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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 |
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