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2023-12-20
|
An effective field theory of damped ferromagnetic systems
|
Using the in-in formalism, we generalize the recently constructed
magnetoelastic EFT arXiv:2112.13873 [hep-th] to describe the damping dynamics
of ferromagnetic systems at long wavelengths. We find that the standard Gilbert
damping term naturally arises as the simplest leading-order symmetry-consistent
non-conservative contribution within the in-in framework. The EFT is easily
generalized to scenarios with anisotropy and inhomogeneity. In particular, we
find the classic Landau-Lifshitz damping term emerges when isotropy is broken
by a constant external background field. This provides a first principle
explanation for distinguishing the two types of damping dynamics that were
originally constructed phenomenologically. Furthermore, the EFT framework could
also incorporate intrinsic anisotropy of the material in a straightforward way
using the spurion method. For systems with inhomogeneity such as nontrivial
spin textures, we find that the leading order derivative correction yields the
generalized Gilbert damping equations that were found in condensed matter
literature. This shows that the EFT approach enables us to derive the form of
higher-derivative-order corrections in a systematic way. Lastly, using the
phonon-magnon coupling deduced in the magnetoelastic EFT, we are able to make a
prediction for the generic form of the phononic contribution to the damping
equation.
|
2312.13093v1
|
2015-10-07
|
Tunable damping, saturation magnetization, and exchange stiffness of half-Heusler NiMnSb thin films
|
The half-metallic half-Heusler alloy NiMnSb is a promising candidate for
applications in spintronic devices due to its low magnetic damping and its rich
anisotropies. Here we use ferromagnetic resonance (FMR) measurements and
calculations from first principles to investigate how the composition of the
epitaxially grown NiMnSb influences the magnetodynamic properties of saturation
magnetization $M_S$, Gilbert damping $\alpha$, and exchange stiffness $A$.
$M_S$ and $A$ are shown to have a maximum for stoichiometric composition, while
the Gilbert damping is minimum. We find excellent quantitative agreement
between theory and experiment for $M_S$ and $\alpha$. The calculated $A$ shows
the same trend as the experimental data, but has a larger magnitude.
Additionally to the unique in-plane anisotropy of the material, these
tunabilities of the magnetodynamic properties can be taken advantage of when
employing NiMnSb films in magnonic devices.
|
1510.01894v1
|
2017-08-07
|
Chiral damping, chiral gyromagnetism and current-induced torques in textured one-dimensional Rashba ferromagnets
|
We investigate Gilbert damping, spectroscopic gyromagnetic ratio and
current-induced torques in the one-dimensional Rashba model with an additional
noncollinear magnetic exchange field. We find that the Gilbert damping differs
between left-handed and right-handed N\'eel-type magnetic domain walls due to
the combination of spatial inversion asymmetry and spin-orbit interaction
(SOI), consistent with recent experimental observations of chiral damping.
Additionally, we find that also the spectroscopic $g$ factor differs between
left-handed and right-handed N\'eel-type domain walls, which we call chiral
gyromagnetism. We also investigate the gyromagnetic ratio in the Rashba model
with collinear magnetization, where we find that scattering corrections to the
$g$ factor vanish for zero SOI, become important for finite spin-orbit
coupling, and tend to stabilize the gyromagnetic ratio close to its
nonrelativistic value.
|
1708.02008v2
|
2017-09-14
|
Intrinsic Damping Phenomena from Quantum to Classical Magnets:An ab-initio Study of Gilbert Damping in Pt/Co Bilayer
|
A fully quantum mechanical description of the precessional damping of Pt/Co
bilayer is presented in the framework of the Keldysh Green function approach
using {\it ab initio} electronic structure calculations. In contrast to
previous calculations of classical Gilbert damping ($\alpha_{GD}$), we
demonstrate that $\alpha_{GD}$ in the quantum case does not diverge in the
ballistic regime due to the finite size of the total spin, $S$. In the limit of
$S\rightarrow\infty$ we show that the formalism recovers the torque correlation
expression for $\alpha_{GD}$ which we decompose into spin-pumping and
spin-orbital torque correlation contributions. The formalism is generalized to
take into account a self consistently determined dephasing mechanism which
preserves the conservation laws and allows the investigation of the effect of
disorder. The dependence of $\alpha_{GD}$ on Pt thickness and disorder strength
is calculated and the spin diffusion length of Pt and spin mixing conductance
of the bilayer are determined and compared with experiments.
|
1709.04911v2
|
2018-04-02
|
Anisotropic Gilbert damping in perovskite La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ thin film
|
The viscous Gilbert damping parameter governing magnetization dynamics is of
primary importance for various spintronics applications. Although, the damping
constant is believed to be anisotropic by theories. It is commonly treated as a
scalar due to lack of experimental evidence. Here, we present an elaborate
angle dependent broadband ferromagnetic resonance study of high quality
epitaxial La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ films. Extrinsic effects are suppressed
and we show convincing evidence of anisotropic damping with twofold symmetry at
room temperature. The observed anisotropic relaxation is attributed to the
magnetization orientation dependence of the band structure. In addition, we
demonstrated that such anisotropy can be tailored by manipulating the stain.
This work provides new insights to understand the mechanism of magnetization
relaxation.
|
1804.00554v1
|
2006-02-03
|
Microscopic description of Landau-Lifshitz-Gilbert type equation based on the s-d model
|
A Landau-Lifshitz-Gilbert type equation has been derived by using s-d model
in which the s-electron system is regarded as an environment coupled weakly
with the localized spins. Based on the irreducible linear response theory, we
show that the relaxation function of the s-electron spin leads to the Gilbert
type damping term which corresponds to the retarded resistance function in the
generalized Langevin equation. The Ohmic form of the Gilbert term stems from
the fact that the imaginary part of the response function (spin susceptibility)
of the itinerant electron system is proportional to the frequency (omega) in
the low omega region. It is confirmed that the Caldeira-Leggett theory based on
the path-integral approach gives the same result.
|
0602075v2
|
2014-09-08
|
Self-similar solutions of the one-dimensional Landau-Lifshitz-Gilbert equation
|
We consider the one-dimensional Landau-Lifshitz-Gilbert (LLG) equation, a
model describing the dynamics for the spin in ferromagnetic materials. Our main
aim is the analytical study of the bi-parametric family of self-similar
solutions of this model. In the presence of damping, our construction provides
a family of global solutions of the LLG equation which are associated to a
discontinuous initial data of infinite (total) energy, and which are smooth and
have finite energy for all positive times. Special emphasis will be given to
the behaviour of this family of solutions with respect to the Gilbert damping
parameter.
We would like to emphasize that our analysis also includes the study of
self-similar solutions of the Schr\"odinger map and the heat flow for harmonic
maps into the 2-sphere as special cases. In particular, the results presented
here recover some of the previously known results in the setting of the
1d-Schr\"odinger map equation.
|
1409.2340v1
|
2017-09-12
|
Green's function formalism for spin transport in metal-insulator-metal heterostructures
|
We develop a Green's function formalism for spin transport through
heterostructures that contain metallic leads and insulating ferromagnets. While
this formalism in principle allows for the inclusion of various magnonic
interactions, we focus on Gilbert damping. As an application, we consider
ballistic spin transport by exchange magnons in a metal-insulator-metal
heterostructure with and without disorder. For the former case, we show that
the interplay between disorder and Gilbert damping leads to spin current
fluctuations. For the case without disorder, we obtain the dependence of the
transmitted spin current on the thickness of the ferromagnet. Moreover, we show
that the results of the Green's function formalism agree in the clean and
continuum limit with those obtained from the linearized stochastic
Landau-Lifshitz-Gilbert equation. The developed Green's function formalism is a
natural starting point for numerical studies of magnon transport in
heterostructures that contain normal metals and magnetic insulators.
|
1709.03775v1
|
2019-09-06
|
The interplay of large two-magnon ferromagnetic resonance linewidths and low Gilbert damping in Heusler thin films
|
We report on broadband ferromagnetic resonance linewidth measurements
performed on epitaxial Heusler thin films. A large and anisotropic two-magnon
scattering linewidth broadening is observed for measurements with the
magnetization lying in the film plane, while linewidth measurements with the
magnetization saturated perpendicular to the sample plane reveal low Gilbert
damping constants of $(1.5\pm0.1)\times 10^{-3}$, $(1.8\pm0.2)\times 10^{-3}$,
and $<8\times 10^{-4}$ for Co$_2$MnSi/MgO, Co$_2$MnAl/MgO, and Co$_2$FeAl/MgO,
respectively. The in-plane measurements are fit to a model combining Gilbert
and two-magnon scattering contributions to the linewidth, revealing a
characteristic disorder lengthscale of 10-100 nm.
|
1909.02738v2
|
2010-02-17
|
Measurement of Gilbert damping parameters in nanoscale CPP-GMR spin-valves
|
In-situ, device level measurement of thermal mag-noise spectral linewidths in
60nm diameter CPP-GMR spin-valve stacks of IrMn/ref/Cu/free, with reference and
free layer of similar CoFe/CoFeGe alloy, are used to simultaneously determine
the intrinsic Gilbert damping for both magnetic layers. It is shown that
careful alignment at a "magic-angle" between free and reference layer static
equilibrium magnetization can allow direct measurement of the broadband
intrinsic thermal spectra in the virtual absence of spin-torque effects which
otherwise grossly distort the spectral line shapes and require linewidth
extrapolations to zero current (which are nonetheless also shown to agree well
with the direct method). The experimental magic-angle spectra are shown to be
in good qualitative and quantitative agreement with both macrospin calculations
and micromagnetic eigenmode analysis. Despite similar composition and
thickness, it is repeatedly found that the IrMn exchange pinned reference layer
has ten times larger intrinsic Gilbert damping (alpha ~ 0.1) than that of the
free-layer (alpha ~ 0.01). It is argued that the large reference layer damping
results from strong, off -resonant coupling to to lossy modes of an IrMn/ref
couple, rather than commonly invoked two-magnon processes.
|
1002.3295v1
|
2018-09-28
|
Isotropic non-local Gilbert damping driven by spin currents in epitaxial Pd/Fe/MgO(001) films
|
Although both theoretical predications and experimental observations
demonstrated that the damping factor is anisotropic at
ferromagnet/semiconductor interface with robust interfacial spin-orbit
coupling, it is not well understood whether non-local Gilbert damping driven by
spin currents in heavy metal/ferromagnetic metal (HM/FM) bilayers is
anisotropic or not. Here, we investigated the in-plane angular- and frequency-
dependence of magnetic relaxation of epitaxial Fe/MgO(001) films with different
capping layers of Pd and Cu. After disentangling the parasitic contributions,
such as two-magnon scattering (TMS), mosaicity, and field-dragging effect, we
unambiguously observed that both local and non-local Gilbert damping are
isotropic in Fe(001) plane, suggesting that the pure spin currents absorption
is independent of Fe magnetization orientation in the epitaxial Pd/Fe
heterostructure. First principles calculation reveals that the effective spin
mixing conductance of Pd/Fe interface is nearly invariant for different
magnetization directions in good agreement with the experimental observations.
These results offer a valuable insight into the transmission and absorption of
pure spin currents, and facilitate us to utilize next-generation spintronic
devices.
|
1809.11020v1
|
2004-09-24
|
Minimal field requirement in precessional magnetization switching
|
We investigate the minimal field strength in precessional magnetization
switching using the Landau-Lifshitz-Gilbert equation in under-critically damped
systems. It is shown that precessional switching occurs when localized
trajectories in phase space become unlocalized upon application of field
pulses. By studying the evolution of the phase space, we obtain the analytical
expression of the critical switching field in the limit of small damping for a
magnetic object with biaxial anisotropy. We also calculate the switching times
for the zero damping situation. We show that applying field along the medium
axis is good for both small field and fast switching times.
|
0409671v1
|
2011-11-04
|
Tunable magnetization relaxation in spin valves
|
In spin values the damping parameters of the free layer are determined
non-locally by the entire magnetic configuration. In a dual spin valve
structure that comprises a free layer embedded between two pinned layers, the
spin pumping mechanism, in combination with the angular momentum conservation,
renders the tensor-like damping parameters tunable by varying the interfacial
and diffusive properties. Simulations based on the Landau-Lifshitz-Gilbert
phenomenology for a macrospin model are performed with the tensor-like damping
and the relaxation time of the free layer magnetization is found to be largely
dependent on while tunable through the magnetic configuration of the
source-drain magnetization.
|
1111.1219v1
|
2012-05-25
|
Spin wave amplification driven by heat flow: the role of damping and exchange interaction
|
In this article we report on micromagnetic simulations performed on a
permalloy nanostructure in presence of a uniform thermal gradient. Our
numerical simulations show that heat flow is an effective mean to compensate
the damping, and that the gradients at which spin-wave amplification is
observed are experimentally accessible. In particular, we have studied the role
of the Gilbert damping parameter on spin-wave amplification.
|
1205.5650v2
|
2015-04-23
|
Magnetization damping in noncollinear spin valves with antiferromagnetic interlayer couplings
|
We study the magnetic damping in the simplest of synthetic antiferromagnets,
i.e. antiferromagnetically exchange-coupled spin valves in which applied
magnetic fields tune the magnetic configuration to become noncollinear. We
formulate the dynamic exchange of spin currents in a noncollinear texture based
on the spindiffusion theory with quantum mechanical boundary conditions at the
ferrromagnet|normal-metal interfaces and derive the Landau-Lifshitz-Gilbert
equations coupled by the static interlayer non-local and the dynamic exchange
interactions. We predict non-collinearity-induced additional damping that can
be sensitively modulated by an applied magnetic field. The theoretical results
compare favorably with published experiments.
|
1504.06042v1
|
2016-05-05
|
Theory of magnon motive force in chiral ferromagnets
|
We predict that magnon motive force can lead to temperature dependent,
nonlinear chiral damping in both conducting and insulating ferromagnets. We
estimate that this damping can significantly influence the motion of skyrmions
and domain walls at finite temperatures. We also find that in systems with low
Gilbert damping moving chiral magnetic textures and resulting magnon motive
forces can induce large spin and energy currents in the transverse direction.
|
1605.01694v2
|
2018-04-19
|
Damping of magnetization dynamics by phonon pumping
|
We theoretically investigate pumping of phonons by the dynamics of a magnetic
film into a non-magnetic contact. The enhanced damping due to the loss of
energy and angular momentum shows interference patterns as a function of
resonance frequency and magnetic film thickness that cannot be described by
viscous ("Gilbert") damping. The phonon pumping depends on magnetization
direction as well as geometrical and material parameters and is observable,
e.g., in thin films of yttrium iron garnet on a thick dielectric substrate.
|
1804.07080v2
|
2024-01-22
|
Damping-Enhanced Magnon Transmission
|
The inevitable Gilbert damping in magnetization dynamics is usually regarded
as detrimental to spin transport. Here we demonstrate in a
ferromagnetic-insulator--normal-metal heterostructure that the strong momentum
dependence and chirality of the eddy-current-induced damping causes also
beneficial scattering properties. Here we show that a potential barrier that
reflects magnon wave packets becomes transparent in the presence of a metallic
cap layer, but only in one direction. We formulate the unidirectional
transmission in terms of a generalized group velocity with an imaginary
component and the magnon skin effect. This trick to turn presumably harmful
dissipation into useful functionalities should be useful for future quantum
magnonic devices.
|
2401.12022v1
|
2013-05-03
|
Co2 FeAl thin films grown on MgO substrates: Correlation between static, dynamic and structural properties
|
Co2FeAl (CFA) thin films with thickness varying from 10 nm to 115 nm have
been deposited on MgO(001) substrates by magnetron sputtering and then capped
by Ta or Cr layer. X-rays diffraction (XRD) revealed that the cubic $[001]$ CFA
axis is normal to the substrate and that all the CFA films exhibit full
epitaxial growth. The chemical order varies from the $B2$ phase to the $A2$
phase when decreasing the thickness. Magneto-optical Kerr effect (MOKE) and
vibrating sample magnetometer measurements show that, depending on the field
orientation, one or two-step switchings occur. Moreover, the films present a
quadratic MOKE signal increasing with the CFA thickness, due to the increasing
chemical order. Ferromagnetic resonance, MOKE transverse bias initial inverse
susceptibility and torque (TBIIST) measurements reveal that the in-plane
anisotropy results from the superposition of a uniaxial and of a fourfold
symmetry term. The fourfold anisotropy is in accord with the crystal structure
of the samples and is correlated to the biaxial strain and to the chemical
order present in the films. In addition, a large negative perpendicular
uniaxial anisotropy is observed. Frequency and angular dependences of the FMR
linewidth show two magnon scattering and mosaicity contributions, which depend
on the CFA thickness. A Gilbert damping coefficient as low as 0.0011 is found.
|
1305.0714v1
|
2016-08-29
|
Sub-micrometer yttrium iron garnet LPE films with low ferromagnetic resonance losses
|
Using liquid phase epitaxy (LPE) technique (111) yttrium iron garnet (YIG)
films with thicknesses of ~100 nm and surface roughnesses as low as 0.3 nm have
been grown as a basic material for spin-wave propagation experiments in
microstructured waveguides. The continuously strained films exhibit nearly
perfect crystallinity without significant mosaicity and with effective lattice
misfits of delta a(perpendicular)/a(substrate) ~10-4 and below. The
film/substrate interface is extremely sharp without broad interdiffusion layer
formation. All LPE films exhibit a nearly bulk-like saturation magnetization of
(1800+-20) Gs and an `easy cone' anisotropy type with extremely small in-plane
coercive fields <0.2 Oe. There is a rather weak in-plane magnetic anisotropy
with a pronounced six-fold symmetry observed for saturation field <1.5 Oe. No
significant out-of-plane anisotropy is observed, but a weak dependence of the
effective magnetization on the lattice misfit is detected. The narrowest
ferromagnetic resonance linewidth is determined to be 1.4 Oe @ 6.5 GHz which is
the lowest value reported so far for YIG films of 100 nm thicknesses and below.
The Gilbert damping coefficient for investigated LPE films is estimated to be
close to 1 x 10-4.
|
1608.08043v1
|
2019-09-12
|
Spin Transport in Thick Insulating Antiferromagnetic Films
|
Spin transport of magnonic excitations in uniaxial insulating
antiferromagnets (AFs) is investigated. In linear response to spin biasing and
a temperature gradient, the spin transport properties of
normal-metal--insulating antiferromagnet--normal-metal heterostructures are
calculated. We focus on the thick-film regime, where the AF is thicker than the
magnon equilibration length. This regime allows the use of a drift-diffusion
approach, which is opposed to the thin-film limit considered by Bender {\it et
al.} 2017, where a stochastic approach is justified. We obtain the temperature-
and thickness-dependence of the structural spin Seebeck coefficient
$\mathcal{S}$ and magnon conductance $\mathcal{G}$. In their evaluation we
incorporate effects from field- and temperature-dependent spin conserving
inter-magnon scattering processes. Furthermore, the interfacial spin transport
is studied by evaluating the contact magnon conductances in a microscopic model
that accounts for the sub-lattice symmetry breaking at the interface. We find
that while inter-magnon scattering does slightly suppress the spin Seebeck
effect, transport is generally unaffected, with the relevant spin decay length
being determined by non-magnon-conserving processes such as Gilbert damping. In
addition, we find that while the structural spin conductance may be enhanced
near the spin flip transition, it does not diverge due to spin impedance at the
normal metal|magnet interfaces.
|
1909.05881v2
|
2020-09-22
|
Magnon-mediated spin currents in Tm3Fe5O12/Pt with perpendicular magnetic anisotropy
|
The control of pure spin currents carried by magnons in magnetic insulator
(MI) garnet films with a robust perpendicular magnetic anisotropy (PMA) is of
great interest to spintronic technology as they can be used to carry, transport
and process information. Garnet films with PMA present labyrinth domain
magnetic structures that enrich the magnetization dynamics, and could be
employed in more efficient wave-based logic and memory computing devices. In
MI/NM bilayers, where NM being a normal metal providing a strong spin-orbit
coupling, the PMA benefits the spin-orbit torque (SOT) driven magnetization's
switching by lowering the needed current and rendering the process faster,
crucial for developing magnetic random-access memories (SOT-MRAM). In this
work, we investigated the magnetic anisotropies in thulium iron garnet (TIG)
films with PMA via ferromagnetic resonance measurements, followed by the
excitation and detection of magnon-mediated pure spin currents in TIG/Pt driven
by microwaves and heat currents. TIG films presented a Gilbert damping constant
{\alpha}~0.01, with resonance fields above 3.5 kOe and half linewidths broader
than 60 Oe, at 300 K and 9.5 GHz. The spin-to-charge current conversion through
TIG/Pt was observed as a micro-voltage generated at the edges of the Pt film.
The obtained spin Seebeck coefficient was 0.54 {\mu}V/K, confirming also the
high interfacial spin transparency.
|
2009.10299v1
|
2021-03-08
|
Emerging magnetic nutation
|
Nutation has been recognized as of great significance for spintronics; but
justifying its presence has proven to be a hard problem. In this paper we show
that nutation can be understood as emerging from a systematic expansion of a
kernel that describes the history of the interaction of a magnetic moment with
a bath of colored noise. The parameter of the expansion is the ratio of the
colored noise timescale to the precession period. In the process we obtain the
Gilbert damping from the same expansion. We recover the known results, when the
coefficients of the two terms are proportional to one another, in the white
noise limit; and show how colored noise leads to situations where this simple
relation breaks down, but what replaces it can be understood by the appropriate
generalization of the fluctuation--dissipation theorem. Numerical simulations
of the stochastic equations support the analytic approach. In particular we
find that the equilibration time is about an order of magnitude longer than the
timescale set by the colored noise for a wide range of values of the latter and
we can identify the presence of nutation in the non-uniform way the
magnetization approaches equilibrium.
|
2103.04787v3
|
2008-11-04
|
Amplitude-Phase Coupling in a Spin-Torque Nano-Oscillator
|
The spin-torque nano-oscillator in the presence of thermal fluctuation is
described by the normal form of the Hopf bifurcation with an additive white
noise. By the application of the reduction method, the amplitude-phase coupling
factor, which has a significant effect on the power spectrum of the spin-torque
nano-oscillator, is calculated from the Landau-Lifshitz-Gilbert-Slonczewski
equation with the nonlinear Gilbert damping. The amplitude-phase coupling
factor exhibits a large variation depending on in-plane anisotropy under the
practical external fields.
|
0811.0425v1
|
2013-09-28
|
High-efficiency GHz frequency doubling without power threshold in thin-film Ni81Fe19
|
We demonstrate efficient second-harmonic generation at moderate input power
for thin film Ni81Fe19 undergoing ferromagnetic resonance (FMR). Powers of the
generated second-harmonic are shown to be quadratic in input power, with an
upconversion ratio three orders of magnitude higher than that demonstrated in
ferrite. The second harmonic signal generated exhibits a significantly lower
linewidth than that predicted by low-power Gilbert damping, and is excited
without threshold. Results are in good agreement with an analytic, approximate
expansion of the Landau-Lifshitz-Gilbert (LLG) equation.
|
1309.7483v1
|
2016-06-30
|
Skyrmion dynamics in a chiral magnet driven by periodically varying spin currents
|
In this work, we investigated the spin dynamics in a slab of chiral magnets
induced by an alternating (ac) spin current. Periodic trajectories of the
skyrmion in real space are discovered under the ac current as a result of the
Magnus and viscous forces, which originate from the Gilbert damping, the spin
transfer torque, and the $ \beta $-nonadiabatic torque effects. The results are
obtained by numerically solving the Landau-Lifshitz-Gilbert equation and can be
explained by the Thiele equation characterizing the skyrmion core motion.
|
1606.09326v2
|
2018-03-19
|
Dynamics of a Magnetic Needle Magnetometer: Sensitivity to Landau-Lifshitz-Gilbert Damping
|
An analysis of a single-domain magnetic needle in the presence of an external
magnetic field ${\bf B}$ is carried out with the aim of achieving a high
precision magnetometer. We determine the uncertainty $\Delta B$ of such a
device due to Gilbert dissipation and the associated internal magnetic field
fluctuations that gives rise to diffusion of the magnetic needle axis direction
${\bf n}$ and the needle orbital angular momentum. The levitation of the
magnetic needle in a magnetic trap and its stability are also analyzed.
|
1803.10064v2
|
2020-08-27
|
Nutation Resonance in Ferromagnets
|
The inertial dynamics of magnetization in a ferromagnet is investigated
theoretically. The analytically derived dynamic response upon microwave
excitation shows two peaks: ferromagnetic and nutation resonances. The exact
analytical expressions of frequency and linewidth of the magnetic nutation
resonance are deduced from the frequency dependent susceptibility determined by
the inertial Landau-Lifshitz-Gilbert equation. The study shows that the
dependence of nutation linewidth on the Gilbert precession damping has a
minimum, which becomes more expressive with increase of the applied magnetic
field.
|
2008.12221v3
|
2009-08-05
|
Persistence effects in deterministic diffusion
|
In systems which exhibit deterministic diffusion, the gross parameter
dependence of the diffusion coefficient can often be understood in terms of
random walk models. Provided the decay of correlations is fast enough, one can
ignore memory effects and approximate the diffusion coefficient according to
dimensional arguments. By successively including the effects of one and two
steps of memory on this approximation, we examine the effects of
``persistence'' on the diffusion coefficients of extended two-dimensional
billiard tables and show how to properly account for these effects, using walks
in which a particle undergoes jumps in different directions with probabilities
that depend on where they came from.
|
0908.0600v1
|
2009-08-10
|
Diffusion coefficients for multi-step persistent random walks on lattices
|
We calculate the diffusion coefficients of persistent random walks on
lattices, where the direction of a walker at a given step depends on the memory
of a certain number of previous steps. In particular, we describe a simple
method which enables us to obtain explicit expressions for the diffusion
coefficients of walks with two-step memory on different classes of one-, two-
and higher-dimensional lattices.
|
0908.1271v1
|
2007-02-01
|
Adiabatic Domain Wall Motion and Landau-Lifshitz Damping
|
Recent theory and measurements of the velocity of current-driven domain walls
in magnetic nanowires have re-opened the unresolved question of whether
Landau-Lifshitz damping or Gilbert damping provides the more natural
description of dissipative magnetization dynamics. In this paper, we argue that
(as in the past) experiment cannot distinguish the two, but that
Landau-Lifshitz damping nevertheless provides the most physically sensible
interpretation of the equation of motion. From this perspective, (i) adiabatic
spin-transfer torque dominates the dynamics with small corrections from
non-adiabatic effects; (ii) the damping always decreases the magnetic free
energy, and (iii) microscopic calculations of damping become consistent with
general statistical and thermodynamic considerations.
|
0702020v3
|
2009-04-09
|
Evaluating the locality of intrinsic precession damping in transition metals
|
The Landau-Lifshitz-Gilbert damping parameter is typically assumed to be a
local quantity, independent of magnetic configuration. To test the validity of
this assumption we calculate the precession damping rate of small amplitude
non-uniform mode magnons in iron, cobalt, and nickel. At scattering rates
expected near and above room temperature, little change in the damping rate is
found as the magnon wavelength is decreased from infinity to a length shorter
than features probed in recent experiments. This result indicates that
non-local effects due to the presence of weakly non-uniform modes, expected in
real devices, should not appreciably affect the dynamic response of the element
at typical operating temperatures. Conversely, at scattering rates expected in
very pure samples around cryogenic temperatures, non-local effects result in an
order of magnitude decrease in damping rates for magnons with wavelengths
commensurate with domain wall widths. While this low temperature result is
likely of little practical importance, it provides an experimentally testable
prediction of the non-local contribution of the spin-orbit torque-correlation
model of precession damping. None of these results exhibit strong dependence on
the magnon propagation direction.
|
0904.1455v1
|
2018-02-15
|
Damping's effect on the magnetodynamics of spin Hall nano-oscillators
|
We study the impact of spin wave damping ($\alpha$) on the auto-oscillation
properties of nano-constriction based spin Hall nano-oscillators (SHNOs). The
SHNOs are based on a 5 nm Pt layer interfaced to a 5 nm
Py$_{100-x-y}$Pt$_{x}$Ag$_{y}$ magnetic layer, where the Pt and Ag contents are
co-varied to keep the saturation magnetization constant (within 10 %), while
$\alpha$ varies close to a factor of three. We systematically investigate the
influence of the Gilbert damping on the magnetodynamics of these SHNOs by means
of electrical microwave measurements. Under the condition of a constant field,
the threshold current scales with the damping in the magnetic layer. The
threshold current as a function of field shows a parabolic-like behavior, which
we attribute to the evolution of the spatial profile of the auto-oscillation
mode. The signal linewidth is smaller for the high-damping materials in low
magnetic fields, although the lowest observed linewidth was measured for the
alloy with least damping.
|
1802.05548v1
|
2004-05-02
|
Spin Dynamics and Multiple Reflections in Ferromagnetic Film in Contact with Normal Metal Layers
|
Spin dynamics of a metallic ferromagnetic film imbedded between normal metal
layers is studied using the spin-pumping theory of Tserkovnyak et al. [Phys.
Rev. Lett. 88, 117601 (2002)]. The scattering matrix for this structure is
obtained using a spin-dependent potential with quantum well in the
ferromagnetic region. Owing to multiple reflections in the well, the excess
Gilbert damping and the gyromagnetic ratio exhibit quantum oscillations as a
function of the thickness of the ferromagnetic film. The wavelength of the
oscillations is given by the depth of the quantum well. For iron film imbedded
between gold layers, the amplitude of the oscillations of the Gilbert damping
is in an order of magnitude agreement with the damping observed by Urban et al.
[Phys. Rev. Lett. 87, 217204 (2001)]. The results are compared with the linear
response theory of Mills [Phys. Rev. B 68, 0144419 (2003)].
|
0405020v1
|
2004-06-18
|
Spin pumping and magnetization dynamics in ferromagnet-Luttinger liquid junctions
|
We study spin transport between a ferromagnet with time-dependent
magnetization and a conducting carbon nanotube or quantum wire, modeled as a
Luttinger liquid. The precession of the magnetization vector of the ferromagnet
due for instance to an outside applied magnetic field causes spin pumping into
an adjacent conductor. Conversely, the spin injection causes increased
magnetization damping in the ferromagnet. We find that, if the conductor
adjacent to the ferromagnet is a Luttinger liquid, spin pumping/damping is
suppressed by interactions, and the suppression has clear Luttinger liquid
power law temperature dependence. We apply our result to a few particular
setups. First we study the effective Landau-Lifshitz-Gilbert (LLG) coupled
equations for the magnetization vectors of the two ferromagnets in a FM-LL-FM
junction. Also, we compute the Gilbert damping for a FM-LL and a FM-LL-metal
junction.
|
0406437v1
|
2004-10-30
|
Dynamics of Domain Wall in a Biaxial Ferromagnet With Spin-torque
|
The dynamics of the domain wall (DW) in a biaxial ferromagnet interacting
with a spin-polarized current are described by sine-gordon (SG) equation
coupled with Gilbert damping term in this paper. Within our frame-work of this
model, we obtain a threshold of the current in the motion of a single DW with
the perturbation theory on kink soliton solution to the corresponding
ferromagnetic system, and the threshold is shown to be dependent on the Gilbert
damping term. Also, the motion properties of the DW are discussed for the zero-
and nonzero-damping cases, which shows that our theory to describe the dynamics
of the DW are self-consistent.
|
0411005v3
|
2005-10-31
|
Time-Resolved Spin Torque Switching and Enhanced Damping in Py/Cu/Py Spin-Valve Nanopillars
|
We report time-resolved measurements of current-induced reversal of a free
magnetic layer in Py/Cu/Py elliptical nanopillars at temperatures T = 4.2 K to
160 K. Comparison of the data to Landau-Lifshitz-Gilbert macrospin simulations
of the free layer switching yields numerical values for the spin torque and the
Gilbert damping parameters as functions of T. The damping is strongly
T-dependent, which we attribute to the antiferromagnetic pinning behavior of a
thin permalloy oxide layer around the perimeter of the free layer. This
adventitious antiferromagnetic pinning layer can have a major impact on spin
torque phenomena.
|
0510798v2
|
2006-09-18
|
General Form of Magnetization Damping: Magnetization dynamics of a spin system evolving nonadiabatically and out of equilibrium
|
Using an effective Hamiltonian including the Zeeman and internal
interactions, we describe the quantum theory of magnetization dynamics when the
spin system evolves non-adiabatically and out of equilibrium. The
Lewis-Riesenfeld dynamical invariant method is employed along with the
Liouville-von Neumann equation for the density matrix. We derive a dynamical
equation for magnetization defined with respect to the density operator with a
general form of magnetization damping that involves the non-equilibrium
contribution in addition to the Landau-Lifshitz-Gilbert equation. Two special
cases of the radiation-spin interaction and the spin-spin exchange interaction
are considered. For the radiation-spin interaction, the damping term is shown
to be of the Gilbert type, while in the spin-spin exchange interaction case the
results depend on a coupled chain of correlation functions.
|
0609431v2
|
2010-12-25
|
Screw-pitch effect and velocity oscillation of domain-wall in ferromagnetic nanowire driven by spin-polarized current
|
We investigate the dynamics of domain wall in ferromagnetic nanowire with
spin-transfer torque. The critical current condition is obtained analytically.
Below the critical current, we get the static domain wall solution which shows
that the spin-polarized current can't drive domain wall moving continuously. In
this case, the spin-transfer torque plays both the anti-precession and
anti-damping roles, which counteracts not only the spin-precession driven by
the effective field but also Gilbert damping to the moment. Above the critical
value, the dynamics of domain wall exhibits the novel screw-pitch effect
characterized by the temporal oscillation of domain wall velocity and width,
respectively. Both the theoretical analysis and numerical simulation
demonstrate that this novel phenomenon arise from the conjunctive action of
Gilbert-damping and spin-transfer torque. We also find that the roles of
spin-transfer torque are entirely contrary for the cases of below and above the
critical current.
|
1012.5473v1
|
2014-06-24
|
Interface enhancement of Gilbert damping from first-principles
|
The enhancement of Gilbert damping observed for Ni80Fe20 (Py) films in
contact with the non-magnetic metals Cu, Pd, Ta and Pt, is quantitatively
reproduced using first-principles scattering theory. The "spin-pumping" theory
that qualitatively explains its dependence on the Py thickness is generalized
to include a number of factors known to be important for spin transport through
interfaces. Determining the parameters in this theory from first-principles
shows that interface spin-flipping makes an essential contribution to the
damping enhancement. Without it, a much shorter spin-flip diffusion length for
Pt would be needed than the value we calculate independently.
|
1406.6225v2
|
2015-09-06
|
Study of spin dynamics and damping on the magnetic nanowire arrays with various nanowire widths
|
We investigate the spin dynamics including Gilbert damping in the
ferromagnetic nanowire arrays. We have measured the ferromagnetic resonance of
ferromagnetic nanowire arrays using vector-network analyzer ferromagnetic
resonance (VNA-FMR) and analyzed the results with the micromagnetic
simulations. We find excellent agreement between the experimental VNA-FMR
spectra and micromagnetic simulations result for various applied magnetic
fields. We find that the demagnetization factor for longitudinal conditions, Nz
(Ny) increases (decreases) as decreasing the nanowire width in the
micromagnetic simulations. For the transverse magnetic field, Nz (Ny) increases
(decreases) as increasing the nanowire width. We also find that the Gilbert
damping constant increases from 0.018 to 0.051 as the increasing nanowire width
for the transverse case, while it is almost constant as 0.021 for the
longitudinal case.
|
1509.01807v1
|
2016-03-25
|
Large spin pumping effect in antisymmetric precession of Ni$_{79}$Fe$_{21}$/Ru/Ni$_{79}$Fe$_{21}$
|
In magnetic trilayer structures, a contribution to the Gilbert damping of
ferromagnetic resonance arises from spin currents pumped from one layer to
another. This contribution has been demonstrated for layers with weakly
coupled, separated resonances, where magnetization dynamics are excited
predominantly in one layer and the other layer acts as a spin sink. Here we
show that trilayer structures in which magnetizations are excited
simultaneously, antisymmetrically, show a spin-pumping effect roughly twice as
large. The antisymmetric (optical) mode of antiferromagnetically coupled
Ni$_{79}$Fe$_{21}$(8nm)/Ru/Ni$_{79}$Fe$_{21}$(8nm) trilayers shows a Gilbert
damping constant greater than that of the symmetric (acoustic) mode by an
amount as large as the intrinsic damping of Py ($\Delta
\alpha\simeq\textrm{0.006}$). The effect is shown equally in field-normal and
field-parallel to film plane geometries over 3-25 GHz. The results confirm a
prediction of the spin pumping model and have implications for the use of
synthetic antiferromagnets (SAF)-structures in GHz devices.
|
1603.07977v1
|
2016-10-21
|
Spin transport and dynamics in all-oxide perovskite La$_{2/3}$Sr$_{1/3}$MnO$_3$/SrRuO$_3$ bilayers probed by ferromagnetic resonance
|
Thin films of perovskite oxides offer the possibility of combining emerging
concepts of strongly correlated electron phenomena and spin current in magnetic
devices. However, spin transport and magnetization dynamics in these complex
oxide materials are not well understood. Here, we experimentally quantify spin
transport parameters and magnetization damping in epitaxial perovskite
ferromagnet/paramagnet bilayers of La$_{2/3}$Sr$_{1/3}$MnO$_3$/SrRuO$_3$
(LSMO/SRO) by broadband ferromagnetic resonance spectroscopy. From the SRO
thickness dependence of Gilbert damping, we estimate a short spin diffusion
length of $\lesssim$1 nm in SRO and an interfacial spin-mixing conductance
comparable to other ferromagnet/paramagnetic-metal bilayers. Moreover, we find
that anisotropic non-Gilbert damping due to two-magnon scattering also
increases with the addition of SRO. Our results demonstrate LSMO/SRO as a
spin-source/spin-sink system that may be a foundation for examining
spin-current transport in various perovskite heterostructures.
|
1610.06661v1
|
2019-02-12
|
Ultra-low damping in lift-off structured yttrium iron garnet thin films
|
We show that using maskless photolithography and the lift-off technique,
patterned yttrium iron garnet thin films possessing ultra-low Gilbert damping
can be accomplished. The films of 70 nm thickness were grown on (001)-oriented
gadolinium gallium garnet by means of pulsed laser deposition, and they exhibit
high crystalline quality, low surface roughness, and the effective
magnetization of 127 emu/cm3. The Gilbert damping parameter is as low as
5x10-4. The obtained structures have well-defined sharp edges which along with
good structural and magnetic film properties pave a path in the fabrication of
high-quality magnonic circuits and oxide-based spintronic devices.
|
1902.04605v1
|
2019-02-20
|
CoFeB/MgO/CoFeB structures with orthogonal easy axes: perpendicular anisotropy and damping
|
We report on the Gilbert damping parameter $\alpha$, the effective
magnetization $4\pi M_{eff}$, and the asymmetry of the $g$-factor in
bottom-CoFeB(0.93~nm)/MgO(0.90--1.25~nm)/CoFeB(1.31~nm)-top as-deposited
systems.
Magnetization of CoFeB layers exhibits a specific noncollinear configuration
with orthogonal easy axes and with $4\pi M_{eff}$ values of $+2.2$ kG and
$-2.3$ kG for the bottom and top layers, respectively. We show that $4\pi
M_{eff}$ depends on the asymmetry $g_\perp - g_\parallel$ of the $g$-factor
measured in the perpendicular and the in-plane directions revealing a highly
nonlinear relationship. In contrast, the Gilbert damping is practically the
same for both layers. Annealing of the films results in collinear easy axes
perpendicular to the plane for both layers. However, the linewidth is strongly
increased due to enhanced inhomogeneous broadening.
|
1902.07563v1
|
2021-06-28
|
Stability of a Magnetically Levitated Nanomagnet in Vacuum: Effects of Gas and Magnetization Damping
|
In the absence of dissipation a non-rotating magnetic nanoparticle can be
stably levitated in a static magnetic field as a consequence of the spin origin
of its magnetization. Here we study the effects of dissipation on the stability
of the system, considering the interaction with the background gas and the
intrinsic Gilbert damping of magnetization dynamics. At large applied magnetic
fields we identify magnetization switching induced by Gilbert damping as the
key limiting factor for stable levitation. At low applied magnetic fields and
for small particle dimensions magnetization switching is prevented due to the
strong coupling of rotation and magnetization dynamics, and the stability is
mainly limited by the gas-induced dissipation. In the latter case, high vacuum
should be sufficient to extend stable levitation over experimentally relevant
timescales. Our results demonstrate the possibility to experimentally observe
the phenomenon of quantum spin stabilized magnetic levitation.
|
2106.14858v3
|
2021-10-31
|
Thermally induced all-optical ferromagnetic resonance in thin YIG films
|
All-optical ferromagnetic resonance (AO-FMR) is a powerful tool for local
detection of micromagnetic parameters, such as magnetic anisotropy, Gilbert
damping or spin stiffness. In this work we demonstrate that the AO-FMR method
can be used in thin films of Yttrium Iron Garnet (YIG) if a metallic capping
layer (Au, Pt) is deposited on top of the film. Magnetization precession is
triggered by heating of the metallic layer with femtosecond laser pulses. The
heating modifies the magneto-crystalline anisotropy of the YIG film and shifts
the quasi-equilibrium orientation of magnetization, which results in
precessional magnetization dynamics. The laser-induced magnetization precession
corresponds to a uniform (Kittel) magnon mode, with the precession frequency
determined by the magnetic anisotropy of the material as well as the external
magnetic field, and the damping time set by a Gilbert damping parameter. The
AO-FMR method thus enables measuring local magnetic properties, with spatial
resolution given only by the laser spot size.
|
2111.00586v1
|
2024-01-01
|
Calculation of Gilbert damping and magnetic moment of inertia using torque-torque correlation model within ab initio Wannier framework
|
Magnetization dynamics in magnetic materials are well described by the
modified semiclassical Landau-Lifshitz-Gilbert (LLG) equation, which includes
the magnetic damping $\alpha$ and the magnetic moment of inertia $\mathrm{I}$
tensors as key parameters. Both parameters are material-specific and physically
represent the time scales of damping of precession and nutation in
magnetization dynamics. $\alpha$ and $\mathrm{I}$ can be calculated quantum
mechanically within the framework of the torque-torque correlation model. The
quantities required for the calculation are torque matrix elements, the real
and imaginary parts of the Green's function and its derivatives. Here, we
calculate these parameters for the elemental magnets such as Fe, Co and Ni in
an ab initio framework using density functional theory and Wannier functions.
We also propose a method to calculate the torque matrix elements within the
Wannier framework. We demonstrate the effectiveness of the method by comparing
it with the experiments and the previous ab initio and empirical studies and
show its potential to improve our understanding of spin dynamics and to
facilitate the design of spintronic devices.
|
2401.00714v1
|
2023-08-18
|
Large thermo-spin effects in Heusler alloy based spin-gapless semiconductor thin films
|
Recently, Heusler alloys-based spin gapless semiconductors (SGSs) with high
Curie temperature (TC) and sizeable spin polarization have emerged as potential
candidates for tunable spintronic applications. We report comprehensive
investigation of the temperature dependent ANE and intrinsic longitudinal spin
Seebeck effect (LSSE) in CoFeCrGa thin films grown on MgO substrates. Our
findings show the anomalous Nernst coefficient for the MgO/CoFeCrGa (95 nm)
film is $\cong 1.86$ micro V/K at room temperature which is nearly two orders
of magnitude higher than that of the bulk polycrystalline sample of CoFeCrGa (=
0.018 micro V/K) but comparable to that of the magnetic Weyl semimetal Co2MnGa
thin film (2-3 micro V/K). Furthermore, the LSSE coefficient for our
MgO/CoFeCrGa(95nm)/Pt(5nm) heterostructure is $\cong 20.5$ $\mu$V/K/$\Omega$ at
room temperature which is twice larger than that of the half-metallic
ferromagnetic La$_{0.7}$Sr$_{0.3}$MnO$_3$ thin films ($\cong$ 20.5
$\mu$V/K/$\Omega$). We show that both ANE and LSSE coefficients follow
identical temperature dependences and exhibit a maximum at $\cong$ 225 K which
is understood as the combined effects of inelastic magnon scatterings and
reduced magnon population at low temperatures. Our analyses not only indicate
that the extrinsic skew scattering is the dominating mechanism for ANE in these
films but also provide critical insights into the functional form of the
observed temperature dependent LSSE at low temperatures. Furthermore, by
employing radio frequency transverse susceptibility and broadband ferromagnetic
resonance in combination with the LSSE measurements, we establish a correlation
among the observed LSSE signal, magnetic anisotropy and Gilbert damping of the
CoFeCrGa thin films, which will be beneficial for fabricating tunable and
highly efficient Heusler alloys based spincaloritronic nanodevices.
|
2308.09843v1
|
2017-12-20
|
Unifying ultrafast demagnetization and intrinsic Gilbert damping in Co/Ni bilayers with electronic relaxation near the Fermi surface
|
The ability to controllably manipulate the laser-induced ultrafast magnetic
dynamics is a prerequisite for future high speed spintronic devices. The
optimization of devices requires the controllability of the ultrafast
demagnetization time, , and intrinsic Gilbert damping, . In previous attempts
to establish the relationship between and , the rare-earth doping of a
permalloy film with two different demagnetization mechanism is not a suitable
candidate. Here, we choose Co/Ni bilayers to investigate the relations between
and by means of time-resolved magneto-optical Kerr effect (TRMOKE) via
adjusting the thickness of the Ni layers, and obtain an approximately
proportional relation between these two parameters. The remarkable agreement
between TRMOKE experiment and the prediction of breathing Fermi-surface model
confirms that a large Elliott-Yafet spin-mixing parameter is relevant to the
strong spin-orbital coupling at the Co/Ni interface. More importantly, a
proportional relation between and in such metallic films or heterostructures
with electronic relaxation near Fermi surface suggests the local spin-flip
scattering domains the mechanism of ultrafast demagnetization, otherwise the
spin-current mechanism domains. It is an effective method to distinguish the
dominant contributions to ultrafast magnetic quenching in metallic
heterostructures by investigating both the ultrafast demagnetization time and
Gilbert damping simultaneously. Our work can open a novel avenue to manipulate
the magnitude and efficiency of Terahertz emission in metallic heterostructures
such as the perpendicular magnetic anisotropic Ta/Pt/Co/Ni/Pt/Ta multilayers,
and then it has an immediate implication of the design of high frequency
spintronic devices.
|
1712.07323v1
|
2015-06-16
|
Fast energy decay for wave equations with variable damping coefficients in the 1-D half line
|
We derive fast decay estimates of the total energy for wave equations with
localized variable damping coefficients, which are dealt with in the one
dimensional half line $(0,\infty)$. The variable damping coefficient vanishes
near the boundary $x = 0$, and is effective critically near spatial infinity $x
= \infty$.
|
1506.04851v1
|
2008-05-22
|
Intrinsic and non-local Gilbert damping in polycrystalline nickel studied by Ti:Sapphire laser fs spectroscopy
|
The use of femtosecond laser pulses generated by a Ti:Sapphire laser system
allows us to gain an insight into the magnetization dynamics on time scales
from sub-picosecond up to 1 ns directly in the time domain. This experimental
technique is used to excite a polycrystalline nickel (Ni) film optically and
probe the dynamics afterwards. Different spin wave modes (the Kittel mode,
perpendicular standing spin-wave modes (PSSW) and dipolar spin-wave modes
(Damon-Eshbach modes)) are identified as the Ni thickness is increased. The
Kittel mode allows determination of the Gilbert damping parameter alpha
extracted from the magnetization relaxation time tau_alpha. The non-local
damping by spin currents emitted into a non-magnetic metallic layer of vanadium
(V), palladium (Pd) and the rare earth dysprosium (Dy) are studied for
wedge-shaped Ni films 1 nm-30 nm. The damping parameter increases from
alpha=0.045 intrinsic for nickel to alpha>0.10 for the heavy materials, such as
Pd and Dy, for the thinnest Ni films below 10 nm thickness. Also, for the
thinnest reference Ni film thickness, an increased magnetic damping below 4 nm
is observed. The origin of this increase is discussed within the framework of
line broadening by locally different precessional frequencies within the laser
spot region.
|
0805.3495v1
|
2015-06-18
|
The absence of intraband scattering in a consistent theory of Gilbert damping in metallic ferromagnets
|
Damping of magnetization dynamics in a ferromagnetic metal is usually
characterized by the Gilbert parameter alpha. Recent calculations of this
quantity, using a formula due to Kambersky, find that it is infinite for a
perfect crystal owing to an intraband scattering term which is of third order
in the spin-orbit parameter xi This surprising result conflicts with recent
work by Costa and Muniz who study damping numerically by direct calculation of
the dynamical transverse spin susceptibility in the presence of spin-orbit
coupling. We resolve this inconsistency by following the Costa-Muniz approach
for a slightly simplified model where it is possible to calculate alpha
analytically. We show that to second order in the spin-orbit parameter xi one
retrieves the Kambersky result for alpha, but to higher order one does not
obtain any divergent intraband terms. The present work goes beyond that of
Costa and Muniz by pointing out the necessity of including the effect of
long-range Coulomb interaction in calculating damping for large xi. A direct
derivation of the Kambersky formula is given which shows clearly the
restriction of its validity to second order in xi so that no intraband
scattering terms appear. This restriction has an important effect on the
damping over a substantial range of impurity content and temperature. The
experimental situation is discussed.
|
1506.05622v2
|
2020-02-07
|
Engineering Co$_2$MnAl$_x$Si$_{1-x}$ Heusler compounds as a model system to correlate spin polarization, intrinsic Gilbert damping and ultrafast demagnetization
|
Engineering of magnetic materials for developing better spintronic
applications relies on the control of two key parameters: the spin polarization
and the Gilbert damping responsible for the spin angular momentum dissipation.
Both of them are expected to affect the ultrafast magnetization dynamics
occurring on the femtosecond time scale. Here, we use engineered Co2MnAlxSi1-x
Heusler compounds to adjust the degree of spin polarization P from 60 to 100%
and investigate how it correlates with the damping. We demonstrate
experimentally that the damping decreases when increasing the spin polarization
from 1.1 10-3 for Co2MnAl with 63% spin polarization to an ultra-low value of
4.10-4 for the half-metal magnet Co2MnSi. This allows us investigating the
relation between these two parameters and the ultrafast demagnetization time
characterizing the loss of magnetization occurring after femtosecond laser
pulse excitation. The demagnetization time is observed to be inversely
proportional to 1-P and as a consequence to the magnetic damping, which can be
attributed to the similarity of the spin angular momentum dissipation processes
responsible for these two effects. Altogether, our high quality Heusler
compounds allow controlling the band structure and therefore the channel for
spin angular momentum dissipation.
|
2002.02686v1
|
2006-08-22
|
Simulation of stress-impedance effects in low magnetostrictive films
|
A theoretical study of stress-impedance effect based on the solution of
Landau-Lifsitz-Gilbert equation has been carried out. The results show that
stress impedance effects depend largely on several extrinsic (external bias
field, external frequency) and intrinsic (orientation and magnitude of uniaxial
anisotropy, damping) parameters.
|
0608488v1
|
2017-03-09
|
Material developments and domain wall based nanosecond-scale switching process in perpendicularly magnetized STT-MRAM cells
|
We investigate the Gilbert damping and the magnetization switching of
perpendicularly magnetized FeCoB-based free layers embedded in tunnel junctions
adequate for spin-torque operated memories. We study the influence of the boron
content in MgO / FeCoB /Ta systems alloys on their Gilbert damping after
crystallization annealing. Increasing the boron content from 20 to 30\%
increases the crystallization temperature, thereby postponing the onset of
elemental diffusion within the free layer. This reduction of the interdiffusion
of the Ta atoms helps maintaining the Gilbert damping at a low level of 0.009
without any penalty on the anisotropy and the magneto-transport properties up
to the 400$^\circ$C annealing required in CMOS back-end of line processing. In
addition, we show that dual MgO free layers of composition
MgO/FeCoB/Ta/FeCoB/MgO have a substantially lower damping than their
MgO/FeCoB/Ta counterparts, reaching damping parameters as low as 0.0039 for a 3
\r{A} thick Tantalum spacer. This confirms that the dominant channel of damping
is the presence of Ta impurities within the FeCoB alloy. On optimized tunnel
junctions, we then study the duration of the switching events induced by
spin-transfer-torque. We focus on the sub-threshold thermally activated
switching in optimal applied field conditions. From the electrical signatures
of the switching, we infer that once the nucleation has occurred, the reversal
proceeds by a domain wall sweeping though the device at a few 10 m/s. The
smaller the device, the faster its switching. We present an analytical model to
account for our findings. The domain wall velocity is predicted to scale
linearly with the current for devices much larger than the wall width. The wall
velocity depends on the Bloch domain wall width, such that the devices with the
lowest exchange stiffness will be the ones that host the domain walls with the
slowest mobilities.
|
1703.03198v3
|
2018-07-31
|
Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences
|
Relaxation effects are of primary importance in the description of magnetic
excitations, leading to a myriad of methods addressing the phenomenological
damping parameters. In this work, we consider several well-established forms of
calculating the intrinsic Gilbert damping within a unified theoretical
framework, mapping out their connections and the approximations required to
derive each formula. This scheme enables a direct comparison of the different
methods on the same footing and a consistent evaluation of their range of
validity. Most methods lead to very similar results for the bulk ferromagnets
Fe, Co and Ni, due to the low spin-orbit interaction strength and the absence
of the spin pumping mechanism. The effects of inhomogeneities, temperature and
other sources of finite electronic lifetime are often accounted for by an
empirical broadening of the electronic energy levels. We show that the
contribution to the damping introduced by this broadening is additive, and so
can be extracted by comparing the results of the calculations performed with
and without spin-orbit interaction. Starting from simulated ferromagnetic
resonance spectra based on the underlying electronic structure, we
unambiguously demonstrate that the damping parameter obtained within the
constant broadening approximation diverges for three-dimensional bulk magnets
in the clean limit, while it remains finite for monolayers. Our work puts into
perspective the several methods available to describe and compute the Gilbert
damping, building a solid foundation for future investigations of magnetic
relaxation effects in any kind of material.
|
1807.11808v3
|
2002-07-30
|
Microscopic relaxation mechanisms and linear magnetization dynamics
|
Linear magnetization dynamics in the presense of a thermal bath is analyzed
for two general classes of microscopic damping mechanisms. The resulting
stochastic differential equations are always in the form of a damped harmonic
oscillator driven by a thermal field. The damping term contains both the
interaction mechanisms and the symmetry of the magnetic system. Back
transformation from the oscillator coordinates to the magnetization variables
results in a macroscopic tensor form of damping that reflects the system
anisotropy. Scalar Landau-Lifshitz-Gilbert damping term is valid only for
systems with axial symmetry. Analysis of FMR linewith measurements versus
frequency, temperature, and film thickness in NiFe films shows good agreement
with a combination of slow-relaxing impurity and magnon-electron confluence
processes.
|
0207721v1
|
2014-05-09
|
Magnetization dynamics and damping due to electron-phonon scattering in a ferrimagnetic exchange model
|
We present a microscopic calculation of magnetization damping for a magnetic
"toy model." The magnetic system consists of itinerant carriers coupled
antiferromagnetically to a dispersionless band of localized spins, and the
magnetization damping is due to coupling of the itinerant carriers to a phonon
bath in the presence of spin-orbit coupling. Using a mean-field approximation
for the kinetic exchange model and assuming the spin-orbit coupling to be of
the Rashba form, we derive Boltzmann scattering integrals for the distributions
and spin coherences in the case of an antiferromagnetic exchange splitting,
including a careful analysis of the connection between lifetime broadening and
the magnetic gap. For the Elliott-Yafet type itinerant spin dynamics we extract
dephasing and magnetization times T_1 and T_2 from initial conditions
corresponding to a tilt of the magnetization vector, and draw a comparison to
phenomenological equations such as the Landau-Lifshitz or the Gilbert damping.
We also analyze magnetization precession and damping for this system including
an anisotropy field and find a carrier mediated dephasing of the localized spin
via the mean-field coupling.
|
1405.2347v1
|
2015-11-13
|
Magnified Damping under Rashba Spin Orbit Coupling
|
The spin orbit coupling spin torque consists of the field-like [REF: S.G. Tan
et al., arXiv:0705.3502, (2007).] and the damping-like terms [REF: H.
Kurebayashi et al., Nature Nanotechnology 9, 211 (2014).] that have been widely
studied for applications in magnetic memory. We focus, in this article, not on
the spin orbit effect producing the above spin torques, but on its magnifying
the damping constant of all field like spin torques. As first order precession
leads to second order damping, the Rashba constant is naturally co-opted,
producing a magnified field-like damping effect. The Landau-Liftshitz-Gilbert
equations are written separately for the local magnetization and the itinerant
spin, allowing the progression of magnetization to be self-consistently locked
to the spin.
|
1511.04227v1
|
2022-05-13
|
Precession dynamics of a small magnet with non-Markovian damping: Theoretical proposal for an experiment to determine the correlation time
|
Recent advances in experimental techniques have made it possible to
manipulate and measure the magnetization dynamics on the femtosecond time scale
which is the same order as the correlation time of the bath degrees of freedom.
In the equations of motion of magnetization, the correlation of the bath is
represented by the non-Markovian damping. For development of the science and
technologies based on the ultrafast magnetization dynamics it is important to
understand how the magnetization dynamics depend on the correlation time. It is
also important to determine the correlation time experimentally. Here we study
the precession dynamics of a small magnet with the non-Markovian damping.
Extending the theoretical analysis of Miyazaki and Seki [J. Chem. Phys. 108,
7052 (1998)] we obtain analytical expressions of the precession angular
velocity and the effective damping constant for any values of the correlation
time under assumption of small Gilbert damping constant. We also propose a
possible experiment for determination of the correlation time.
|
2205.06399v1
|
2022-10-16
|
Magnetic damping anisotropy in the two-dimensional van der Waals material Fe$_3$GeTe$_2$ from first principles
|
Magnetization relaxation in the two-dimensional itinerant ferromagnetic van
der Waals material Fe$_3$GeTe$_2$, below the Curie temperature, is
fundamentally important for applications to low-dimensional spintronics
devices. We use first-principles scattering theory to calculate the
temperature-dependent Gilbert damping for bulk and single-layer Fe$_3$GeTe$_2$.
The calculated damping frequency of bulk Fe$_3$GeTe$_2$ increases monotonically
with temperature because of the dominance of resistivitylike behavior. By
contrast, a very weak temperature dependence is found for the damping frequency
of a single layer, which is attributed to strong surface scattering in this
highly confined geometry. A systematic study of the damping anisotropy reveals
that orientational anisotropy is present in both bulk and single-layer
Fe3GeTe2. Rotational anisotropy is significant at low temperatures for both the
bulk and a single layer and is gradually diminished by temperature-induced
disorder. The rotational anisotropy can be significantly enhanced by up to 430%
in gated single-layer Fe$_3$GeTe$_2$.
|
2210.08429v1
|
2016-09-26
|
Relativistic theory of spin relaxation mechanisms in the Landau-Lifshitz-Gilbert equation of spin dynamics
|
Starting from the Dirac-Kohn-Sham equation we derive the relativistic
equation of motion of spin angular momentum in a magnetic solid under an
external electromagnetic field. This equation of motion can be written in the
form of the well-known Landau-Lifshitz-Gilbert equation for a harmonic external
magnetic field, and leads to a more general magnetization dynamics equation for
a general time-dependent magnetic field. In both cases with an electronic
spin-relaxation term which stems from the spin-orbit interaction. We thus
rigorously derive, from fundamental principles, a general expression for the
anisotropic damping tensor which is shown to contain an isotropic Gilbert
contribution as well as an anisotropic Ising-like and a chiral,
Dzyaloshinskii-Moriya-like contribution. The expression for the spin relaxation
tensor comprises furthermore both electronic interband and intraband
transitions. We also show that when the externally applied electromagnetic
field possesses spin angular momentum, this will lead to an optical spin torque
exerted on the spin moment.
|
1609.07901v1
|
2023-08-07
|
$\textit{In situ}$ electric-field control of ferromagnetic resonance in the low-loss organic-based ferrimagnet V[TCNE]$_{x\sim 2}$
|
We demonstrate indirect electric-field control of ferromagnetic resonance
(FMR) in devices that integrate the low-loss, molecule-based, room-temperature
ferrimagnet vanadium tetracyanoethylene (V[TCNE]$_{x \sim 2}$) mechanically
coupled to PMN-PT piezoelectric transducers. Upon straining the V[TCNE]$_x$
films, the FMR frequency is tuned by more than 6 times the resonant linewidth
with no change in Gilbert damping for samples with $\alpha = 6.5 \times
10^{-5}$. We show this tuning effect is due to a strain-dependent magnetic
anisotropy in the films and find the magnetoelastic coefficient $|\lambda_S|
\sim (1 - 4.4)$ ppm, backed by theoretical predictions from DFT calculations
and magnetoelastic theory. Noting the rapidly expanding application space for
strain-tuned FMR, we define a new metric for magnetostrictive materials,
$\textit{magnetostrictive agility}$, given by the ratio of the magnetoelastic
coefficient to the FMR linewidth. This agility allows for a direct comparison
between magnetostrictive materials in terms of their comparative efficacy for
magnetoelectric applications requiring ultra-low loss magnetic resonance
modulated by strain. With this metric, we show V[TCNE]$_x$ is competitive with
other magnetostrictive materials including YIG and Terfenol-D. This combination
of ultra-narrow linewidth and magnetostriction in a system that can be directly
integrated into functional devices without requiring heterogeneous integration
in a thin-film geometry promises unprecedented functionality for electric-field
tuned microwave devices ranging from low-power, compact filters and circulators
to emerging applications in quantum information science and technology.
|
2308.03353v1
|
2002-11-22
|
Nonlinear microscopic relaxation of uniform magnetization precession
|
Dynamic relaxation for nonlinear magnetization excitation is analyzed. For
direct processes, such as magnon-electron scattering and two-magnon scattering,
the relaxation rate is determined from the linear case simply by utilizing the
magnetization oscillation frequency for nonlinear excitation. For an indirect
process, such as slow-relaxing impurities, the analysis gives an additional
relaxation term proportional to the excitation level. In all cases the
effective magnetization damping is increased compared to
Landau-Lifshitz-Gilbert damping.
|
0211499v1
|
2005-10-11
|
Non-damping magnetization oscillations in a single-domain ferromagnet
|
Non-damped oscillations of the magnetization vector of a ferromagnetic system
subject to a spin polarized current and an external magnetic field are studied
theoretically by solving the Landau-Lifshitz-Gilbert equation. It is shown that
the frequency and amplitude of such oscillations can be controlled by means of
an applied magnetic field and a spin current. The possibility of injection of
the oscillating spin current into a non-magnetic system is also discussed.
|
0510280v1
|
2007-03-27
|
Gauge Field Formulation of Adiabatic Spin Torques
|
Previous calculation of spin torques for small-amplitude magnetization
dynamics around a uniformly magnetized state [J. Phys. Soc. Jpn. {\bf 75}
(2006) 113706] is extended here to the case of finite-amplitude dynamics. This
is achieved by introducing an `` adiabatic'' spin frame for conduction
electrons, and the associated SU(2) gauge field. In particular, the Gilbert
damping is shown to arise from the time variation of the spin-relaxation source
terms in this new frame, giving a new physical picture of the damping. The
present method will allow a `` first-principle'' derivation of spin torques
without any assumptions such as rotational symmetry in spin space.
|
0703705v1
|
2008-05-09
|
Spin dynamics in (III,Mn)V ferromagnetic semiconductors: the role of correlations
|
We address the role of correlations between spin and charge degrees of
freedom on the dynamical properties of ferromagnetic systems governed by the
magnetic exchange interaction between itinerant and localized spins. For this
we introduce a general theory that treats quantum fluctuations beyond the
Random Phase Approximation based on a correlation expansion of the Green's
function equations of motion. We calculate the spin susceptibility, spin--wave
excitation spectrum, and magnetization precession damping. We find that
correlations strongly affect the magnitude and carrier concentration dependence
of the spin stiffness and magnetization Gilbert damping.
|
0805.1320v2
|
2010-01-16
|
Resonance Damping in Ferromagnets and Ferroelectrics
|
The phenomenological equations of motion for the relaxation of ordered phases
of magnetized and polarized crystal phases can be developed in close analogy
with one another. For the case of magnetized systems, the driving magnetic
field intensity toward relaxation was developed by Gilbert. For the case of
polarized systems, the driving electric field intensity toward relaxation was
developed by Khalatnikov. The transport times for relaxation into thermal
equilibrium can be attributed to viscous sound wave damping via
magnetostriction for the magnetic case and electrostriction for the
polarization case.
|
1001.2845v1
|
2016-05-15
|
Propagation of Thermally Induced Magnonic Spin Currents
|
The propagation of magnons in temperature gradients is investigated within
the framework of an atomistic spin model with the stochastic
Landau-Lifshitz-Gilbert equation as underlying equation of motion. We analyze
the magnon accumulation, the magnon temperature profile as well as the
propagation length of the excited magnons. The frequency distribution of the
generated magnons is investigated in order to derive an expression for the
influence of the anisotropy and the damping parameter on the magnon propagation
length. For soft ferromagnetic insulators with low damping a propagation length
in the range of some $\mu$m can be expected for exchange driven magnons.
|
1605.04543v1
|
2021-03-05
|
Universal spin wave damping in magnetic Weyl semimetals
|
We analyze the decay of spin waves into Stoner excitations in magnetic Weyl
semimetals. The lifetime of a mode is found to have a universal dependence on
its frequency and momentum, and on a few parameters that characterize the
relativistic Weyl spectrum. At the same time, Gilbert damping by Weyl electrons
is absent. The decay rate of spin waves is calculated perturbatively using the
s-d model of itinerant Weyl or Dirac electrons coupled to local moments. We
show that many details of the Weyl spectrum, such as the momentum-space
locations, dispersions and sizes of the Weyl Fermi pockets, can be deduced
indirectly by probing the spin waves of local moments using inelastic neutron
scattering.
|
2103.03885v1
|
2023-02-17
|
Control of magnon-photon coupling by spin torque
|
We demonstrate the influence of damping and field-like torques in the
magnon-photon coupling process by classically integrating the generalized
Landau-Lifshitz-Gilbert equation with RLC equation in which a phase correlation
between dynamic magnetization and microwave current through combined Amp\`ere
and Faraday effects are considered. We show that the gap between two hybridized
modes can be controlled in samples with damping parameter in the order of
$10^{-3}$ by changing the direction of the dc current density $J$ if a certain
threshold is reached. Our results suggest that an experimental realization of
the proposed magnon-photon coupling control mechanism is feasible in yttrium
iron garnet/Pt hybrid structures.
|
2302.08910v1
|
2017-03-21
|
Using rf voltage induced ferromagnetic resonance to study the spin-wave density of states and the Gilbert damping in perpendicularly magnetized disks
|
We study how the shape of the spinwave resonance lines in rf-voltage induced
FMR can be used to extract the spinwave density of states and the damping
within the precessing layer in nanoscale tunnel junctions that possess
perpendicular anisotropy. We work with a field applied along the easy axis to
preserve the uniaxial symmetry of the system. We describe the set-up to study
the susceptibility contributions of the spin waves in the field-frequency
space. We then identify the maximum device size above which the spinwaves can
no longer be studied in isolation as the linewidths of their responses make
them overlap. The rf-voltage induced signal is the sum of two voltages that
have comparable magnitudes: a first voltage that originates from the transverse
susceptibility and rectification by magnetoresistance and a second voltage that
arises from the non-linear longitudinal susceptibility and the resultant
time-averaged change of the micromagnetic configuration. The transverse and
longitudinal susceptibility signals have different dc bias dependences such
that they can be separated by measuring how the device rectifies the rf voltage
at different dc bias voltages. The transverse and longitudinal susceptibility
signals have different lineshapes; their joint studies can yield the Gilbert
damping of the free layer of the device with a degree of confidence that
compares well with standard FMR. Our method is illustrated on FeCoB-based free
layers in which the individual spin-waves can be sufficiently resolved only for
disk diameters below 200 nm. The resonance line shapes on devices with 90 nm
diameters are consistent with a Gilbert damping of 0.011. This damping of 0.011
exceeds the value of 0.008 measured on the unpatterned films, which indicates
that device-level measurements are needed for a correct evaluation of
dissipation.
|
1703.07310v2
|
2015-11-16
|
Determination of intrinsic damping of perpendicularly magnetized ultrathin films from time resolved precessional magnetization measurements
|
Magnetization dynamics are strongly influenced by damping. An effective
damping constant {\alpha}eff is often determined experimentally from the
spectral linewidth of the free induction decay of the magnetization after the
system is excited to its non-equilibrium state. Such an {\alpha}eff, however,
reflects both intrinsic damping as well as inhomogeneous broadening. In this
paper we compare measurements of the magnetization dynamics in ultrathin
non-epitaxial films having perpendicular magnetic anisotropy using two
different techniques, time-resolved magneto optical Kerr effect (TRMOKE) and
hybrid optical-electrical ferromagnetic resonance (OFMR). By using an external
magnetic field that is applied at very small angles to the film plane in the
TRMOKE studies, we develop an explicit closed-form analytical expression for
the TRMOKE spectral linewidth and show how this can be used to reliably extract
the intrinsic Gilbert damping constant. The damping constant determined in this
way is in excellent agreement with that determined from the OFMR method on the
same samples. Our studies indicate that the asymptotic high-field approach that
is often used in the TRMOKE method to distinguish the intrinsic damping from
the effective damping may result in significant error, because such high
external magnetic fields are required to make this approach valid that they are
out of reach. The error becomes larger the lower is the intrinsic damping
constant, and thus may account for the anomalously high damping constants that
are often reported in TRMOKE studies. In conventional ferromagnetic resonance
(FMR) studies, inhomogeneous contributions can be readily distinguished from
intrinsic damping contributions from the magnetic field dependence of the FMR
linewidth. Using the analogous approach, we show how reliable values of the
intrinsic damping can be extracted from TRMOKE.
|
1511.04802v1
|
2019-08-19
|
Spectral determinant for the damped wave equation on an interval
|
We evaluate the spectral determinant for the damped wave equation on an
interval of length $T$ with Dirichlet boundary conditions, proving that it does
not depend on the damping. This is achieved by analysing the square of the
damped wave operator using the general result by Burghelea, Friedlander, and
Kappeler on the determinant for a differential operator with matrix
coefficients.
|
1908.06862v1
|
2020-10-12
|
Decays rates for Kelvin-Voigt damped wave equations II: the geometric control condition
|
We study in this article decay rates for Kelvin-Voigt damped wave equations
under a geometric control condition. We prove that when the damping coefficient
is sufficiently smooth ($C^1$ vanishing nicely) we show that exponential decay
follows from geometric control conditions (see~\cite{BuCh, Te12} for similar
results under stronger assumptions on the damping function).
|
2010.05614v2
|
2019-06-21
|
Unique determination of the damping coefficient in the wave equation using point source and receiver data
|
In this article, we consider the inverse problems of determining the damping
coefficient appearing in the wave equation. We prove the unique determination
of the coefficient from the data coming from a single coincident
source-receiver pair. Since our problem is under-determined, so some extra
assumption on the coefficient is required to prove the uniqueness.
|
1906.08987v1
|
2002-07-19
|
Gilbert Damping in Magnetic Multilayers
|
We study the enhancement of the ferromagnetic relaxation rate in thin films
due to the adjacent normal metal layers. Using linear response theory, we
derive the dissipative torque produced by the s-d exchange interaction at the
ferromagnet-normal metal interface. For a slow precession, the enhancement of
Gilbert damping constant is proportional to the square of the s-d exchange
constant times the zero-frequency limit of the frequency derivative of the
local dynamic spin susceptibility of the normal metal at the interface.
Electron-electron interactions increase the relaxation rate by the Stoner
factor squared. We attribute the large anisotropic enhancements of the
relaxation rate observed recently in multilayers containing palladium to this
mechanism. For free electrons, the present theory compares favorably with
recent spin-pumping result of Tserkovnyak et al. [Phys. Rev. Lett.
\textbf{88},117601 (2002)].
|
0207471v1
|
2002-08-06
|
Spin pumping and magnetization dynamics in metallic multilayers
|
We study the magnetization dynamics in thin ferromagnetic films and small
ferromagnetic particles in contact with paramagnetic conductors. A moving
magnetization vector causes \textquotedblleft pumping\textquotedblright of
spins into adjacent nonmagnetic layers. This spin transfer affects the
magnetization dynamics similar to the Landau-Lifshitz-Gilbert phenomenology.
The additional Gilbert damping is significant for small ferromagnets, when the
nonmagnetic layers efficiently relax the injected spins, but the effect is
reduced when a spin accumulation build-up in the normal metal opposes the spin
pumping. The damping enhancement is governed by (and, in turn, can be used to
measure) the mixing conductance or spin-torque parameter of the
ferromagnet--normal-metal interface. Our theoretical findings are confirmed by
agreement with recent experiments in a variety of multilayer systems.
|
0208091v2
|
2005-12-29
|
Current-induced magnetization dynamics in disordered itinerant ferromagnets
|
Current-driven magnetization dynamics in ferromagnetic metals are studied in
a self-consistent adiabatic local-density approximation in the presence of
spin-conserving and spin-dephasing impurity scattering. Based on a quantum
kinetic equation, we derive Gilbert damping and spin-transfer torques entering
the Landau-Lifshitz equation to linear order in frequency and wave vector.
Gilbert damping and a current-driven dissipative torque scale identically and
compete, with the result that a steady current-driven domain-wall motion is
insensitive to spin dephasing in the limit of weak ferromagnetism. A uniform
magnetization is found to be much more stable against spin torques in the
itinerant than in the \textit{s}-\textit{d} model for ferromagnetism. A dynamic
spin-transfer torque reminiscent of the spin pumping in multilayers is
identified and shown to govern the current-induced domain-wall distortion.
|
0512715v4
|
2006-11-22
|
Magnetization damping in a local-density approximation
|
The linear response of itinerant transition metal ferromagnets to transverse
magnetic fields is studied in a self-consistent adiabatic local-density
approximation. The susceptibility is calculated from a microscopic Hamiltonian,
including spin-conserving impurities, impurity induced spin-orbit interaction
and magnetic impurities using the Keldysh formalism. The Gilbert damping
constant in the Landau-Lifshitz-Gilbert equation is identified, parametrized by
an effective transverse spin dephasing rate, and is found to be inversely
proportional to the exchange splitting. Our result justify the phenomenological
treatment of transverse spin dephasing in the study of current-induced
magnetization dynamics in weak, itinerant ferromagnets by Tserkovnyak
\textit{et al.}. We show that neglect of gradient corrections in the
quasiclassical transport equations leads to incorrect results when the exchange
potential becomes of the order of the Fermi energy.
|
0611588v1
|
2007-08-03
|
Strong spin-orbit induced Gilbert damping and g-shift in iron-platinum nanoparticles
|
The shape of ferromagnetic resonance spectra of highly dispersed, chemically
disordered Fe_{0.2}Pt_{0.8} nanospheres is perfectly described by the solution
of the Landau-Lifshitz-Gilbert (LLG) equation excluding effects by crystalline
anisotropy and superparamagnetic fluctuations. Upon decreasing temperature, the
LLG damping $\alpha(T)$ and a negative g-shift, g(T)-g_0, increase proportional
to the particle magnetic moments determined from the Langevin analysis of the
magnetization isotherms. These novel features are explained by the scattering
of the $q \to 0$ magnon from an electron-hole (e/h) pair mediated by the
spin-orbit coupling, while the sd-exchange can be ruled out. The large
saturation values, $\alpha(0)=0.76$ and $g(0)/g_0-1=-0.37$, indicate the
dominance of an overdamped 1 meV e/h-pair which seems to originate from the
discrete levels of the itinerant electrons in the d_p=3 nm nanoparticles.
|
0708.0463v1
|
2008-05-01
|
Chaotic Spin Dynamics of a Long Nanomagnet Driven by a Current
|
We study the spin dynamics of a long nanomagnet driven by an electrical
current. In the case of only DC current, the spin dynamics has a sophisticated
bifurcation diagram of attractors. One type of attractors is a weak chaos. On
the other hand, in the case of only AC current, the spin dynamics has a rather
simple bifurcation diagram of attractors. That is, for small Gilbert damping,
when the AC current is below a critical value, the attractor is a limit cycle;
above the critical value, the attractor is chaotic (turbulent). For normal
Gilbert damping, the attractor is always a limit cycle in the physically
interesting range of the AC current. We also developed a Melnikov integral
theory for a theoretical prediction on the occurrence of chaos. Our Melnikov
prediction seems performing quite well in the DC case. In the AC case, our
Melnikov prediction seems predicting transient chaos. The sustained chaotic
attractor seems to have extra support from parametric resonance leading to a
turbulent state.
|
0805.0147v1
|
2010-10-08
|
A unified first-principles study of Gilbert damping, spin-flip diffusion and resistivity in transition metal alloys
|
Using a formulation of first-principles scattering theory that includes
disorder and spin-orbit coupling on an equal footing, we calculate the
resistivity $\rho$, spin flip diffusion length $l_{sf}$ and the Gilbert damping
parameter $\alpha$ for Ni$_{1-x}$Fe$_x$ substitutional alloys as a function of
$x$. For the technologically important Ni$_{80}$Fe$_{20}$ alloy, permalloy, we
calculate values of $\rho = 3.5 \pm 0.15$ $\mu$Ohm-cm, $l_{sf}=5.5 \pm 0.3$ nm,
and $\alpha= 0.0046 \pm 0.0001$ compared to experimental low-temperature values
in the range $4.2-4.8$ $\mu$Ohm-cm for $\rho$, $5.0-6.0$ nm for $l_{sf}$, and
$0.004-0.013$ for $\alpha$ indicating that the theoretical formalism captures
the most important contributions to these parameters.
|
1010.1626v3
|
2011-02-22
|
Ab-initio calculation of the Gilbert damping parameter via linear response formalism
|
A Kubo-Greenwood-like equation for the Gilbert damping parameter $\alpha$ is
presented that is based on the linear response formalism. Its implementation
using the fully relativistic Korringa-Kohn-Rostoker (KKR) band structure method
in combination with Coherent Potential Approximation (CPA) alloy theory allows
it to be applied to a wide range of situations. This is demonstrated with
results obtained for the bcc alloy system Fe$_x$Co$_{1-x}$ as well as for a
series of alloys of permalloy with 5d transition metals.
To account for the thermal displacements of atoms as a scattering mechanism,
an alloy-analogy model is introduced. The corresponding calculations for Ni
correctly describe the rapid change of $\alpha$ when small amounts of
substitutional Cu are introduced.
|
1102.4551v1
|
2012-08-07
|
Observation of Coherent Helimagnons and Gilbert damping in an Itinerant Magnet
|
We study the magnetic excitations of itinerant helimagnets by applying
time-resolved optical spectroscopy to Fe0.8Co0.2Si. Optically excited
oscillations of the magnetization in the helical state are found to disperse to
lower frequency as the applied magnetic field is increased; the fingerprint of
collective modes unique to helimagnets, known as helimagnons. The use of
time-resolved spectroscopy allows us to address the fundamental magnetic
relaxation processes by directly measuring the Gilbert damping, revealing the
versatility of spin dynamics in chiral magnets. (*These authors contributed
equally to this work)
|
1208.1462v1
|
2012-11-02
|
Dynamic Spin Injection into Chemical Vapor Deposited Graphene
|
We demonstrate dynamic spin injection into chemical vapor deposition (CVD)
grown graphene by spin pumping from permalloy (Py) layers. Ferromagnetic
resonance measurements at room temperature reveal a strong enhancement of the
Gilbert damping at the Py/graphene interface, exceeding that observed in even
Py/platinum interfaces. Similar results are also shown on Co/graphene layers.
This enhancement in the Gilbert damping is understood as the consequence of
spin pumping at the interface driven by magnetization dynamics. Our
observations suggest a strong enhancement of spin-orbit coupling in CVD
graphene, in agreement with earlier spin valve measurements.
|
1211.0492v1
|
2013-01-10
|
First-principles calculation of the Gilbert damping parameter via the linear response formalism with application to magnetic transition-metals and alloys
|
A method for the calculations of the Gilbert damping parameter $\alpha$ is
presented, which based on the linear response formalism, has been implemented
within the fully relativistic Korringa-Kohn-Rostoker band structure method in
combination with the coherent potential approximation alloy theory. To account
for thermal displacements of atoms as a scattering mechanism, an alloy-analogy
model is introduced. This allows the determination of $\alpha$ for various
types of materials, such as elemental magnetic systems and ordered magnetic
compounds at finite temperature, as well as for disordered magnetic alloys at
$T = 0$ K and above. The effects of spin-orbit coupling, chemical and
temperature induced structural disorder are analyzed. Calculations have been
performed for the 3$d$ transition-metals bcc Fe, hcp Co, and fcc Ni, their
binary alloys bcc Fe$_{1-x}$Co$_{x}$, fcc Ni$_{1-x}$Fe$_x$, fcc
Ni$_{1-x}$Co$_x$ and bcc Fe$_{1-x}$V$_{x}$, and for 5d impurities in
transition-metal alloys. All results are in satisfying agreement with
experiment.
|
1301.2114v1
|
2014-01-24
|
Wavenumber-dependent Gilbert damping in metallic ferromagnets
|
New terms to the dynamical equation of magnetization motion, associated with
spin transport, have been reported over the past several years. Each newly
identified term is thought to possess both a real and an imaginary effective
field leading to fieldlike and dampinglike torques on magnetization. Here we
show that three metallic ferromagnets possess an imaginary effective-field term
which mirrors the well-known real effective-field term associated with exchange
in spin waves. Using perpendicular standing spin wave resonance between 2-26
GHz, we evaluate the magnitude of the finite-wavenumber ($k$) dependent Gilbert
damping $\alpha$ in three typical device ferromagnets, Ni$_{79}$Fe$_{21}$, Co,
and Co$_{40}$Fe$_{40}$B$_{20}$, and demonstrate for the first time the presence
of a $k^2$ term as $\Delta\alpha=\Delta\alpha_0+A_{k}\cdot k^2$ in all three
metals. We interpret the new term as the continuum analog of spin pumping,
predicted recently, and show that its magnitude, $A_{k}$=0.07-0.1 nm$^2$, is
consistent with transverse spin relaxation lengths as measured by conventional
(interlayer) spin pumping.
|
1401.6467v2
|
2014-12-11
|
Deviation From the Landau-Lifshitz-Gilbert equation in the Inertial regime of the Magnetization
|
We investigate in details the inertial dynamics of a uniform magnetization in
the ferromagnetic resonance (FMR) context. Analytical predictions and numerical
simulations of the complete equations within the Inertial
Landau-Lifshitz-Gilbert (ILLG) model are presented. In addition to the usual
precession resonance, the inertial model gives a second resonance peak
associated to the nutation dynamics provided that the damping is not too large.
The analytical resolution of the equations of motion yields both the precession
and nutation angular frequencies. They are function of the inertial dynamics
characteristic time $\tau$, the dimensionless damping $\alpha$ and the static
magnetic field $H$. A scaling function with respect to $\alpha\tau\gamma H$ is
found for the nutation angular frequency, also valid for the precession angular
frequency when $\alpha\tau\gamma H\gg 1$. Beyond the direct measurement of the
nutation resonance peak, we show that the inertial dynamics of the
magnetization has measurable effects on both the width and the angular
frequency of the precession resonance peak when varying the applied static
field. These predictions could be used to experimentally identify the inertial
dynamics of the magnetization proposed in the ILLG model.
|
1412.3783v1
|
2015-08-04
|
A Critical Analysis of the Feasibility of Pure Strain-Actuated Giant Magnetostrictive Nanoscale Memories
|
Concepts for memories based on the manipulation of giant magnetostrictive
nanomagnets by stress pulses have garnered recent attention due to their
potential for ultra-low energy operation in the high storage density limit.
Here we discuss the feasibility of making such memories in light of the fact
that the Gilbert damping of such materials is typically quite high. We report
the results of numerical simulations for several classes of toggle precessional
and non-toggle dissipative magnetoelastic switching modes. Material candidates
for each of the several classes are analyzed and forms for the anisotropy
energy density and ranges of material parameters appropriate for each material
class are employed. Our study indicates that the Gilbert damping as well as the
anisotropy and demagnetization energies are all crucial for determining the
feasibility of magnetoelastic toggle-mode precessional switching schemes. The
roles of thermal stability and thermal fluctuations for stress-pulse switching
of giant magnetostrictive nanomagnets are also discussed in detail and are
shown to be important in the viability, design, and footprint of
magnetostrictive switching schemes.
|
1508.00629v2
|
2015-12-16
|
Parity-time symmetry breaking in magnetic systems
|
The understanding of out-of-equilibrium physics, especially dynamic
instabilities and dynamic phase transitions, is one of the major challenges of
contemporary science, spanning the broadest wealth of research areas that range
from quantum optics to living organisms. Focusing on nonequilibrium dynamics of
an open dissipative spin system, we introduce a non-Hermitian Hamiltonian
approach, in which non-Hermiticity reflects dissipation and deviation from
equilibrium. The imaginary part of the proposed spin Hamiltonian describes the
effects of Gilbert damping and applied Slonczewski spin-transfer torque. In the
classical limit, our approach reproduces Landau-Lifshitz-Gilbert-Slonczewski
dynamics of a large macrospin. We reveal the spin-transfer torque-driven
parity-time symmetry-breaking phase transition corresponding to a transition
from precessional to exponentially damped spin dynamics. Micromagnetic
simulations for nanoscale ferromagnetic disks demonstrate the predicted effect.
Our findings can pave the way to a general quantitative description of
out-of-equilibrium phase transitions driven by spontaneous parity-time symmetry
breaking.
|
1512.05408v2
|
2017-01-11
|
The Cauchy problem for the Landau-Lifshitz-Gilbert equation in BMO and self-similar solutions
|
We prove a global well-posedness result for the Landau-Lifshitz equation with
Gilbert damping provided that the BMO semi-norm of the initial data is small.
As a consequence, we deduce the existence of self-similar solutions in any
dimension. In the one-dimensional case, we characterize the self-similar
solutions associated with an initial data given by some ($\mathbb{S}^2$-valued)
step function and establish their stability. We also show the existence of
multiple solutions if the damping is strong enough. Our arguments rely on the
study of a dissipative quasilinear Schr\"odinger obtained via the stereographic
projection and techniques introduced by Koch and Tataru.
|
1701.03083v2
|
2017-01-27
|
Structural scale $q-$derivative and the LLG-Equation in a scenario with fractionality
|
In the present contribution, we study the Landau-Lifshitz-Gilbert equation
with two versions of structural derivatives recently proposed: the scale
$q-$derivative in the non-extensive statistical mechanics and the axiomatic
metric derivative, which presents Mittag-Leffler functions as eigenfunctions.
The use of structural derivatives aims to take into account long-range forces,
possible non-manifest or hidden interactions and the dimensionality of space.
Having this purpose in mind, we build up an evolution operator and a deformed
version of the LLG equation. Damping in the oscillations naturally show up
without an explicit Gilbert damping term.
|
1701.08076v2
|
2018-10-17
|
Perpendicularly magnetized YIG films with small Gilbert damping constant and anomalous spin transport properties
|
The Y3Fe5O12 (YIG) films with perpendicular magnetic anisotropy (PMA) have
recently attracted a great deal of attention for spintronics applications.
Here, we report the induced PMA in the ultrathin YIG films grown on
(Gd2.6Ca0.4)(Ga4.1Mg0.25Zr0.65)O12 (SGGG) substrates by epitaxial strain
without preprocessing. Reciprocal space mapping shows that the films are
lattice-matched to the substrates without strain relaxation. Through
ferromagnetic resonance and polarized neutron reflectometry measurements, we
find that these YIG films have ultra-low Gilbert damping constant with a
magnetic dead layer as thin as about 0.3 nm at the YIG/SGGG interfaces.
Moreover, the transport behavior of the Pt/YIG/SGGG films reveals an
enhancement of spin mixing conductance and a large non-monotonic magnetic field
dependence of anomalous Hall effect as compared with the Pt/YIG/Gd3Ga5O12 (GGG)
films. The non-monotonic anomalous Hall signal is extracted in the temperature
range from 150 to 350 K, which has been ascribed to the possible non-collinear
magnetic order at the Pt/YIG interface induced by uniaxial strain.
|
1810.07384v2
|
2019-03-07
|
Current-induced motion of twisted skyrmions
|
Twisted skyrmions, whose helicity angles are different from that of Bloch
skyrmions and N\'eel skyrmions, have already been demonstrated in experiments
recently. In this work, we first contrast the magnetic structure and origin of
the twisted skyrmion with other three types of skyrmion including Bloch
skyrmion, N\'eel skyrmion and antiskyrmion. Following, we investigate the
dynamics of twisted skyrmions driven by the spin transfer toque (STT) and the
spin Hall effect (SHE) by using micromagnetic simulations. It is found that the
spin Hall angle of the twisted skyrmion is related to the dissipative force
tensor and the Gilbert damping both for the motions induced by the STT and the
SHE, especially for the SHE induced motion, the skyrmion Hall angle depends
substantially on the skyrmion helicity. At last, we demonstrate that the
trajectory of the twisted skyrmion can be controlled in a two dimensional plane
with a Gilbert damping gradient. Our results provide the understanding of
current-induced motion of twisted skyrmions, which may contribute to the
applications of skyrmion-based racetrack memories.
|
1903.02812v1
|
2019-07-03
|
Anisotropy of spin-transfer torques and Gilbert damping induced by Rashba coupling
|
Spin-transfer torques (STT), Gilbert damping (GD), and effective spin
renormalization (ESR) are investigated microscopically in a 2D Rashba
ferromagnet with spin-independent Gaussian white-noise disorder. Rashba
spin-orbit coupling induced anisotropy of these phenomena is thoroughly
analysed. For the case of two partly filled spin subbands, a remarkable
relation between the anisotropic STT, GD, and ESR is established. In the
absence of magnetic field and other torques on magnetization, this relation
corresponds to a current-induced motion of a magnetic texture with the
classical drift velocity of conduction electrons. Finally, we compute spin
susceptibility of the system and generalize the notion of spin-polarized
current.
|
1907.02041v3
|
2021-11-05
|
Giant oscillatory Gilbert damping in superconductor/ferromagnet/superconductor junctions
|
Interfaces between materials with differently ordered phases present unique
opportunities for exotic physical properties, especially the interplay between
ferromagnetism and superconductivity in the ferromagnet/superconductor
heterostructures. The investigation of zero- and pi-junctions has been of
particular interest for both fundamental physical science and emerging
technologies. Here, we report the experimental observation of giant oscillatory
Gilbert damping in the superconducting Nb/NiFe/Nb junctions with respect to the
NiFe thickness. This observation suggests an unconventional spin pumping and
relaxation via zero-energy Andreev bound states that exist only in the
Nb/NiFe/Nb pi-junctions, but not in the Nb/NiFe/Nb zero-junctions. Our findings
could be important for further exploring the exotic physical properties of
ferromagnet/superconductor heterostructures, and potential applications of
ferromagnet pi-junctions in quantum computing, such as half-quantum flux
qubits.
|
2111.03233v1
|
2022-11-14
|
Magnetization Dynamics in Synthetic Antiferromagnets with Perpendicular Magnetic Anisotropy
|
Understanding the rich physics of magnetization dynamics in perpendicular
synthetic antiferromagnets (p-SAFs) is crucial for developing next-generation
spintronic devices. In this work, we systematically investigate the
magnetization dynamics in p-SAFs combining time-resolved magneto-optical Kerr
effect (TR-MOKE) measurements with theoretical modeling. These model analyses,
based on a Landau-Lifshitz-Gilbert approach incorporating exchange coupling,
provide details about the magnetization dynamic characteristics including the
amplitudes, directions, and phases of the precession of p-SAFs under varying
magnetic fields. These model-predicted characteristics are in excellent
quantitative agreement with TR-MOKE measurements on an asymmetric p-SAF. We
further reveal the damping mechanisms of two procession modes co-existing in
the p-SAF and successfully identify individual contributions from different
sources, including Gilbert damping of each ferromagnetic layer, spin pumping,
and inhomogeneous broadening. Such a comprehensive understanding of
magnetization dynamics in p-SAFs, obtained by integrating high-fidelity TR-MOKE
measurements and theoretical modeling, can guide the design of p-SAF-based
architectures for spintronic applications.
|
2211.07744v2
|
2023-05-17
|
Material Parameters for Faster Ballistic Switching of an In-plane Magnetized Nanomagnet
|
High-speed magnetization switching of a nanomagnet is necessary for faster
information processing. The ballistic switching by a pulsed magnetic filed is a
promising candidate for the high-speed switching. It is known that the
switching speed of the ballistic switching can be increased by increasing the
magnitude of the pulsed magnetic field. However it is difficult to generate a
strong and short magnetic field pulse in a small device. Here we explore
another direction to achieve the high-speed ballistic switching by designing
material parameters such as anisotropy constant, saturation magnetization, and
the Gilbert damping constant. We perform the macrospin simulations for the
ballistic switching of in-plane magnetized nano magnets with varying material
parameters. The results are analyzed based on the switching dynamics on the
energy density contour. We show that the pulse width required for the ballistic
switching can be reduced by increasing the magnetic anisotropy constant or by
decreasing the saturation magnetization. We also show that there exists an
optimal value of the Gilbert damping constant that minimizes the pulse width
required for the ballistic switching.
|
2305.10111v1
|
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