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2023-09-18
Coherent Tunneling and Strain Sensitivity of an All Heusler Alloy Magnetic Tunneling Junction: A First-Principles Study
Half-metallic Co-based full Heusler alloys have captured considerable attention of the researchers in the realm of spintronic applications, owing to their remarkable characteristics such as exceptionally high spin polarization at Fermi level, ultra-low Gilbert damping, and high Curie temperature. In this comprehensive study, employing density functional theory, we delve into the stability and electron transport properties of a magnetic tunneling junction (MTJ) comprising a Co$_2$MnSb/HfIrSb interface. Utilizing a standard model given by Julliere, we estimate the tunnel magnetoresistance (TMR) ratio of this heterojunction under external electric field, revealing a significantly high TMR ratio (500%) that remains almost unaltered for electric field magnitudes up to 0.5 V/A. In-depth investigation of K-dependent majority spin transmissions uncovers the occurrence of coherent tunneling for the Mn-Mn/Ir interface, particularly when a spacer layer beyond a certain thickness is employed. Additionally, we explore the impact of bi-axial strain on the MTJ by varying the in-plane lattice constants between -4% and +4%. Our spin-dependent transmission calculations demonstrate that the Mn-Mn/Ir interface manifests strain-sensitive transmission properties under both compressive and tensile strain, and yields a remarkable three-fold increase in majority spin transmission under tensile strain conditions. These compelling outcomes place the Co2MnSb/HfIrSb junction among the highly promising candidates for nanoscale spintronic devices, emphasizing the potential significance of the system in the advancement of the field.
2309.09755v1
2023-11-14
Berry curvature induced giant intrinsic spin-orbit torque in single layer magnetic Weyl semimetal thin films
Topological quantum materials can exhibit unconventional surface states and anomalous transport properties, but their applications to spintronic devices are restricted as they require the growth of high-quality thin films with bulk-like properties. Here, we study 10--30 nm thick epitaxial ferromagnetic Co$_{\rm 2}$MnGa films with high structural order. Very high values of the anomalous Hall conductivity, $\sigma_{\rm xy}=1.35\times10^{5}$ $\Omega^{-1} m^{-1}$, and the anomalous Hall angle, $\theta_{\rm H}=15.8\%$, both comparable to bulk values. We observe a dramatic crystalline orientation dependence of the Gilbert damping constant of a factor of two and a giant intrinsic spin Hall conductivity, $\mathit{\sigma_{\rm SHC}}=(6.08\pm 0.02)\times 10^{5}$ ($\hbar/2e$) $\Omega^{-1} m^{-1}$, which is an order of magnitude higher than literature values of single-layer Ni$_{\rm 80}$Fe$_{\rm 20}$, Ni, Co, Fe, and multilayer Co$_{\rm 2}$MnGa stacks. Theoretical calculations of the intrinsic spin Hall conductivity, originating from a strong Berry curvature, corroborate the results and yield values comparable to the experiment. Our results open up for the design of spintronic devices based on single layers of topological quantum materials.
2311.08145v2
2023-12-26
All solution grown epitaxial magnonic crystal of thulium iron garnet thin film
Magnonics has shown the immense potential of compatibility with CMOS devices and the ability to be utilized in futuristic quantum computing. Therefore, the magnonic crystals, both metallic and insulating, are under extensive exploration. The presence of high spin-orbit interaction induced by the presence of rare-earth elements in thulium iron garnet (TmIG) increases its potential in magnonic applications. Previously, TmIG thin films were grown using ultra-high vacuum-based techniques. Here, we present a cost-effective solution-based approach that enables the excellent quality interface and surface roughness of the epitaxial TmIG/GGG. The deposited TmIG (12.2 nm) thin film's physical and spin dynamic properties are investigated in detail. The confirmation of the epitaxy using X-ray diffraction in $\phi$-scan geometry along with the X-ray reflectivity and atomic force for the thickness and roughness analysis and topography, respectively. The epitaxial TmIG/GGG have confirmed the perpendicular magnetic anisotropy utilizing the polar-magneto-optic Kerr effect. Analyzing the ferromagnetic resonance study of TmIG/GGG thin films provides the anisotropy constant K$_U$ = 20.6$\times$10$^3$ $\pm$ 0.2$\times$10$^3$ N/m$^2$ and the Gilbert damping parameter $\alpha$ = 0.0216 $\pm$ 0.0028. The experimental findings suggest that the solution-processed TmIG/GGG thin films have the potential to be utilized in device applications.
2312.15973v1
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
2010-03-24
Dynamical shift condition for unequal mass black hole binaries
Certain numerical frameworks used for the evolution of binary black holes make use of a gamma driver, which includes a damping factor. Such simulations typically use a constant value for damping. However, it has been found that very specific values of the damping factor are needed for the calculation of unequal mass binaries. We examine carefully the role this damping plays, and provide two explicit, non-constant forms for the damping to be used with mass-ratios further from one. Our analysis of the resultant waveforms compares well against the constant damping case.
1003.4681v1
2023-09-19
Impact of strain on the SOT-driven dynamics of thin film Mn$_3$Sn
Mn$_3$Sn, a metallic antiferromagnet with an anti-chiral 120$^\circ$ spin structure, generates intriguing magneto-transport signatures such as a large anomalous Hall effect, spin-polarized current with novel symmetries, anomalous Nernst effect, and magneto-optic Kerr effect. When grown epitaxially as MgO(110)[001]$\parallel$ Mn$_3$Sn($0\bar{1}\bar{1}0$)[0001], Mn$_3$Sn experiences a uniaxial tensile strain, which changes the bulk six-fold anisotropy landscape to a perpendicular magnetic anisotropy with two stable states. In this work, we investigate the field-assisted spin orbit-torque (SOT)-driven response of the order parameter in single-domain Mn$_3$Sn with uniaxial tensile strain. We find that for a non-zero external magnetic field, the order parameter can be switched between the two stable states if the magnitude of the input current is between two field-dependent critical currents. Below the lower critical current, the order parameter exhibits a stationary state in the vicinity of the initial stable state. On the other hand, above the higher critical current, the order parameter shows oscillatory dynamics which could be tuned from the 100's of megahertz to the gigahertz range. We obtain approximate expressions of the two critical currents and find them to agree very well with the numerical simulations for experimentally relevant magnetic fields. We also obtain unified functional form of the switching time versus the input current for different magnetic fields. Finally, we show that for lower values of Gilbert damping ($\alpha \leq 2\times 10^{-3}$), the critical currents and the final steady states depend significantly on the damping constant. The numerical and analytic results presented in our work can be used by both theorists and experimentalists to understand the SOT-driven order dynamics in PMA Mn$_3$Sn and design future experiments and devices.
2309.10246v2
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
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
2013-05-21
Characterization and Synthesis of Rayleigh Damped Elastodynamic Networks
We consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (also known as Rayleigh or proportional damping). We give here a characterization of the frequency response of such networks. We also answer the synthesis question for such networks, i.e., how to construct a Rayleigh damped elastodynamic network with a given frequency response. Our analysis shows that not all damped elastodynamic networks can be realized when the proportionality constants between the damping matrix and the mass and stiffness matrices are fixed.
1305.4961v1
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
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
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
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
2014-12-11
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
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
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
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
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
2019-03-07
Current-induced motion of twisted skyrmions
Twisted skyrmions, whose helicity angles are different from that of Bloch skyrmions and N\'eel skyrmions, have already been demonstrated in experiments recently. In this work, we first contrast the magnetic structure and origin of the twisted skyrmion with other three types of skyrmion including Bloch skyrmion, N\'eel skyrmion and antiskyrmion. Following, we investigate the dynamics of twisted skyrmions driven by the spin transfer toque (STT) and the spin Hall effect (SHE) by using micromagnetic simulations. It is found that the spin Hall angle of the twisted skyrmion is related to the dissipative force tensor and the Gilbert damping both for the motions induced by the STT and the SHE, especially for the SHE induced motion, the skyrmion Hall angle depends substantially on the skyrmion helicity. At last, we demonstrate that the trajectory of the twisted skyrmion can be controlled in a two dimensional plane with a Gilbert damping gradient. Our results provide the understanding of current-induced motion of twisted skyrmions, which may contribute to the applications of skyrmion-based racetrack memories.
1903.02812v1
2019-07-03
Anisotropy of spin-transfer torques and Gilbert damping induced by Rashba coupling
Spin-transfer torques (STT), Gilbert damping (GD), and effective spin renormalization (ESR) are investigated microscopically in a 2D Rashba ferromagnet with spin-independent Gaussian white-noise disorder. Rashba spin-orbit coupling induced anisotropy of these phenomena is thoroughly analysed. For the case of two partly filled spin subbands, a remarkable relation between the anisotropic STT, GD, and ESR is established. In the absence of magnetic field and other torques on magnetization, this relation corresponds to a current-induced motion of a magnetic texture with the classical drift velocity of conduction electrons. Finally, we compute spin susceptibility of the system and generalize the notion of spin-polarized current.
1907.02041v3
2021-11-05
Giant oscillatory Gilbert damping in superconductor/ferromagnet/superconductor junctions
Interfaces between materials with differently ordered phases present unique opportunities for exotic physical properties, especially the interplay between ferromagnetism and superconductivity in the ferromagnet/superconductor heterostructures. The investigation of zero- and pi-junctions has been of particular interest for both fundamental physical science and emerging technologies. Here, we report the experimental observation of giant oscillatory Gilbert damping in the superconducting Nb/NiFe/Nb junctions with respect to the NiFe thickness. This observation suggests an unconventional spin pumping and relaxation via zero-energy Andreev bound states that exist only in the Nb/NiFe/Nb pi-junctions, but not in the Nb/NiFe/Nb zero-junctions. Our findings could be important for further exploring the exotic physical properties of ferromagnet/superconductor heterostructures, and potential applications of ferromagnet pi-junctions in quantum computing, such as half-quantum flux qubits.
2111.03233v1
2022-11-14
Magnetization Dynamics in Synthetic Antiferromagnets with Perpendicular Magnetic Anisotropy
Understanding the rich physics of magnetization dynamics in perpendicular synthetic antiferromagnets (p-SAFs) is crucial for developing next-generation spintronic devices. In this work, we systematically investigate the magnetization dynamics in p-SAFs combining time-resolved magneto-optical Kerr effect (TR-MOKE) measurements with theoretical modeling. These model analyses, based on a Landau-Lifshitz-Gilbert approach incorporating exchange coupling, provide details about the magnetization dynamic characteristics including the amplitudes, directions, and phases of the precession of p-SAFs under varying magnetic fields. These model-predicted characteristics are in excellent quantitative agreement with TR-MOKE measurements on an asymmetric p-SAF. We further reveal the damping mechanisms of two procession modes co-existing in the p-SAF and successfully identify individual contributions from different sources, including Gilbert damping of each ferromagnetic layer, spin pumping, and inhomogeneous broadening. Such a comprehensive understanding of magnetization dynamics in p-SAFs, obtained by integrating high-fidelity TR-MOKE measurements and theoretical modeling, can guide the design of p-SAF-based architectures for spintronic applications.
2211.07744v2
2023-05-23
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
2014-03-16
Interpolating local constants in families
We extend the theory of local constants to l-adic families of representations of GL_n(F) where F is a p-adic field with l not equal to p. We construct zeta integrals and gamma factors for representations coming from the conjectural "local Langlands correspondence in families" of Emerton-Helm, proving a rationality result and functional equation. We also construct a universal gamma factor with coefficients in the integral Bernstein center.
1403.3914v2
2016-06-01
Existence of arbitrarily smooth solutions of the LLG equation in 3D with natural boundary conditions
We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions with homogeneous Neumann boundary conditions admits arbitrarily smooth solutions, given that the initial data is sufficiently close to a constant function.
1606.00086v1
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
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
2017-05-09
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
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
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
2009-05-20
Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation
We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the damping term in a unique fashion. We also derive a trace formula for this problem.
0905.3242v1
2002-06-27
Initial-amplitude dependence in weakly damped oscillators
A pedagogically instructive experimental procedure is suggested for distinguishing between different damping terms in a weakly damped oscillator, which highclights the connection between non-linear damping and initial-amplitude dependence. The most common damping terms such as contact friction, air resistance, viscous drag, and electromagnetic damping have velocity dependences of the form constant, v, or v^2. The corresponding energy dependences of the form \sqrt{E}, E, or E\sqrt{E} in the energy loss equation give rise to characteristic dependence of the amplitude decay slope on the initial amplitude.
0206086v1
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$0.001, among the lowest ever reported for ferromagnetic metals.
2004.04840v3
2016-05-22
Low Gilbert damping in Co2FeSi and Fe2CoSi films
Thin highly textured Fe$_{\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
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
2007-03-12
Quantum estimation of a damping constant
We discuss an interferometric approach to the estimation of quantum mechanical damping. We study specific classes of entangled and separable probe states consisting of superpositions of coherent states. Based on the assumption of limited quantum resources we show that entanglement improves the estimation of an unknown damping constant.
0703091v2
2006-01-19
Drift of particles in self-similar systems and its Liouvillian interpretation
We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three systems the particles typically drift at constant velocity and spread ballistically. These transport properties are analyzed in terms of the spectral properties of the operator evolving the probability densities. For systems (i) and (ii), we explain the drift from the properties of the Pollicott-Ruelle resonance spectrum and corresponding eigenvectors
0601042v1
2010-04-30
Limit theory for planar Gilbert tessellations
A Gilbert tessellation arises by letting linear segments (cracks) in the plane unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an already existing one, it stops growing in this direction. The resulting process tessellates the plane. The purpose of the present paper is to establish law of large numbers, variance asymptotics and a central limit theorem for geometric functionals of such tessellations. The main tool applied is the stabilization theory for geometric functionals.
1005.0023v1
2017-06-15
Absence of correlations in the energy exchanges of an exactly solvable model of heat transport with many degrees of freedom
A process based on the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] is described whereby lattice cells share their energies among many identical degrees of freedom while, in each cell, only two of them are associated with energy exchanges connecting neighbouring cells. It is shown that, up to dimensional constants, the heat conductivity is half the interaction rate, regardless of the degrees of freedom. Moreover, as this number becomes large, correlations between the energy variables involved in the exchanges vanish. In this regime, the process thus boils down to the time-evolution of the local temperatures which is prescribed by the discrete heat equation.
1706.04849v1
2015-05-29
Microscopic Theory for Coupled Atomistic Magnetization and Lattice Dynamics
A coupled atomistic spin and lattice dynamics approach is developed which merges the dynamics of these two degrees of freedom into a single set of coupled equations of motion. The underlying microscopic model comprises local exchange interactions between the electron spin and magnetic moment and the local couplings between the electronic charge and lattice displacements. An effective action for the spin and lattice variables is constructed in which the interactions among the spin and lattice components are determined by the underlying electronic structure. In this way, expressions are obtained for the electronically mediated couplings between the spin and lattice degrees of freedom, besides the well known inter-atomic force constants and spin-spin interactions. These former susceptibilities provide an atomistic ab initio description for the coupled spin and lattice dynamics. It is important to notice that this theory is strictly bilinear in the spin and lattice variables and provides a minimal model for the coupled dynamics of these subsystems and that the two subsystems are treated on the same footing. Questions concerning time-reversal and inversion symmetry are rigorously addressed and it is shown how these aspects are absorbed in the tensor structure of the interaction fields. By means of these results regarding the spin-lattice coupling, simple explanations of ionic dimerization in double anti-ferromagnetic materials, as well as, charge density waves induced by a non-uniform spin structure are given. In the final parts, a set of coupled equations of motion for the combined spin and lattice dynamics are constructed, which subsequently can be reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations for spin dynamics and damped driven mechanical oscillator for the ...
1505.08005v3
2022-11-03
Skyrmion Jellyfish in Driven Chiral Magnets
Chiral magnets can host topological particles known as skyrmions, which carry an exactly quantised topological charge $Q=-1$. In the presence of an oscillating magnetic field ${\bf B}_1(t)$, a single skyrmion embedded in a ferromagnetic background will start to move with constant velocity ${\bf v}_{\text{trans}}$. The mechanism behind this motion is similar to the one used by a jellyfish when it swims through water. We show that the skyrmion's motion is a universal phenomenon, arising in any magnetic system with translational modes. By projecting the equation of motion onto the skyrmion's translational modes and going to quadratic order in ${\bf B}_1(t)$, we obtain an analytical expression for ${\bf v}_{\text{trans}}$ as a function of the system's linear response. The linear response and consequently ${\bf v}_{\text{trans}}$ are influenced by the skyrmion's internal modes and scattering states, as well as by the ferromagnetic background's Kittel mode. The direction and speed of ${\bf v}_{\text{trans}}$ can be controlled by changing the polarisation, frequency and phase of the driving field ${\bf B}_1(t)$. For systems with small Gilbert damping parameter $\alpha$, we identify two distinct physical mechanisms used by the skyrmion to move. At low driving frequencies, the skyrmion's motion is driven by friction, and $v_{\text{trans}}\sim\alpha$, whereas at higher frequencies above the ferromagnetic gap, the skyrmion moves by magnon emission, and $v_{\text{trans}}$ becomes independent of $\alpha$.
2211.01714v5
2023-04-05
Threshold current of field-free perpendicular magnetization switching using anomalous spin-orbit torque
Spin-orbit torque (SOT) is a candidate technique in next generation magnetic random-access memory (MRAM). Recently, experiments show that some material with low-symmetric crystalline or magnetic structures can generate anomalous SOT that has an out-of-plane component, which is crucial in switching perpendicular magnetization of adjacent ferromagnetic (FM) layer in the field-free condition. In this work, we analytically derive the threshold current of field-free perpendicular magnetization switching using the anomalous SOT. And we numerically calculate the track of the magnetic moment in a FM free layer when an applied current is smaller and greater than the threshold current. After that, we study the applied current dependence of the switching time and the switching energy consumption, which shows the minimum energy consumption decreases as out-of-plane torque proportion increases. Then we study the dependences of the threshold current on anisotropy strength, out-of-plane torque proportion, FM free layer thickness and Gilbert damping constant, and the threshold current shows negative correlation with the out-of-plane torque proportion and positive correlation with the other three parameters. Finally, we demonstrate that when the applied current is smaller than the threshold current, although it cannot switch the magnetization of FM free layer, it can still equivalently add an effective exchange bias field H_{bias} on the FM free layer. The H_{bias} is proportional to the applied current J_{SOT}, which facilitates the determination of the anomalous SOT efficiency. This work helps us to design new spintronic devices that favor field-free switching perpendicular magnetization using the anomalous SOT, and provides a way to adjust the exchange bias field, which is helpful in controlling FM layer magnetization depinning.
2304.02248v2
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
2020-11-11
Reduction of back switching by large damping ferromagnetic material
Recent studies on magnetization dynamics induced by spin-orbit torque have revealed a weak dependence of the critical current for magnetization switching on the damping constant of a ferromagnetic free layer. This study, however, reveals that the damping constant nevertheless plays a key role in magnetization switching induced by spin-orbit torque. An undesirable switching, returning to an initial state, named as back switching, occurs in a ferromagnet with an easy axis parallel to the current direction. Numerical and theoretical analyses reveal that back switching is strongly suppressed when the damping constant of the ferromagnet is large.
2011.05566v1
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
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
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
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
2021-09-24
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
2003-09-11
Theory of Current-Induced Magnetization Precession
We solve appropriate drift-diffusion and Landau-Lifshitz-Gilbert equations to demonstrate that unpolarized current flow from a non-magnet into a ferromagnet can produce a precession-type instability of the magnetization. The fundamental origin of the instability is the difference in conductivity between majority spins and minority spins in the ferromagnet. This leads to spin accumulation and spin currents that carry angular momentum across the interface. The component of this angular momentum perpendicular to the magnetization drives precessional motion that is opposed by Gilbert damping. Neglecting magnetic anisotropy and magnetostatics, our approximate analytic and exact numerical solutions using realistic values for the material parameters show (for both semi-infinite and thin film geometries) that a linear instability occurs when both the current density and the excitation wave vector parallel to the interface are neither too small nor too large. For many aspects of the problem, the variation of the magnetization in the direction of the current flows makes an important contribution.
0309289v1
2009-05-28
Hydrodynamic theory of coupled current and magnetization dynamics in spin-textured ferromagnets
We develop the hydrodynamical theory of collinear spin currents coupled to magnetization dynamics in metallic ferromagnets. The collective spin density couples to the spin current through a U(1) Berry-phase gauge field determined by the local texture and dynamics of the magnetization. We determine phenomenologically the dissipative corrections to the equation of motion for the electronic current, which consist of a dissipative spin-motive force generated by magnetization dynamics and a magnetic texture-dependent resistivity tensor. The reciprocal dissipative, adiabatic spin torque on the magnetic texture follows from the Onsager principle. We investigate the effects of thermal fluctuations and find that electronic dynamics contribute to a nonlocal Gilbert damping tensor in the Landau-Lifshitz-Gilbert equation for the magnetization. Several simple examples, including magnetic vortices, helices, and spirals, are analyzed in detail to demonstrate general principles.
0905.4544v2
2010-11-26
Dependence of nonlocal Gilbert damping on the ferromagnetic layer type in FM/Cu/Pt heterostructures
We have measured the size effect in nonlocal Gilbert relaxation rate in FM(t$_{FM}$) / Cu (5nm) [/ Pt (2nm)] / Al(2nm) heterostructures, FM = \{ Ni$_{81}$Fe$_{19}$, Co$_{60}$Fe$_{20}$B$_{20}$, pure Co\}. Common behavior is observed for three FM layers, where the additional relaxation obeys both a strict inverse power law dependence $\Delta G =K \:t^{n}$, $n=-\textrm{1.04}\pm\textrm{0.06}$ and a similar magnitude $K=\textrm{224}\pm\textrm{40 Mhz}\cdot\textrm{nm}$. As the tested FM layers span an order of magnitude in spin diffusion length $\lambda_{SDL}$, the results are in support of spin diffusion, rather than nonlocal resistivity, as the origin of the effect.
1011.5868v1
2012-06-21
Fast domain wall propagation in uniaxial nanowires with transverse fields
Under a magnetic field along its axis, domain wall motion in a uniaxial nanowire is much slower than in the fully anisotropic case, typically by several orders of magnitude (the square of the dimensionless Gilbert damping parameter). However, with the addition of a magnetic field transverse to the wire, this behaviour is dramatically reversed; up to a critical field strength, analogous to the Walker breakdown field, domain walls in a uniaxial wire propagate faster than in a fully anisotropic wire (without transverse field). Beyond this critical field strength, precessional motion sets in, and the mean velocity decreases. Our results are based on leading-order analytic calculations of the velocity and critical field as well as numerical solutions of the Landau-Lifshitz-Gilbert equation.
1206.4819v2
2013-03-05
Angle-Dependent Spin-Wave Resonance Spectroscopy of (Ga,Mn)As Films
A modeling approach for standing spin-wave resonances based on a finite-difference formulation of the Landau-Lifshitz-Gilbert equation is presented. In contrast to a previous study [Bihler et al., Phys. Rev. B 79, 045205 (2009)], this formalism accounts for elliptical magnetization precession and magnetic properties arbitrarily varying across the layer thickness, including the magnetic anisotropy parameters, the exchange stiffness, the Gilbert damping, and the saturation magnetization. To demonstrate the usefulness of our modeling approach, we experimentally study a set of (Ga,Mn)As samples grown by low-temperature molecular-beam epitaxy by means of electrochemical capacitance-voltage measurements and angle-dependent standing spin-wave resonance spectroscopy. By applying our modeling approach, the angle dependence of the spin-wave resonance data can be reproduced in a simulation with one set of simulation parameters for all external field orientations. We find that the approximately linear gradient in the out-of-plane magnetic anisotropy is related to a linear gradient in the hole concentrations of the samples.
1303.1192v1
2013-04-26
Landau-Lifshitz theory of the longitudinal spin Seebeck effect
Thermal-bias-induced spin angular momentum transfer between a paramagnetic metal and ferromagnetic insulator is studied theoretically based on the stochastic Landau-Lifshitz-Gilbert (LLG) phenomenology. Magnons in the ferromagnet establish a nonequilibrium steady state by equilibrating with phonons via bulk Gilbert damping and electrons in the paramagnet via spin pumping, according to the fluctuation-dissipation theorem. Subthermal magnons and the associated spin currents are treated classically, while the appropriate quantum crossover is imposed on high-frequency magnetic fluctuations. We identify several length scales in the ferromagnet, which govern qualitative changes in the dependence of the thermally-induced spin current on the magnetic film thickness.
1304.7295v2
2014-02-27
On the longitudinal spin current induced by a temperature gradient in a ferromagnetic insulator
Based on the solution of the stochastic Landau-Lifshitz-Gilbert equation discretized for a ferromagnetic chain subject to a uniform temperature gradient, we present a detailed numerical study of the spin dynamics with a focus particularly on finite-size effects. We calculate and analyze the net longitudinal spin current for various temperature gradients, chain lengths, and external static magnetic fields. In addition, we model an interface formed by a nonuniformly magnetized finite-size ferromagnetic insulator and a normal metal and inspect the effects of enhanced Gilbert damping on the formation of the space-dependent spin current within the chain. A particular aim of this study is the inspection of the spin Seebeck effect beyond the linear response regime. We find that within our model the microscopic mechanism of the spin Seebeck current is the magnon accumulation effect quantified in terms of the exchange spin torque. According to our results, this effect drives the spin Seebeck current even in the absence of a deviation between the magnon and phonon temperature profiles. Our theoretical findings are in line with the recently observed experimental results by M. Agrawal et al., Phys. Rev. Lett. 111, 107204 (2013).
1402.6899v1
2015-01-19
Effect of Exchange Interaction on Magnetic Thermal Fluctuation and Spin Susceptibility
The expression of the thermal fluctuation parameter in the stochastic Landau-Lifshitz-Gilbert equation has been derived from a fundamental quantum theory of spins and phonons, in which the exchange interaction between nearest atoms has been included. Our studies show that the thermal fluctuation decreases exponentially with increasing exchange interaction. The non-uniform fluctuation of local spins make the spin susceptibility much different from the result derived by the macro-spin model or single spin model. The related spin susceptibility depends not only on the strength of exchange interaction, but also on the lattice structure. The non-uniform fluctuation can lead to an extra broadening of the resonance line width along with the broadening arisen from the Gilbert damping.
1501.04503v2
2015-07-23
Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor
The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-B"uttiker theory. Scattering theory provides a microscopic derivation of the Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.
1507.06505v2
2018-02-28
Roles of chiral renormalization on magnetization dynamics in chiral magnets
In metallic ferromagnets, the interaction between local magnetic moments and conduction electrons renormalizes parameters of the Landau-Lifshitz-Gilbert equation such as the gyromagnetic ratio and the Gilbert damping, and makes them dependent on the magnetic configurations. Although the effects of the renormalization for nonchiral ferromagnets are usually minor and hardly detectable, we show that the renormalization does play a crucial role for chiral magnets. Here the renormalization is chiral and as such we predict experimentally identifiable effects on the phenomenology of magnetization dynamics. In particular, our theory for the self-consistent magnetization dynamics of chiral magnets allows for a concise interpretation of domain wall creep motion. We also argue that the conventional creep theory of the domain wall motion, which assumes Markovian dynamics, needs critical reexamination since the gyromagnetic ratio makes the motion non-Markovian. The non-Markovian nature of the domain wall dynamics is experimentally checkable by the chirality of the renormalization.
1803.00017v2
2018-12-20
Laser Controlled Spin Dynamics of Ferromagnetic Thin Film from Femtosecond to Nanosecond Timescale
Laser induced modulation of the magnetization dynamics occurring over various time-scales have been unified here for a Ni80Fe20 thin film excited by amplified femtosecond laser pulses. The weak correlation between demagnetization time and pump fluence with substantial enhancement in remagnetization time is demonstrated using three-temperature model considering the temperatures of electron, spin and lattice. The picosecond magnetization dynamics is modeled using the Landau-Lifshitz-Gilbert equation. With increasing pump fluence the Gilbert damping parameter shows significant enhancement from its intrinsic value due to increment in the ratio of electronic temperature to Curie temperature within very short time scale. The precessional frequency experiences noticeable red shift with increasing pump fluence. The changes in the local magnetic properties due to accumulation and dissipation of thermal energy within the probed volume are described by the evolution of temporal chirp parameter in a comprehensive manner. A unification of ultrafast magnetic processes and its control over broad timescale would enable the integration of various magnetic processes in a single device and use one effect to control another.
1812.08404v1
2008-11-25
The quantum-mechanical basis of an extended Landau-Lifshitz-Gilbert equation for a current-carrying ferromagnetic wire
An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for a simple model which includes impurity scattering. This is done by comparing the energies and lifetimes of a spin wave calculated from the LLG equation and from the explicit model. Two terms are of particular importance since they describe non-adiabatic spin-transfer torque and damping processes which do not rely on spin-orbit coupling. It is shown that these terms may have a significant influence on the velocity of a current-driven domain wall and they become dominant in the case of a narrow wall.
0811.4118v1
2019-03-13
Higher-order linearly implicit full discretization of the Landau--Lifshitz--Gilbert equation
For the Landau--Lifshitz--Gilbert (LLG) equation of micromagnetics we study linearly implicit backward difference formula (BDF) time discretizations up to order $5$ combined with higher-order non-conforming finite element space discretizations, which are based on the weak formulation due to Alouges but use approximate tangent spaces that are defined by $L^2$-averaged instead of nodal orthogonality constraints. We prove stability and optimal-order error bounds in the situation of a sufficiently regular solution. For the BDF methods of orders $3$ to~$5$, this requires %a mild time step restriction $\tau \leqslant ch$ and that the damping parameter in the LLG equations be above a positive threshold; this condition is not needed for the A-stable methods of orders $1$ and $2$, for which furthermore a discrete energy inequality irrespective of solution regularity is proved.
1903.05415v2
2019-12-01
Coarse-graining in micromagnetic simulations of dynamic hysteresis loops
Micromagnetic simulations based on the stochastic Landau-Lifshitz-Gilbert equation are used to calculate dynamic magnetic hysteresis loops relevant to magnetic hyperthermia. With the goal to effectively simulate room-temperature loops for large iron-oxide-based systems at relatively slow sweep rates on the order of 1 Oe/ns or less, a previously derived renormalization group approach for coarse-graining (Grinstein and Koch, Phys. Rev. Lett. 20, 207201, 2003) is modified and applied to calculating loops for a magnetite nanorod. The nanorod modelled is the building block for larger nanoparticles that were employed in preclinical studies (Dennis et al., Nanotechnology 20, 395103, 2009). The scaling algorithm is shown to produce nearly identical loops over several decades in the model grain size. Sweep-rate scaling involving the Gilbert damping parameter is also demonstrated to allow orders of magnitude speed-up of the loop calculations.
1912.00310v3
2020-02-17
Self-similar shrinkers of the one-dimensional Landau-Lifshitz-Gilbert equation
The main purpose of this paper is the analytical study of self-shrinker solutions of the one-dimensional Landau-Lifshitz-Gilbert equation (LLG), a model describing the dynamics for the spin in ferromagnetic materials. We show that there is a unique smooth family of backward self-similar solutions to the LLG equation, up to symmetries, and we establish their asymptotics. Moreover, we obtain that in the presence of damping, the trajectories of the self-similar profiles converge to great circles on the sphere $\mathbb{S}^2$, at an exponential rate. In particular, the results presented in this paper provide examples of blow-up in finite time, where the singularity develops due to rapid oscillations forming limit circles.
2002.06858v2