamics in ultrathin non-epitaxial films having perpendicular magnetic anisotropy using two different techniques, time-resolved magneto optical Kerr effect (TRMOKE) and hybrid optical-electrical ferromagnetic resonance (OFMR). By using an external magnetic field that is applied at very small angles to the film plane in the TRMOKE studies, we develop an explicit closed-form analytical expression for the TRMOKE spectral linewidth and show how this can be used to reliably extract the intrinsic Gilbert damping constant. The damping constant determined in this way is in excellent agreement with that determined from the OFMR method on the same samples. Our studies indicate that the asymptotic high-field approach that is often used in the TRMOKE method to distinguish the intrinsic damping from the effective damping may result in significant error, because such high external magnetic fields are required to make this approach valid that they are out of reach. The error becomes larger the lower is the intrinsic damping constant, and thus may account for the anomalously high damping constants that are often reported in TRMOKE studies. In conventional ferromagnetic resonance (FMR) studies, inhomogeneous contributions can be readily distinguished from intrinsic damping contributions from the magnetic field dependence of the FMR linewidth. Using the analogous approach, we show how reliable values of the intrinsic damping can be extracted from TRMOKE.
1511.04802v1
2002-07-19
Gilbert Damping in Magnetic Multilayers
We study the enhancement of the ferromagnetic relaxation rate in thin films due to the adjacent normal metal layers. Using linear response theory, we derive the dissipative torque produced by the s-d exchange interaction at the ferromagnet-normal metal interface. For a slow precession, the enhancement of Gilbert damping constant is proportional to the square of the s-d exchange constant times the zero-frequency limit of the frequency derivative of the local dynamic spin susceptibility of the normal metal at the interface. Electron-electron interactions increase the relaxation rate by the Stoner factor squared. We attribute the large anisotropic enhancements of the relaxation rate observed recently in multilayers containing palladium to this mechanism. For free electrons, the present theory compares favorably with recent spin-pumping result of Tserkovnyak et al. [Phys. Rev. Lett. \textbf{88},117601 (2002)].
0207471v1
2002-08-06
Spin pumping and magnetization dynamics in metallic multilayers
We study the magnetization dynamics in thin ferromagnetic films and small ferromagnetic particles in contact with paramagnetic conductors. A moving magnetization vector causes \textquotedblleft pumping\textquotedblright of spins into adjacent nonmagnetic layers. This spin transfer affects the magnetization dynamics similar to the Landau-Lifshitz-Gilbert phenomenology. The additional Gilbert damping is significant for small ferromagnets, when the nonmagnetic layers efficiently relax the injected spins, but the effect is reduced when a spin accumulation build-up in the normal metal opposes the spin pumping. The damping enhancement is governed by (and, in turn, can be used to measure) the mixing conductance or spin-torque parameter of the ferromagnet--normal-metal interface. Our theoretical findings are confirmed by agreement with recent experiments in a variety of multilayer systems.
0208091v2
2003-08-19
Magnetization relaxation in (Ga,Mn)As ferromagnetic semiconductors
We describe a theory of Mn local-moment magnetization relaxation due to p-d kinetic-exchange coupling with the itinerant-spin subsystem in the ferromagnetic semiconductor (Ga,Mn)As alloy. The theoretical Gilbert damping coefficient implied by this mechanism is calculated as a function of Mn moment density, hole concentration, and quasiparticle lifetime. Comparison with experimental ferromagnetic resonance data suggests that in annealed strongly metallic samples, p-d coupling contributes significantly to the damping rate of the magnetization precession at low temperatures. By combining the theoretical Gilbert coefficient with the values of the magnetic anisotropy energy, we estimate that the typical critical current for spin-transfer magnetization switching in all-semiconductor trilayer devices can be as low as $\sim 10^{5} {\rm A cm}^{-2}$.
0308386v3
2005-12-29
Current-induced magnetization dynamics in disordered itinerant ferromagnets
Current-driven magnetization dynamics in ferromagnetic metals are studied in a self-consistent adiabatic local-density approximation in the presence of spin-conserving and spin-dephasing impurity scattering. Based on a quantum kinetic equation, we derive Gilbert damping and spin-transfer torques entering the Landau-Lifshitz equation to linear order in frequency and wave vector. Gilbert damping and a current-driven dissipative torque scale identically and compete, with the result that a steady current-driven domain-wall motion is insensitive to spin dephasing in the limit of weak ferromagnetism. A uniform magnetization is found to be much more stable against spin torques in the itinerant than in the \textit{s}-\textit{d} model for ferromagnetism. A dynamic spin-transfer torque reminiscent of the spin pumping in multilayers is identified and shown to govern the current-induced domain-wall distortion.
0512715v4
2006-11-22
Magnetization damping in a local-density approximation
The linear response of itinerant transition metal ferromagnets to transverse magnetic fields is studied in a self-consistent adiabatic local-density approximation. The susceptibility is calculated from a microscopic Hamiltonian, including spin-conserving impurities, impurity induced spin-orbit interaction and magnetic impurities using the Keldysh formalism. The Gilbert damping constant in the Landau-Lifshitz-Gilbert equation is identified, parametrized by an effective transverse spin dephasing rate, and is found to be inversely proportional to the exchange splitting. Our result justify the phenomenological treatment of transverse spin dephasing in the study of current-induced magnetization dynamics in weak, itinerant ferromagnets by Tserkovnyak \textit{et al.}. We show that neglect of gradient corrections in the quasiclassical transport equations leads to incorrect results when the exchange potential becomes of the order of the Fermi energy.
0611588v1
2007-08-03
Strong spin-orbit induced Gilbert damping and g-shift in iron-platinum nanoparticles
The shape of ferromagnetic resonance spectra of highly dispersed, chemically disordered Fe_{0.2}Pt_{0.8} nanospheres is perfectly described by the solution of the Landau-Lifshitz-Gilbert (LLG) equation excluding effects by crystalline anisotropy and superparamagnetic fluctuations. Upon decreasing temperature, the LLG damping $\alpha(T)$ and a negative g-shift, g(T)-g_0, increase proportional to the particle magnetic moments determined from the Langevin analysis of the magnetization isotherms. These novel features are explained by the scattering of the $q \to 0$ magnon from an electron-hole (e/h) pair mediated by the spin-orbit coupling, while the sd-exchange can be ruled out. The large saturation values, $\alpha(0)=0.76$ and $g(0)/g_0-1=-0.37$, indicate the dominance of an overdamped 1 meV e/h-pair which seems to originate from the discrete levels of the itinerant electrons in the d_p=3 nm nanoparticles.
0708.0463v1
2008-05-01
Chaotic Spin Dynamics of a Long Nanomagnet Driven by a Current
We study the spin dynamics of a long nanomagnet driven by an electrical current. In the case of only DC current, the spin dynamics has a sophisticated bifurcation diagram of attractors. One type of attractors is a weak chaos. On the other hand, in the case of only AC current, the spin dynamics has a rather simple bifurcation diagram of attractors. That is, for small Gilbert damping, when the AC current is below a critical value, the attractor is a limit cycle; above the critical value, the attractor is chaotic (turbulent). For normal Gilbert damping, the attractor is always a limit cycle in the physically interesting range of the AC current. We also developed a Melnikov integral theory for a theoretical prediction on the occurrence of chaos. Our Melnikov prediction seems performing quite well in the DC case. In the AC case, our Melnikov prediction seems predicting transient chaos. The sustained chaotic attractor seems to have extra support from parametric resonance leading to a turbulent state.
0805.0147v1
2010-10-08
A unified first-principles study of Gilbert damping, spin-flip diffusion and resistivity in transition metal alloys
Using a formulation of first-principles scattering theory that includes disorder and spin-orbit coupling on an equal footing, we calculate the resistivity $\rho$, spin flip diffusion length $l_{sf}$ and the Gilbert damping parameter $\alpha$ for Ni$_{1-x}$Fe$_x$ substitutional alloys as a function of $x$. For the technologically important Ni$_{80}$Fe$_{20}$ alloy, permalloy, we calculate values of $\rho = 3.5 \pm 0.15$ $\mu$Ohm-cm, $l_{sf}=5.5 \pm 0.3$ nm, and $\alpha= 0.0046 \pm 0.0001$ compared to experimental low-temperature values in the range $4.2-4.8$ $\mu$Ohm-cm for $\rho$, $5.0-6.0$ nm for $l_{sf}$, and $0.004-0.013$ for $\alpha$ indicating that the theoretical formalism captures the most important contributions to these parameters.
1010.1626v3
2011-02-22
Ab-initio calculation of the Gilbert damping parameter via linear response formalism
A Kubo-Greenwood-like equation for the Gilbert damping parameter $\alpha$ is presented that is based on the linear response formalism. Its implementation using the fully relativistic Korringa-Kohn-Rostoker (KKR) band structure method in combination with Coherent Potential Approximation (CPA) alloy theory allows it to be applied to a wide range of situations. This is demonstrated with results obtained for the bcc alloy system Fe$_x$Co$_{1-x}$ as well as for a series of alloys of permalloy with 5d transition metals. To account for the thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. The corresponding calculations for Ni correctly describe the rapid change of $\alpha$ when small amounts of substitutional Cu are introduced.
1102.4551v1
2012-07-28
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
2012-08-07
Observation of Coherent Helimagnons and Gilbert damping in an Itinerant Magnet
We study the magnetic excitations of itinerant helimagnets by applying time-resolved optical spectroscopy to Fe0.8Co0.2Si. Optically excited oscillations of the magnetization in the helical state are found to disperse to lower frequency as the applied magnetic field is increased; the fingerprint of collective modes unique to helimagnets, known as helimagnons. The use of time-resolved spectroscopy allows us to address the fundamental magnetic relaxation processes by directly measuring the Gilbert damping, revealing the versatility of spin dynamics in chiral magnets. (*These authors contributed equally to this work)
1208.1462v1
2012-11-02
Dynamic Spin Injection into Chemical Vapor Deposited Graphene
We demonstrate dynamic spin injection into chemical vapor deposition (CVD) grown graphene by spin pumping from permalloy (Py) layers. Ferromagnetic resonance measurements at room temperature reveal a strong enhancement of the Gilbert damping at the Py/graphene interface, exceeding that observed in even Py/platinum interfaces. Similar results are also shown on Co/graphene layers. This enhancement in the Gilbert damping is understood as the consequence of spin pumping at the interface driven by magnetization dynamics. Our observations suggest a strong enhancement of spin-orbit coupling in CVD graphene, in agreement with earlier spin valve measurements.
1211.0492v1
2013-01-10
First-principles calculation of the Gilbert damping parameter via the linear response formalism with application to magnetic transition-metals and alloys
A method for the calculations of the Gilbert damping parameter $\alpha$ is presented, which based on the linear response formalism, has been implemented within the fully relativistic Korringa-Kohn-Rostoker band structure method in combination with the coherent potential approximation alloy theory. To account for thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. This allows the determination of $\alpha$ for various types of materials, such as elemental magnetic systems and ordered magnetic compounds at finite temperature, as well as for disordered magnetic alloys at $T = 0$ K and above. The effects of spin-orbit coupling, chemical and temperature induced structural disorder are analyzed. Calculations have been performed for the 3$d$ transition-metals bcc Fe, hcp Co, and fcc Ni, their binary alloys bcc Fe$_{1-x}$Co$_{x}$, fcc Ni$_{1-x}$Fe$_x$, fcc Ni$_{1-x}$Co$_x$ and bcc Fe$_{1-x}$V$_{x}$, and for 5d impurities in transition-metal alloys. All results are in satisfying agreement with experiment.
1301.2114v1
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
2014-01-24
Wavenumber-dependent Gilbert damping in metallic ferromagnets
New terms to the dynamical equation of magnetization motion, associated with spin transport, have been reported over the past several years. Each newly identified term is thought to possess both a real and an imaginary effective field leading to fieldlike and dampinglike torques on magnetization. Here we show that three metallic ferromagnets possess an imaginary effective-field term which mirrors the well-known real effective-field term associated with exchange in spin waves. Using perpendicular standing spin wave resonance between 2-26 GHz, we evaluate the magnitude of the finite-wavenumber ($k$) dependent Gilbert damping $\alpha$ in three typical device ferromagnets, Ni$_{79}$Fe$_{21}$, Co, and Co$_{40}$Fe$_{40}$B$_{20}$, and demonstrate for the first time the presence of a $k^2$ term as $\Delta\alpha=\Delta\alpha_0+A_{k}\cdot k^2$ in all three metals. We interpret the new term as the continuum analog of spin pumping, predicted recently, and show that its magnitude, $A_{k}$=0.07-0.1 nm$^2$, is consistent with transverse spin relaxation lengths as measured by conventional (interlayer) spin pumping.
1401.6467v2
2014-12-11
Deviation From the Landau-Lifshitz-Gilbert equation in the Inertial regime of the Magnetization
We investigate in details the inertial dynamics of a uniform magnetization in the ferromagnetic resonance (FMR) context. Analytical predictions and numerical simulations of the complete equations within the Inertial Landau-Lifshitz-Gilbert (ILLG) model are presented. In addition to the usual precession resonance, the inertial model gives a second resonance peak associated to the nutation dynamics provided that the damping is not too large. The analytical resolution of the equations of motion yields both the precession and nutation angular frequencies. They are function of the inertial dynamics characteristic time $\tau$, the dimensionless damping $\alpha$ and the static magnetic field $H$. A scaling function with respect to $\alpha\tau\gamma H$ is found for the nutation angular frequency, also valid for the precession angular frequency when $\alpha\tau\gamma H\gg 1$. Beyond the direct measurement of the nutation resonance peak, we show that the inertial dynamics of the magnetization has measurable effects on both the width and the angular frequency of the precession resonance peak when varying the applied static field. These predictions could be used to experimentally identify the inertial dynamics of the magnetization proposed in the ILLG model.
1412.3783v1
2015-01-02
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
2015-08-04
A Critical Analysis of the Feasibility of Pure Strain-Actuated Giant Magnetostrictive Nanoscale Memories
Concepts for memories based on the manipulation of giant magnetostrictive nanomagnets by stress pulses have garnered recent attention due to their potential for ultra-low energy operation in the high storage density limit. Here we discuss the feasibility of making such memories in light of the fact that the Gilbert damping of such materials is typically quite high. We report the results of numerical simulations for several classes of toggle precessional and non-toggle dissipative magnetoelastic switching modes. Material candidates for each of the several classes are analyzed and forms for the anisotropy energy density and ranges of material parameters appropriate for each material class are employed. Our study indicates that the Gilbert damping as well as the anisotropy and demagnetization energies are all crucial for determining the feasibility of magnetoelastic toggle-mode precessional switching schemes. The roles of thermal stability and thermal fluctuations for stress-pulse switching of giant magnetostrictive nanomagnets are also discussed in detail and are shown to be important in the viability, design, and footprint of magnetostrictive switching schemes.
1508.00629v2
2015-12-16
Parity-time symmetry breaking in magnetic systems
The understanding of out-of-equilibrium physics, especially dynamic instabilities and dynamic phase transitions, is one of the major challenges of contemporary science, spanning the broadest wealth of research areas that range from quantum optics to living organisms. Focusing on nonequilibrium dynamics of an open dissipative spin system, we introduce a non-Hermitian Hamiltonian approach, in which non-Hermiticity reflects dissipation and deviation from equilibrium. The imaginary part of the proposed spin Hamiltonian describes the effects of Gilbert damping and applied Slonczewski spin-transfer torque. In the classical limit, our approach reproduces Landau-Lifshitz-Gilbert-Slonczewski dynamics of a large macrospin. We reveal the spin-transfer torque-driven parity-time symmetry-breaking phase transition corresponding to a transition from precessional to exponentially damped spin dynamics. Micromagnetic simulations for nanoscale ferromagnetic disks demonstrate the predicted effect. Our findings can pave the way to a general quantitative description of out-of-equilibrium phase transitions driven by spontaneous parity-time symmetry breaking.
1512.05408v2
2017-01-11
The Cauchy problem for the Landau-Lifshitz-Gilbert equation in BMO and self-similar solutions
We prove a global well-posedness result for the Landau-Lifshitz equation with Gilbert damping provided that the BMO semi-norm of the initial data is small. As a consequence, we deduce the existence of self-similar solutions in any dimension. In the one-dimensional case, we characterize the self-similar solutions associated with an initial data given by some ($\mathbb{S}^2$-valued) step function and establish their stability. We also show the existence of multiple solutions if the damping is strong enough. Our arguments rely on the study of a dissipative quasilinear Schr\"odinger obtained via the stereographic projection and techniques introduced by Koch and Tataru.
1701.03083v2
2017-01-27
Structural scale $q-$derivative and the LLG-Equation in a scenario with fractionality
In the present contribution, we study the Landau-Lifshitz-Gilbert equation with two versions of structural derivatives recently proposed: the scale $q-$derivative in the non-extensive statistical mechanics and the axiomatic metric derivative, which presents Mittag-Leffler functions as eigenfunctions. The use of structural derivatives aims to take into account long-range forces, possible non-manifest or hidden interactions and the dimensionality of space. Having this purpose in mind, we build up an evolution operator and a deformed version of the LLG equation. Damping in the oscillations naturally show up without an explicit Gilbert damping term.
1701.08076v2
2018-10-17
Perpendicularly magnetized YIG films with small Gilbert damping constant and anomalous spin transport properties
The Y3Fe5O12 (YIG) films with perpendicular magnetic anisotropy (PMA) have recently attracted a great deal of attention for spintronics applications. Here, we report the induced PMA in the ultrathin YIG films grown on (Gd2.6Ca0.4)(Ga4.1Mg0.25Zr0.65)O12 (SGGG) substrates by epitaxial strain without preprocessing. Reciprocal space mapping shows that the films are lattice-matched to the substrates without strain relaxation. Through ferromagnetic resonance and polarized neutron reflectometry measurements, we find that these YIG films have ultra-low Gilbert damping constant with a magnetic dead layer as thin as about 0.3 nm at the YIG/SGGG interfaces. Moreover, the transport behavior of the Pt/YIG/SGGG films reveals an enhancement of spin mixing conductance and a large non-monotonic magnetic field dependence of anomalous Hall effect as compared with the Pt/YIG/Gd3Ga5O12 (GGG) films. The non-monotonic anomalous Hall signal is extracted in the temperature range from 150 to 350 K, which has been ascribed to the possible non-collinear magnetic order at the Pt/YIG interface induced by uniaxial strain.
1810.07384v2
2019-03-07
Current-induced motion of twisted skyrmions
Twisted skyrmions, whose helicity angles are different from that of Bloch skyrmions and N\'eel skyrmions, have already been demonstrated in experiments recently. In this work, we first contrast the magnetic structure and origin of the twisted skyrmion with other three types of skyrmion including Bloch skyrmion, N\'eel skyrmion and antiskyrmion. Following, we investigate the dynamics of twisted skyrmions driven by the spin transfer toque (STT) and the spin Hall effect (SHE) by using micromagnetic simulations. It is found that the spin Hall angle of the twisted skyrmion is related to the dissipative force tensor and the Gilbert damping both for the motions induced by the STT and the SHE, especially for the SHE induced motion, the skyrmion Hall angle depends substantially on the skyrmion helicity. At last, we demonstrate that the trajectory of the twisted skyrmion can be controlled in a two dimensional plane with a Gilbert damping gradient. Our results provide the understanding of current-induced motion of twisted skyrmions, which may contribute to the applications of skyrmion-based racetrack memories.
1903.02812v1
2019-07-03
Anisotropy of spin-transfer torques and Gilbert damping induced by Rashba coupling
Spin-transfer torques (STT), Gilbert damping (GD), and effective spin renormalization (ESR) are investigated microscopically in a 2D Rashba ferromagnet with spin-independent Gaussian white-noise disorder. Rashba spin-orbit coupling induced anisotropy of these phenomena is thoroughly analysed. For the case of two partly filled spin subbands, a remarkable relation between the anisotropic STT, GD, and ESR is established. In the absence of magnetic field and other torques on magnetization, this relation corresponds to a current-induced motion of a magnetic texture with the classical drift velocity of conduction electrons. Finally, we compute spin susceptibility of the system and generalize the notion of spin-polarized current.
1907.02041v3
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
2021-11-05
Giant oscillatory Gilbert damping in superconductor/ferromagnet/superconductor junctions
Interfaces between materials with differently ordered phases present unique opportunities for exotic physical properties, especially the interplay between ferromagnetism and superconductivity in the ferromagnet/superconductor heterostructures. The investigation of zero- and pi-junctions has been of particular interest for both fundamental physical science and emerging technologies. Here, we report the experimental observation of giant oscillatory Gilbert damping in the superconducting Nb/NiFe/Nb junctions with respect to the NiFe thickness. This observation suggests an unconventional spin pumping and relaxation via zero-energy Andreev bound states that exist only in the Nb/NiFe/Nb pi-junctions, but not in the Nb/NiFe/Nb zero-junctions. Our findings could be important for further exploring the exotic physical properties of ferromagnet/superconductor heterostructures, and potential applications of ferromagnet pi-junctions in quantum computing, such as half-quantum flux qubits.
2111.03233v1
2022-11-14
Magnetization Dynamics in Synthetic Antiferromagnets with Perpendicular Magnetic Anisotropy
Understanding the rich physics of magnetization dynamics in perpendicular synthetic antiferromagnets (p-SAFs) is crucial for developing next-generation spintronic devices. In this work, we systematically investigate the magnetization dynamics in p-SAFs combining time-resolved magneto-optical Kerr effect (TR-MOKE) measurements with theoretical modeling. These model analyses, based on a Landau-Lifshitz-Gilbert approach incorporating exchange coupling, provide details about the magnetization dynamic characteristics including the amplitudes, directions, and phases of the precession of p-SAFs under varying magnetic fields. These model-predicted characteristics are in excellent quantitative agreement with TR-MOKE measurements on an asymmetric p-SAF. We further reveal the damping mechanisms of two procession modes co-existing in the p-SAF and successfully identify individual contributions from different sources, including Gilbert damping of each ferromagnetic layer, spin pumping, and inhomogeneous broadening. Such a comprehensive understanding of magnetization dynamics in p-SAFs, obtained by integrating high-fidelity TR-MOKE measurements and theoretical modeling, can guide the design of p-SAF-based architectures for spintronic applications.
2211.07744v2
2023-05-17
Material Parameters for Faster Ballistic Switching of an In-plane Magnetized Nanomagnet
High-speed magnetization switching of a nanomagnet is necessary for faster information processing. The ballistic switching by a pulsed magnetic filed is a promising candidate for the high-speed switching. It is known that the switching speed of the ballistic switching can be increased by increasing the magnitude of the pulsed magnetic field. However it is difficult to generate a strong and short magnetic field pulse in a small device. Here we explore another direction to achieve the high-speed ballistic switching by designing material parameters such as anisotropy constant, saturation magnetization, and the Gilbert damping constant. We perform the macrospin simulations for the ballistic switching of in-plane magnetized nano magnets with varying material parameters. The results are analyzed based on the switching dynamics on the energy density contour. We show that the pulse width required for the ballistic switching can be reduced by increasing the magnetic anisotropy constant or by decreasing the saturation magnetization. We also show that there exists an optimal value of the Gilbert damping constant that minimizes the pulse width required for the ballistic switching.
2305.10111v1
2023-05-23
Current-driven motion of magnetic topological defects in ferromagnetic superconductors
Recent years have seen a number of instances where magnetism and superconductivity intrinsically coexist. Our focus is on the case where spin-triplet superconductivity arises out of ferromagnetism, and we make a hydrodynamic analysis of the effect of a charge supercurrent on magnetic topological defects like domain walls and merons. We find that the emergent electromagnetic field that arises out of the superconducting order parameter provides a description for not only the physical quantities such as the local energy flux density and the interaction between current and defects but also the energy dissipation through magnetic dynamics of the Gilbert damping, which becomes more prominent compared to the normal state as superconductivity attenuates the energy dissipation through the charge sector. In particular, we reveal that the current-induced dynamics of domain walls and merons in the presence of the Gilbert damping give rise to the nonsingular $4\pi$ and $2\pi$ phase slips, respectively, revealing the intertwined dynamics of spin and charge degrees of freedom in ferromagnetic superconductors.
2305.13564v1
2023-07-03
Magnetic lump motion in saturated ferromagnetic films
In this paper, we study in detail the nonlinear propagation of magnetic soliton in a ferromagnetic film. The sample is magnetized to saturation by an external field perpendicular to film plane. A new generalized (2+1)-dimensional short-wave asymptotic model is derived. The bilinear-like forms of this equation are constructed, and exact magnetic line soliton solutions are exhibited. It is observed that a series of stable lumps can be generated by an unstable magnetic soliton under Gaussian disturbance. Such magnetic lumps are highly stable and can maintain their shapes and velocities during evolution or collision. The interaction between lump and magnetic soliton, as well as interaction between two lumps, are numerically investigated. We further discuss the nonlinear motion of lumps in ferrites with Gilbert-damping and inhomogeneous exchange effects. The results show that the Gilbert-damping effects make the amplitude and velocity of the magnetic lump decay exponentially during propagation. And the shock waves are generated from a lump when quenching the strength of inhomogeneous exchange.
2307.00903v1
2005-03-24
Fast magnetization switching of Stoner particles: A nonlinear dynamics picture
The magnetization reversal of Stoner particles is investigated from the point of view of nonlinear dynamics within the Landau-Lifshitz-Gilbert formulation. The following results are obtained. 1) We clarify that the so-called Stoner-Wohlfarth (SW) limit becomes exact when damping constant is infinitely large. Under the limit, the magnetization moves along the steepest energy descent path. The minimal switching field is the one at which there is only one stable fixed point in the system. 2) For a given magnetic anisotropy, there is a critical value for the damping constant, above which the minimal switching field is the same as that of the SW-limit. 3) We illustrate how fixed points and their basins change under a field along different directions. This change explains well why a non-parallel field gives a smaller minimal switching field and a short switching time. 4) The field of a ballistic magnetization reversal should be along certain direction window in the presence of energy dissipation. The width of the window depends on both of the damping constant and the magnetic anisotropy. The upper and lower bounds of the direction window increase with the damping constant. The window width oscillates with the damping constant for a given magnetic anisotropy. It is zero for both zero and infinite damping. Thus, the perpendicular field configuration widely employed in the current experiments is not the best one since the damping constant in a real system is far from zero.
0503594v1
2003-02-17
Magnetization dynamics with a spin-transfer torque
The magnetization reversal and dynamics of a spin valve pillar, whose lateral size is 64$\times$64 nm$^2$, are studied by using micromagnetic simulation in the presence of spin transfer torque. Spin torques display both characteristics of magnetic damping (or anti-damping) and of an effective magnetic field. For a steady-state current, both M-I and M-H hysteresis loops show unique features, including multiple jumps, unusual plateaus and precessional states. These states originate from the competition between the energy dissipation due to Gilbert damping and the energy accumulation due to the spin torque supplied by the spin current. The magnetic energy oscillates as a function of time even for a steady-state current. For a pulsed current, the minimum width and amplitude of the spin torque for achieving current-driven magnetization reversal are quantitatively determined. The spin torque also shows very interesting thermal activation that is fundamentally different from an ordinary damping effect.
0302337v1
2003-10-13
Domain wall mobility in nanowires: transverse versus vortex walls
The motion of domain walls in ferromagnetic, cylindrical nanowires is investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole-dipole interaction, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. The transverse domain wall is observed for diameters smaller than the exchange length of the given material. Here, the system behaves effectively one-dimensional and the domain wall mobility agrees with a result derived for a one-dimensional wall by Slonczewski. For low damping the domain wall mobility decreases with decreasing damping constant. With increasing diameter, a crossover to a vortex wall sets in which enhances the domain wall mobility drastically. For a vortex wall the domain wall mobility is described by the Walker-formula, with a domain wall width depending on the diameter of the wire. The main difference is the dependence on damping: for a vortex wall the domain wall mobility can be drastically increased for small values of the damping constant up to a factor of $1/\alpha^2$.
0310277v1
2013-10-29
Observational Study of Large Amplitude Longitudinal Oscillations in a Solar Filament
On 20 August 2010 an energetic disturbance triggered damped large-amplitude longitudinal (LAL) oscillations in almost an entire filament. In the present work we analyze this periodic motion in the filament to characterize the damping and restoring mechanism of the oscillation. Our method involves placing slits along the axis of the filament at different angles with respect to the spine of the filament, finding the angle at which the oscillation is clearest, and fitting the resulting oscillation pattern to decaying sinusoidal and Bessel functions. These functions represent the equations of motion of a pendulum damped by mass accretion. With this method we determine the period and the decaying time of the oscillation. Our preliminary results support the theory presented by Luna and Karpen (2012) that the restoring force of LAL oscillations is solar gravity in the tubes where the threads oscillate, and the damping mechanism is the ongoing accumulation of mass onto the oscillating threads. Following an earlier paper, we have determined the magnitude and radius of curvature of the dipped magnetic flux tubes hosting a thread along the filament, as well as the mass accretion rate of the filament threads, via the fitted parameters.
1310.7657v1
2014-12-08
Magnetization Dynamics driven by Non-equilibrium Spin-Orbit Coupled Electron Gas
The dynamics of magnetization coupled to an electron gas via s-d exchange interaction is investigated by using density matrix technique. Our theory shows that non-equilibrium spin accumulation induces a spin torque and the electron bath leads to a damping of the magnetization. For the two-dimensional magnetization thin film coupled to the electron gas with Rashba spin-orbit coupling, the result for the spin-orbit torques is consistent with the previous semi-classical theory. Our theory predicts a damping of the magnetization, which is absent in the semi-classical theory. The magnitude of the damping due to the electron bath is comparable to the intrinsic Gilbert damping and may be important in describing the magnetization dynamics of the system.
1412.2479v1
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
2017-03-06
Damping dependence of spin-torque effects in thermally assisted magnetization reversal
Thermal fluctuations of nanomagnets driven by spin-polarized currents are treated via the Landau-Lifshitz-Gilbert equation as generalized to include both the random thermal noise field and Slonczewski spin-transfer torque terms. The magnetization reversal time of such a nanomagnet is then evaluated for wide ranges of damping by using a method which generalizes the solution of the so-called Kramers turnover problem for mechanical Brownian particles, thereby bridging the very low damping and intermediate damping Kramers escape rates, to the analogous magnetic turnover problem. The reversal time is then evaluated for a nanomagnet with the free energy density given in the standard form of superimposed easy-plane and in-plane easy-axis anisotropies with the dc bias field along the easy axis.
1703.01879v5
2017-05-09
Low spin wave damping in the insulating chiral magnet Cu$_{2}$OSeO$_{3}$
Chiral magnets with topologically nontrivial spin order such as Skyrmions have generated enormous interest in both fundamental and applied sciences. We report broadband microwave spectroscopy performed on the insulating chiral ferrimagnet Cu$_{2}$OSeO$_{3}$. For the damping of magnetization dynamics we find a remarkably small Gilbert damping parameter of about $1\times10^{-4}$ at 5 K. This value is only a factor of 4 larger than the one reported for the best insulating ferrimagnet yttrium iron garnet. We detect a series of sharp resonances and attribute them to confined spin waves in the mm-sized samples. Considering the small damping, insulating chiral magnets turn out to be promising candidates when exploring non-collinear spin structures for high frequency applications.
1705.03416v1
2018-09-04
Separation of the two-magnon scattering contribution to damping for the determination of the spin mixing conductance
We present angle dependent measurements of the damping properties of epitaxial Fe layers with MgO, Al and Pt capping layers. Based on the preferential distribution of lattice defects following the crystal symmetry, we make use of a model of the defect density to separate the contribution of two-magnon scattering to the damping from the isotropic contribution originating in the spin pumping effect, the viscous Gilbert damping and the magnetic proximity effect. The separation of the two-magnon contribution, which depends strongly on the defect density, allows for the measurement of a value of the effective spin mixing conductance which is closer to the value exclusively due to spin pumping. The influence of the defect density for bilayers systems due to the different capping layers and to the unavoidable spread in defect density from sample to sample is thus removed. This shows the potential of studying spin pumping phenomena in fully ordered systems in which this separation is possible, contrary to polycrystalline or amorphous metallic thin films.
1809.01042v1
2006-02-09
Magnetization damping in polycrystalline Co ultra-thin films: Evidence for non-local effects
The magnetic properties and magnetization dynamics of polycrystalline ultra-thin Co layers were investigated using a broadband ferromagnetic resonance (FMR) technique at room temperature. A variable thickness (1 nm $\leq t \leq$ 10 nm) Co layer is sandwiched between 10 nm thick Cu layers (10 nm Cu| t Co|10 nm Cu), while materials in contact with the Cu outer interfaces are varied to determine their influence on the magnetization damping. The resonance field and the linewidth were studied for in-plane magnetic fields in field swept experiments at a fixed frequency, from 4 to 25 GHz. The Co layers have a lower magnetization density than the bulk, and an interface contribution to the magnetic anisotropy normal to the film plane. The Gilbert damping, as determined from the frequency dependence of the linewidth, increases with decreasing Co layer thickness for films with outer Pt layers. This enhancement is not observed in structures without Pt layers. The result can be understood in terms of a non-local contribution to the damping due to spin pumping from Co through the Cu layer and spin relaxation in Pt layers. Pt layers just 1.5 nm thick are found to be sufficient to enhance the damping and thus act as efficient "spin-sinks". In structures with Pt outer layers, this non-local contribution to the damping becomes predominant when the Co layer is thinner than 4 nm.
0602243v2
2020-04-09
Magnetic Damping in Epitaxial Fe Alloyed with Vanadium and Aluminum
To develop low-moment, low-damping metallic ferromagnets for power-efficient spintronic devices, it is crucial to understand how magnetic relaxation is impacted by the addition of nonmagnetic elements. Here, we compare magnetic relaxation in epitaxial Fe films alloyed with light nonmagnetic elements of V and Al. FeV alloys exhibit lower intrinsic damping compared to pure Fe, reduced by nearly a factor of 2, whereas damping in FeAl alloys increases with Al content. Our experimental and computational results indicate that reducing the density of states at the Fermi level, rather than the average atomic number, has a more significant impact in lowering damping in Fe alloyed with light elements. Moreover, FeV is confirmed to exhibit an intrinsic Gilbert damping parameter of $\simeq$0.001, among the lowest ever reported for ferromagnetic metals.
2004.04840v3
2014-05-19
Comparison of micromagnetic parameters of ferromagnetic semiconductors (Ga,Mn)(As,P) and (Ga,Mn)As
We report on the determination of micromagnetic parameters of epilayers of the ferromagnetic semiconductor (Ga,Mn)As, which has easy axis in the sample plane, and (Ga,Mn)(As,P) which has easy axis perpendicular to the sample plane. We use an optical analog of ferromagnetic resonance where the laser-pulse-induced precession of magnetization is measured directly in the time domain. By the analysis of a single set of pump-and-probe magneto-optical data we determined the magnetic anisotropy fields, the spin stiffness and the Gilbert damping constant in these two materials. We show that incorporation of 10% of phosphorus in (Ga,Mn)As with 6% of manganese leads not only to the expected sign change of the perpendicular to plane anisotropy field but also to an increase of the Gilbert damping and to a reduction of the spin stiffness. The observed changes in the micromagnetic parameters upon incorporating P in (Ga,Mn)As are consistent with the reduced hole density, conductivity, and Curie temperature of the (Ga,Mn)(As,P) material. We report that the magnetization precession damping is stronger for the n = 1 spin wave resonance mode than for the n = 0 uniform magnetization precession mode.
1405.4677v1
2015-03-24
Spin dynamics and frequency dependence of magnetic damping study in soft ferromagnetic FeTaC film with a stripe domain structure
Perpendicular magnetic anisotropy (PMA) and low magnetic damping are the key factors for the free layer magnetization switching by spin transfer torque technique in magnetic tunnel junction devices. The magnetization precessional dynamics in soft ferromagnetic FeTaC thin film with a stripe domain structure was explored in broad band frequency range by employing micro-strip ferromagnetic resonance technique. The polar angular variation of resonance field and linewidth at different frequencies have been analyzed numerically using Landau-Lifshitz-Gilbert equation by taking into account the total free energy density of the film. The numerically estimated parameters Land\'{e} $g$-factor, PMA constant, and effective magnetization are found to be 2.1, 2$\times10^{5}$ erg/cm$^{3}$ and 7145 Oe, respectively. The frequency dependence of Gilbert damping parameter ($\alpha$) is evaluated by considering both intrinsic and extrinsic effects into the total linewidth analysis. The value of $\alpha$ is found to be 0.006 at 10 GHz and it increases with decreasing precessional frequency.
1503.07043v5
2016-05-22
Low Gilbert damping in Co2FeSi and Fe2CoSi films
Thin highly textured Fe$_{\mathrm{1+x}}$Co$_{\mathrm{2-x}}$Si ($0 \leq$ x $\leq 1$) films were prepared on MgO (001) substrates by magnetron co-sputtering. The magneto-optic Kerr effect (MOKE) and ferromagnetic resonance (FMR) measurements were used to investigate the composition dependence of the magnetization, the magnetic anisotropy, the gyromagnetic ratio and the relaxation of the films. The effective magnetization for the thin Fe$_{\mathrm{1+x}}$Co$_{\mathrm{2-x}}$Si films, determined by FMR measurements, are consistent with the Slater Pauling prediction. Both MOKE and FMR measurements reveal a pronounced fourfold anisotropy distribution for all films. In addition we found a strong influence of the stoichiometry on the anisotropy as the cubic anisotropy strongly increases with increasing Fe concentration. The gyromagnetic ratio is only weakly dependent on the composition. We find low Gilbert damping parameters for all films with values down to $0.0012\pm0.00012$ for Fe$_{1.75}$Co$_{1.25}$Si. The effective damping parameter for Co$_2$FeSi is found to be $0.0018\pm 0.0004$. We also find a pronounced anisotropic relaxation, which indicates significant contributions of two-magnon scattering processes that is strongest along the easy axes of the films. This makes thin Fe$_{\mathrm{1+x}}$Co$_{\mathrm{2-x}}$Si films ideal materials for the application in STT-MRAM devices.
1605.06797v1
2017-09-21
Low Gilbert Damping Constant in Perpendicularly Magnetized W/CoFeB/MgO Films with High Thermal Stability
Perpendicular magnetic materials with low damping constant and high thermal stability have great potential for realizing high-density, non-volatile, and low-power consumption spintronic devices, which can sustain operation reliability for high processing temperatures. In this work, we study the Gilbert damping constant ({\alpha}) of perpendicularly magnetized W/CoFeB/MgO films with a high perpendicular magnetic anisotropy (PMA) and superb thermal stability. The {\alpha} of these PMA films annealed at different temperatures is determined via an all-optical Time-Resolved Magneto-Optical Kerr Effect method. We find that {\alpha} of these W/CoFeB/MgO PMA films decreases with increasing annealing temperature, reaches a minimum of {\alpha} = 0.016 at an annealing temperature of 350 {\deg}C, and then increases to 0.024 after post-annealing at 400 {\deg}C. The minimum {\alpha} observed at 350 {\deg}C is rationalized by two competing effects as the annealing temperature becomes higher: the enhanced crystallization of CoFeB and dead-layer growth occurring at the two interfaces of the CoFeB layer. We further demonstrate that {\alpha} of the 400 {\deg}C-annealed W/CoFeB/MgO film is comparable to that of a reference Ta/CoFeB/MgO PMA film annealed at 300 {\deg}C, justifying the enhanced thermal stability of the W-seeded CoFeB films.
1709.07483v1
2022-02-06
Enhancing Perpendicular Magnetic Anisotropy in Garnet Ferrimagnet by Interfacing with Few-Layer WTe2
Engineering magnetic anisotropy in a ferro- or ferrimagnetic (FM) thin film is crucial in spintronic device. One way to modify the magnetic anisotropy is through the surface of the FM thin film. Here, we report the emergence of a perpendicular magnetic anisotropy (PMA) induced by interfacial interactions in a heterostructure comprised of a garnet ferrimagnet, Y3Fe5O12 (YIG), and the low-symmetry, high spin orbit coupling (SOC) transition metal dichalcogenide, WTe2. At the same time, we also observed an enhancement in Gilbert damping in the WTe2 covered YIG area. Both the magnitude of interface-induced PMA and the Gilbert damping enhancement have no observable WTe2 thickness dependence down to single quadruple-layer, indicating that the interfacial interaction plays a critical role. The ability of WTe2 to enhance the PMA in FM thin film, combined with its previously reported capability to generate out-of-plane damping like spin torque, makes it desirable for magnetic memory applications.
2202.02834v1
2018-10-25
Time-retarded damping and magnetic inertia in the Landau-Lifshitz-Gilbert equation self-consistently coupled to electronic time-dependent nonequilibrium Green functions
The conventional Landau-Lifshitz-Gilbert (LLG) equation is a widely used tool to describe dynamics of local magnetic moments, viewed as classical vectors of fixed length, with their change assumed to take place simultaneously with the cause. Here we demonstrate that recently developed [M. D. Petrovi\'{c} {\em et al.}, {\tt arXiv:1802.05682}] self-consistent coupling of the LLG equation to time-dependent quantum-mechanical description of electrons microscopically generates time-retarded damping in the LLG equation described by a memory kernel which is also spatially dependent. For sufficiently slow dynamics of local magnetic moments, the memory kernel can be expanded to extract the Gilbert damping (proportional to first time derivative of magnetization) and magnetic inertia (proportional to second time derivative of magnetization) terms whose parameters, however, are time-dependent in contrast to time-independent parameters used in the conventional LLG equation. We use examples of single or multiple magnetic moments precessing in an external magnetic field, as well as field-driven motion of a magnetic domain wall (DW), to quantify the difference in their time evolution computed from conventional LLG equation vs. TDNEGF+LLG quantum-classical hybrid approach. The faster DW motion predicted by TDNEGF+LLG approach reveals that important quantum effects, stemming from finite amount of time which it takes for conduction electron spin to react to the motion of classical local magnetic moments, are missing from conventional classical micromagnetics simulations. We also demonstrate large discrepancy between TDNEGF+LLG-computed numerically exact and, therefore, nonperturbative result for charge current pumped by a moving DW and the same quantity computed by perturbative spin motive force formula combined with the conventional LLG equation.
1810.11016v2
2019-08-08
Annihilation of topological solitons in magnetism with spin wave burst finale: The role of nonequilibrium electrons causing nonlocal damping and spin pumping over ultrabroadband frequency range
We not only reproduce burst of short-wavelength spin waves (SWs) observed in recent experiment [S. Woo et al., Nat. Phys. 13, 448 (2017)] on magnetic-field-driven annihilation of two magnetic domain walls (DWs) but, furthermore, we predict that this setup additionally generates highly unusual} pumping of electronic spin currents in the absence of any bias voltage. Prior to the instant of annihilation, their power spectrum is ultrabroadband, so they can be converted into rapidly changing in time charge currents, via the inverse spin Hall effect, as a source of THz radiation of bandwidth $\simeq 27$ THz where the lowest frequency is controlled by the applied magnetic field. The spin pumping stems from time-dependent fields introduced into the quantum Hamiltonian of electrons by the classical dynamics of localized magnetic moments (LMMs) comprising the domains. The pumped currents carry spin-polarized electrons which, in turn, exert backaction on LMMs in the form of nonlocal damping which is more than twice as large as conventional local Gilbert damping. The nonlocal damping can substantially modify the spectrum of emitted SWs when compared to widely-used micromagnetic simulations where conduction electrons are completely absent. Since we use fully microscopic (i.e., Hamiltonian-based) framework, self-consistently combining time-dependent electronic nonequilibrium Green functions with the Landau-Lifshitz-Gilbert equation, we also demonstrate that previously derived phenomenological formulas miss ultrabroadband spin pumping while underestimating the magnitude of nonlocal damping due to nonequilibrium electrons.
1908.03194v5
2006-06-05
Phenomenological theory of current driven exchange switching in ferromagnetic nanojunctions
Phenomenological approach is developed in the theory of spin-valve type ferromagnetic junctions to describe exchange switching by current flowing perpendicular to interfaces. Forward and backward current switching effects are described and they may be principally different in nature. Mobile electron spins are considered as being free in all the contacting ferromagnetic layers. Joint action of the following two current effects is investigated: the nonequilibrium longitudinal spin-injection effective field and the transverse spin-transfer surface torque. Dispersion relation for fluctuations is derived and solved for a junction model having spatially localized spin transfer torque: depth of the torque penetration into the free layer is assumed much smaller than the total free layer thickness. Some critical value of the well known Gilbert damping constant is established for the first time. Spin transfer torque dominates in the instability threshold determination for small enough damping constants, while the spin-injection effective field dominates for high damping. Fine interplay between spin transfer torque and spin injection is necessary to provide a hysteretic behavior of the resistance versus current dependence. The state diagram building up shows the possibility of non-stationary (time dependent) nonlinear states arising due to instability development. Calculations lead to the instability rise time values of the order of 0.1 ns. Spin wave resonance frequency spectrum softening occurs under the current growing to the instability threshold. Magnetization fluctuations above the threshold rise oscillating with time for low damping, but rise aperiodically and much more rapid for high damping.
0606102v2
2015-07-29
Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau-Lifschitz-Gilbert equation
The real-time dynamics of a classical spin in an external magnetic field and locally exchange coupled to an extended one-dimensional system of non-interacting conduction electrons is studied numerically. Retardation effects in the coupled electron-spin dynamics are shown to be the source for the relaxation of the spin in the magnetic field. Total energy and spin is conserved in the non-adiabatic process. Approaching the new local ground state is therefore accompanied by the emission of dispersive wave packets of excitations carrying energy and spin and propagating through the lattice with Fermi velocity. While the spin dynamics in the regime of strong exchange coupling J is rather complex and governed by an emergent new time scale, the motion of the spin for weak J is regular and qualitatively well described by the Landau-Lifschitz-Gilbert (LLG) equation. Quantitatively, however, the full quantum-classical hybrid dynamics differs from the LLG approach. This is understood as a breakdown of weak-coupling perturbation theory in J in the course of time. Furthermore, it is shown that the concept of the Gilbert damping parameter is ill-defined for the case of a one-dimensional system.
1507.08227v2
2008-09-26
Damping and magnetic anisotropy of ferromagnetic GaMnAs thin films
The magnetic properties of annealed, epitaxial Ga0.93Mn0.07As layers under tensile and compressive stress have been investigated by X-band (9GHz) and Q-band (35GHz) ferromagnetic resonance (FMR) spectroscopy. From the analysis of the linewidths of the uniform mode spectra the FMR Gilbert damping factor "alpha" has been determined. At T=4K we obtain a minimum damping factor of "alpha" = 0.003 for the compressively stressed layer. Its value is not isotropic. It has a minimum value for the easy axes orientations of the magnetic field and increases with the measuring temperature. Its average value is for both type of films of the order of 0.01 in spite of strong differences in the inhomogeneous linewidth which vary between 20 Oe and 600 Oe for the layers grown on GaAs and GaInAs substrates respectively.
0809.4644v2
2013-08-02
Spin pumping damping and magnetic proximity effect in Pd and Pt spin-sink layers
We investigated the spin pumping damping contributed by paramagnetic layers (Pd, Pt) in both direct and indirect contact with ferromagnetic Ni$_{81}$Fe$_{19}$ films. We find a nearly linear dependence of the interface-related Gilbert damping enhancement $\Delta\alpha$ on the heavy-metal spin-sink layer thicknesses t$_\textrm{N}$ in direct-contact Ni$_{81}$Fe$_{19}$/(Pd, Pt) junctions, whereas an exponential dependence is observed when Ni$_{81}$Fe$_{19}$ and (Pd, Pt) are separated by \unit[3]{nm} Cu. We attribute the quasi-linear thickness dependence to the presence of induced moments in Pt, Pd near the interface with Ni$_{81}$Fe$_{19}$, quantified using X-ray magnetic circular dichroism (XMCD) measurements. Our results show that the scattering of pure spin current is configuration-dependent in these systems and cannot be described by a single characteristic length.
1308.0450v2
2015-02-05
Nonlinear analysis of magnetization dynamics excited by spin Hall effect
We investigate the possibility of exciting self-oscillation in a perpendicular ferromagnet by the spin Hall effect on the basis of a nonlinear analysis of the Landau-Lifshitz-Gilbert (LLG) equation. In the self-oscillation state, the energy supplied by the spin torque during a precession on a constant energy curve should equal the dissipation due to damping. Also, the current to balance the spin torque and the damping torque in the self-oscillation state should be larger than the critical current to destabilize the initial state. We find that the second condition in the spin Hall system is not satisfied by deriving analytical solutions of the energy supplied by the spin transfer effect and the dissipation due to the damping from the nonlinear LLG equation. This indicates that the self-oscillation of a perpendicular ferromagnet cannot be excited solely by the spin Hall torque.
1502.01420v2
2015-03-04
Critical current destabilizing perpendicular magnetization by the spin Hall effect
The critical current needed to destabilize the magnetization of a perpendicular ferromagnet via the spin Hall effect is studied. Both the dampinglike and fieldlike torques associated with the spin current generated by the spin Hall effect is included in the Landau-Lifshitz-Gilbert equation to model the system. In the absence of the fieldlike torque, the critical current is independent of the damping constant and is much larger than that of conventional spin torque switching of collinear magnetic systems, as in magnetic tunnel junctions. With the fieldlike torque included, we find that the critical current scales with the damping constant as $\alpha^{0}$ (i.e., damping independent),$\alpha$, and $\alpha^{1/2}$ depending on the sign of the fieldlike torque and other parameters such as the external field. Numerical and analytical results show that the critical current can be significantly reduced when the fieldlike torque possesses the appropriate sign, i.e. when the effective field associated with the fieldlike torque is pointing opposite to the spin direction of the incoming electrons. These results provide a pathway to reducing the current needed to switch magnetization using the spin Hall effect.
1503.01478v2
2015-10-23
Laser-induced THz magnetization precession for a tetragonal Heusler-like nearly compensated ferrimagnet
Laser-induced magnetization precessional dynamics was investigated in epitaxial films of Mn$_3$Ge, which is a tetragonal Heusler-like nearly compensated ferrimagnet. The ferromagnetic resonance (FMR) mode was observed, the precession frequency for which exceeded 0.5 THz and originated from the large magnetic anisotropy field of approximately 200 kOe for this ferrimagnet. The effective damping constant was approximately 0.03. The corresponding effective Landau-Lifshitz constant of approximately 60 Mrad/s and is comparable to those of the similar Mn-Ga materials. The physical mechanisms for the Gilbert damping and for the laser-induced excitation of the FMR mode were also discussed in terms of the spin-orbit-induced damping and the laser-induced ultrafast modulation of the magnetic anisotropy, respectively.
1510.06793v1
2017-04-11
CoFeAlB alloy with low damping and low magnetization for spin transfer torque switching
We investigate the effect of Al doping on the magnetic properties of the alloy CoFeB. Comparative measurements of the saturation magnetization, the Gilbert damping parameter $\alpha$ and the exchange constant as a function of the annealing temperature for CoFeB and CoFeAlB thin films are presented. Our results reveal a strong reduction of the magnetization for CoFeAlB in comparison to CoFeB. If the prepared CoFeAlB films are amorphous, the damping parameter $\alpha$ is unaffected by the Al doping in comparison to the CoFeB alloy. In contrast, in the case of a crystalline CoFeAlB film, $\alpha$ is found to be reduced. Furthermore, the x-ray characterization and the evolution of the exchange constant with the annealing temperature indicate a similar crystallization process in both alloys. The data proves the suitability of CoFeAlB for spin torque switching properties where a reduction of the switching current in comparison with CoFeB is expected.
1704.03326v1
2018-09-25
Theory of damping in magnetization dynamics, dispelling a myth and pointing a way forward
There is a widely-held belief amongst theoreticians that the Gilbert damping parameter {\alpha} in magnetization dynamics is infinite for a pure metal at T=0. The basic error leading to this belief is pointed out explicitly and the various methods of calculation used are viewed in a unified way based on the Lorentzian lineshape of ferromagnetic resonance spectra. A general torque formula for {\alpha} is proposed as a good starting-point for treating inhomogeneous materials such as alloys, compounds and layered structures. Local spin density functional theory provides a simple physical picture, in terms of a non-uniform precessional cone angle in ferromagnetic resonance, of how such inhomogeneity contributes to the damping. In a complementary many-body theory this contribution is given by a vertex correction to the torque-torque response function.
1809.09429v1
2018-10-31
Anisotropic and controllable Gilbert-Bloch dissipation in spin valves
Spin valves form a key building block in a wide range of spintronic concepts and devices from magnetoresistive read heads to spin-transfer-torque oscillators. We elucidate the dependence of the magnetic damping in the free layer on the angle its equilibrium magnetization makes with that in the fixed layer. The spin pumping-mediated damping is anisotropic and tensorial, with Gilbert- and Bloch-like terms. Our investigation reveals a mechanism for tuning the free layer damping in-situ from negligible to a large value via the orientation of fixed layer magnetization, especially when the magnets are electrically insulating. Furthermore, we expect the Bloch contribution that emerges from the longitudinal spin accumulation in the non-magnetic spacer to play an important role in a wide range of other phenomena in spin valves.
1811.00020v2
2019-07-27
Two improved Gauss-Seidel projection methods for Landau-Lifshitz-Gilbert equation
In this paper, we present two improved Gauss-Seidel projection methods with unconditional stability. The first method updates the gyromagnetic term and the damping term simultaneously and follows by a projection step. The second method introduces two sets of approximate solutions, where we update the gyromagnetic term and the damping term simultaneously for one set of approximate solutions and apply the projection step to the other set of approximate solutions in an alternating manner. Compared to the original Gauss-Seidel projection method which has to solve heat equations $7$ times at each time step, the improved methods solve heat equations $5$ times and $3$ times, respectively. First-order accuracy in time and second-order accuracy in space are verified by examples in both 1D and 3D. In addition, unconditional stability with respect to both the grid size and the damping parameter is confirmed numerically. Application of both methods to a realistic material is also presented with hysteresis loops and magnetization profiles. Compared with the original method, the recorded running times suggest that savings of both methods are about $2/7$ and $4/7$ for the same accuracy requirement, respectively.
1907.11853v1
2020-10-01
Modeling coupled spin and lattice dynamics
A unified model of molecular and atomistic spin dynamics is presented enabling simulations both in microcanonical and canonical ensembles without the necessity of additional phenomenological spin damping. Transfer of energy and angular momentum between the lattice and the spin systems is achieved by a coupling term based upon the spin-orbit interaction. The characteristic spectra of the spin and phonon systems are analyzed for different coupling strength and temperatures. The spin spectral density shows magnon modes together with the uncorrelated noise induced by the coupling to the lattice. The effective damping parameter is investigated showing an increase with both coupling strength and temperature. The model paves the way to understanding magnetic relaxation processes beyond the phenomenological approach of the Gilbert damping and the dynamics of the energy transfer between lattice and spins.
2010.00642v1
2021-04-22
Impact of Fe$_{80}$B$_{20}$ insertion on the properties of dual-MgO perpendicular magnetic tunnel junctions
We explore the impact of Fe80B20 inserted at both Co$_{20}$Fe$_{80}$B$_{20}$/MgO interfaces of dual-MgO free layers (FLs) in bottom-pinned magnetic tunnel junctions (MTJs). MTJ stacks are annealed for 30 min at 350 $^\circ$C and 400 $^\circ$C in a vacuum after film deposition. Current-in-plane tunneling measurements are carried out to characterize magnetotransport properties of the MTJs. Conventional magnetometry measurements and ferromagnetic resonance are conducted to estimate the saturation magnetization, the effective perpendicular anisotropy field and the Gilbert damping of dual-MgO FLs as a function of the Fe$_{80}$B$_{20}$ thickness and annealing temperatures. With ultrathin Fe$_{80}$B$_{20}$ (0.2 - 0.4 nm) inserted, perpendicular magnetic anisotropy (PMA) of FLs increases with similar tunnel magneto-resistance (TMR) and low damping values. As Fe$_{80}$B$_{20}$ layer thickness further increases (0.6 - 1.2 nm), both TMR and PMA degrade, and damping increases dramatically. This study demonstrates a novel approach to tune properties of MTJ stacks with dual-MgO FLs up to 400 $^\circ$C annealing, which enables MTJ stacks for various applications.
2104.10918v1
2021-09-24
Damping in yttrium iron garnet film with an interface
We report strong damping enhancement in a 200 nm thick yttrium iron garnet (YIG) film due to spin inhomogeneity at the interface. The growth-induced thin interfacial gadolinium iron garnet (GdIG) layer antiferromagnetically (AFM) exchange couples with the rest of the YIG layer. The out-of-plane angular variation of ferromagnetic resonance (FMR) linewidth $\Delta H$ reflects a large inhomogeneous distribution of effective magnetization $\Delta 4 \pi M_{eff}$ due to the presence of an exchange springlike moments arrangement in YIG. We probe the spin inhomogeneity at the YIG-GdIG interface by performing an in-plane angular variation of resonance field $H_{r}$, leading to a unidirectional feature. The large extrinsic $\Delta 4\pi M_{eff}$ contribution, apart from the inherent intrinsic Gilbert contribution, manifests enhanced precessional damping in YIG film.
2109.12071v1