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2008-08-28
|
Gilbert Damping in Conducting Ferromagnets II: Model Tests of the Torque-Correlation Formula
|
We report on a study of Gilbert damping due to particle-hole pair excitations
in conducting ferromagnets. We focus on a toy two-band model and on a four-band
spherical model which provides an approximate description of ferromagnetic
(Ga,Mn)As. These models are sufficiently simple that disorder-ladder-sum vertex
corrections to the long-wavelength spin-spin response function can be summed to
all orders. An important objective of this study is to assess the reliability
of practical approximate expressions which can be combined with electronic
structure calculations to estimate Gilbert damping in more complex systems.
|
0808.3923v1
|
2010-01-26
|
Effect of spin-conserving scattering on Gilbert damping in ferromagnetic semiconductors
|
The Gilbert damping in ferromagnetic semiconductors is theoretically
investigated based on the $s$-$d$ model. In contrast to the situation in
metals, all the spin-conserving scattering in ferromagnetic semiconductors
supplies an additional spin relaxation channel due to the momentum dependent
effective magnetic field of the spin-orbit coupling, thereby modifies the
Gilbert damping. In the presence of a pure spin current, we predict a new
contribution due to the interplay of the anisotropic spin-orbit coupling and a
pure spin current.
|
1001.4576v1
|
2011-05-20
|
Magnetization Dissipation in the Ferromagnetic Semiconductor (Ga,Mn)As
|
We compute the Gilbert damping in (Ga,Mn)As based on the scattering theory of
magnetization relaxation. The disorder scattering is included
non-perturbatively. In the clean limit, the spin-pumping from the localized
d-electrons to the itinerant holes dominates the relaxation processes. In the
diffusive regime, the breathing Fermi-surface effect is balanced by the effects
of interband scattering, which cause the Gilbert damping constant to saturate
at around 0.005. In small samples, the system shape induces a large anisotropy
in the Gilbert damping.
|
1105.4148v2
|
2008-12-17
|
Origin of intrinsic Gilbert damping
|
The damping of magnetization, represented by the rate at which it relaxes to
equilibrium, is successfully modeled as a phenomenological extension in the
Landau-Lifschitz-Gilbert equation. This is the damping torque term known as
Gilbert damping and its direction is given by the vector product of the
magnetization and its time derivative. Here we derive the Gilbert term from
first principles by a non-relativistic expansion of the Dirac equation. We find
that the Gilbert term arises when one calculates the time evolution of the spin
observable in the presence of the full spin-orbital coupling terms, while
recognizing the relationship between the curl of the electric field and the
time varying magnetic induction.
|
0812.3184v2
|
2019-07-01
|
Magnon decay theory of Gilbert damping in metallic antiferromagnets
|
Gilbert damping is a key property governing magnetization dynamics in ordered
magnets. We present a theoretical study of intrinsic Gilbert damping induced by
magnon decay in antiferromagnetic metals through $s$-$d$ exchange interaction.
Our theory delineates the qualitative features of damping in metallic
antiferromagnets owing to their bipartite nature, in addition to providing
analytic expressions for the damping parameters. Magnon-induced intraband
electron scattering is found to predominantly cause magnetization damping,
whereas the N\'eel field is found to be damped via disorder. Depending on the
conduction electron band structure, we predict that magnon-induced interband
electron scattering around band crossings may be exploited to engineer a strong
N\'eel field damping.
|
1907.01045v1
|
2022-11-24
|
Influence of non-local damping on magnon properties of ferromagnets
|
We study the influence of non-local damping on magnon properties of Fe, Co,
Ni and Fe$_{1-x}$Co$_{x}$ ($x=30\%,50\%$) alloys. The Gilbert damping parameter
is typically considered as a local scalar both in experiment and in theoretical
modelling. However, recent works have revealed that Gilbert damping is a
non-local quantity that allows for energy dissipation between atomic sites.
With the Gilbert damping parameters calculated from a state-of-the-art
real-space electronic structure method, magnon lifetimes are evaluated from
spin dynamics and linear response, where a good agreement is found between
these two methods. It is found that non-local damping affects the magnon
lifetimes in different ways depending on the system. Specifically, we find that
in Fe, Co, and Ni the non-local damping decreases the magnon lifetimes, while
in $\rm Fe_{70}Co_{30}$ and Fe$_{50}$Co$_{50}$ an opposite, non-local damping
effect is observed, and our data show that it is much stronger in the former.
|
2211.13486v1
|
2010-02-26
|
Correlation Effects in the Stochastic Landau-Lifshitz-Gilbert Equation
|
We analyze the Landau-Lifshitz-Gilbert equation when the precession motion of
the magnetic moments is additionally subjected to an uniaxial anisotropy and is
driven by a multiplicative coupled stochastic field with a finite correlation
time $\tau$. The mean value for the spin wave components offers that the
spin-wave dispersion relation and its damping is strongly influenced by the
deterministic Gilbert damping parameter $\alpha$, the strength of the
stochastic forces $D$ and its temporal range $\tau$. The spin-spin-correlation
function can be calculated in the low correlation time limit by deriving an
evolution equation for the joint probability function. The stability analysis
enables us to find the phase diagram within the $\alpha-D$ plane for different
values of $\tau$ where damped spin wave solutions are stable. Even for zero
deterministic Gilbert damping the magnons offer a finite lifetime. We detect a
parameter range where the deterministic and the stochastic damping mechanism
are able to compensate each other leading to undamped spin-waves. The onset is
characterized by a critical value of the correlation time. An enhancement of
$\tau$ leads to an increase of the oscillations of the correlation function.
|
1002.4958v1
|
2019-02-26
|
Enhanced Gilbert Damping in Re doped FeCo Films: A Combined Experimental and Theoretical Study
|
The effects of rhenium doping in the range 0 to 10 atomic percent on the
static and dynamic magnetic properties of Fe65Co35 thin films have been studied
experimentally as well as with first principles electronic structure
calculations focusing on the change of the saturation magnetization and the
Gilbert damping parameter. Both experimental and theoretical results show that
the saturation magnetization decreases with increasing Re doping level, while
at the same time Gilbert damping parameter increases. The experimental low
temperature saturation magnetic induction exhibits a 29 percent decrease, from
2.31 T to 1.64 T, in the investigated doping concentration range, which is more
than predicted by the theoretical calculations. The room temperature value of
the damping parameter obtained from ferromagnetic resonance measurements,
correcting for extrinsic contributions to the damping, is for the undoped
sample 0.0027, which is close to the theoretically calculated Gilbert damping
parameter. With 10 atomic percent Re doping, the damping parameter increases to
0.0090, which is in good agreement with the theoretical value of 0.0073. The
increase in damping parameter with Re doping is explained by the increase in
density of states at Fermi level, mostly contributed by the spin-up channel of
Re. Moreover, both experimental and theoretical values for the damping
parameter are observed to be weakly decreasing with decreasing temperature.
|
1902.09896v1
|
2023-06-07
|
Helicity-dependent optical control of the magnetization state emerging from the Landau-Lifshitz-Gilbert equation
|
It is well known that the Gilbert relaxation time of a magnetic moment scales
inversely with the magnitude of the externally applied field, H, and the
Gilbert damping, {\alpha}. Therefore, in ultrashort optical pulses, where H can
temporarily be extremely large, the Gilbert relaxation time can momentarily be
extremely short, reaching even picosecond timescales. Here we show that for
typical ultrashort pulses, the optical control of the magnetization emerges by
merely considering the optical magnetic field in the Landau-Lifshitz-Gilbert
(LLG) equation. Surprisingly, when circularly polarized optical pulses are
introduced to the LLG equation, an optically induced helicity-dependent torque
results. We find that the strength of the interaction is determined by
{\eta}={\alpha}{\gamma}H/f_opt, where f_opt and {\gamma} are the optical
frequency and gyromagnetic ratio. Our results illustrate the generality of the
LLG equation to the optical limit and the pivotal role of the Gilbert damping
in the general interaction between optical magnetic fields and spins in solids.
|
2306.04617v2
|
2018-04-03
|
Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms
|
The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains
as the cornerstone of contemporary magnetisation dynamics studies, wherein the
Gilbert damping parameter has been attributed to first-order relativistic
effects. To include magnetic inertial effects the LLG equation has previously
been extended with a supplemental inertia term and the arising inertial
dynamics has been related to second-order relativistic effects. Here we start
from the relativistic Dirac equation and, performing a Foldy-Wouthuysen
transformation, derive a generalised Pauli spin Hamiltonian that contains
relativistic correction terms to any higher order. Using the Heisenberg
equation of spin motion we derive general relativistic expressions for the
tensorial Gilbert damping and magnetic inertia parameters, and show that these
tensors can be expressed as series of higher-order relativistic correction
terms. We further show that, in the case of a harmonic external driving field,
these series can be summed and we provide closed analytical expressions for the
Gilbert and inertial parameters that are functions of the frequency of the
driving field.
|
1804.09242v1
|
2016-08-02
|
Ferromagnetic Damping/Anti-damping in a Periodic 2D Helical surface; A Non-Equilibrium Keldysh Green Function Approach
|
In this paper, we investigate theoretically the spin-orbit torque as well as
the Gilbert damping for a two band model of a 2D helical surface state with a
Ferromagnetic (FM) exchange coupling. We decompose the density matrix into the
Fermi sea and Fermi surface components and obtain their contributions to the
electronic transport as well as the spin-orbit torque (SOT). Furthermore, we
obtain the expression for the Gilbert damping due to the surface state of a 3D
Topological Insulator (TI) and predicted its dependence on the direction of the
magnetization precession axis.
|
1608.00984v2
|
2016-02-19
|
A systematic study of magnetodynamic properties at finite temperatures in doped permalloy from first principles calculations
|
By means of first principles calculations, we have systematically
investigated how the magnetodynamic properties Gilbert damping, magnetization
and exchange stiffness are affected when permalloy (Py)
(Fe$_{0.19}$Ni$_{0.81}$) is doped with 4d or 5d transition metal impurities. We
find that the trends in the Gilbert damping can be understood from relatively
few basic parameters such as the density of states at the Fermi level, the
spin-orbit coupling and the impurity concentration. % The temperature
dependence of the Gilbert damping is found to be very weak which we relate to
the lack of intraband transitions in alloys. % Doping with $4d$ elements has no
major impact on the studied Gilbert damping, apart from diluting the host.
However, the $5d$ elements have a profound effect on the damping and allows it
to be tuned over a large interval while maintaining the magnetization and
exchange stiffness. % As regards spin stiffness, doping with early transition
metals results in considerable softening, whereas late transition metals have a
minor impact. % Our result agree well with earlier calculations where
available. In comparison to experiments, the computed Gilbert damping appears
slightly underestimated while the spin stiffness show good general agreement.
|
1602.06201v2
|
2002-11-01
|
Exploring dynamical magnetism with time-dependent density-functional theory: from spin fluctuations to Gilbert damping
|
We use time-dependent spin-density-functional theory to study dynamical
magnetic phenomena. First, we recall that the local-spin-density approximation
(LSDA) fails to account correctly for magnetic fluctuations in the paramagnetic
state of iron and other itinerant ferromagnets. Next, we construct a
gradient-dependent density functional that does not suffer from this problem of
the LSDA. This functional is then used to derive, for the first time, the
phenomenological Gilbert equation of micromagnetics directly from
time-dependent density-functional theory. Limitations and extensions of Gilbert
damping are discussed on this basis, and some comparisons with phenomenological
theories and experiments are made.
|
0211021v1
|
2012-04-24
|
Nonlocal feedback in ferromagnetic resonance
|
Ferromagnetic resonance in thin films is analyzed under the influence of
spatiotemporal feedback effects. The equation of motion for the magnetization
dynamics is nonlocal in both space and time and includes isotropic, anisotropic
and dipolar energy contributions as well as the conserved Gilbert- and the
non-conserved Bloch-damping. We derive an analytical expression for the
peak-to-peak linewidth. It consists of four separate parts originated by
Gilbert damping, Bloch-damping, a mixed Gilbert-Bloch component and a
contribution arising from retardation. In an intermediate frequency regime the
results are comparable with the commonly used Landau-Lifshitz-Gilbert theory
combined with two-magnon processes. Retardation effects together with Gilbert
damping lead to a linewidth the frequency dependence of which becomes strongly
nonlinear. The relevance and the applicability of our approach to ferromagnetic
resonance experiments is discussed.
|
1204.5342v1
|
2017-04-24
|
Spin injection into silicon detected by broadband ferromagnetic resonance spectroscopy
|
We studied the spin injection in a NiFe(Py)/Si system using broadband
ferromagnetic resonance spectroscopy. The Gilbert damping parameter of the Py
layer on top of the Si channel was determined as a function of the Si doping
concentration and Py layer thickness. For fixed Py thickness we observed an
increase of the Gilbert damping parameter with decreasing resistivity of the Si
channel. For a fixed Si doping concentration we measured an increasing Gilbert
damping parameter for decreasing Py layer thickness. No increase of the Gilbert
damping parameter was found Py/Si samples with an insulating interlayer. We
attribute our observations to an enhanced spin injection into the
low-resistivity Si by spin pumping.
|
1704.07006v1
|
2019-11-07
|
Quantum Oscillations of Gilbert Damping in Ferromagnetic/Graphene Bilayer Systems
|
We study the spin dynamics of a ferromagnetic insulator on which graphene is
placed. We show that the Gilbert damping is enhanced by the proximity exchange
coupling at the interface. The modulation of the Gilbert damping constant is
proportional to the product of the spin-up and spin-down densities of states of
graphene. Consequently, the Gilbert damping constant in a strong magnetic field
oscillates as a function of the external magnetic field that originates from
the Landau level structure of graphene. We find that a measurement of the
oscillation period enables the strength of the exchange coupling constant to be
determined. The results demonstrate in theory that the ferromagnetic resonance
measurements may be used to detect the spin resolved electronic structure of
the adjacent materials, which is critically important for future spin device
evaluations.
|
1911.02775v2
|
2021-03-11
|
Magnetoelastic Gilbert damping in magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films
|
We report an enhanced magnetoelastic contribution to the Gilbert damping in
highly magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films. This effect is
mitigated for perpendicular-to-plane fields, leading to a large anisotropy of
the Gilbert damping in all of the films (up to a factor of 10 at room
temperature). These claims are supported by broadband measurements of the
ferromagnetic resonance linewidths over a range of temperatures (5 to 400 K),
which serve to elucidate the effect of both the magnetostriction and phonon
relaxation on the magnetoelastic Gilbert damping.
|
2103.07008v1
|
2022-01-27
|
Effect of vertex corrections on the enhancement of Gilbert damping in spin pumping into a two-dimensional electron gas
|
We theoretically consider the effect of vertex correction on spin pumping
from a ferromagnetic insulator (FI) into a two-dimensional electron gas (2DEG)
in which the Rashba and Dresselhaus spin-orbit interactions coexist. The
Gilbert damping in the FI is enhanced by elastic spin-flipping or magnon
absorption. We show that the Gilbert damping due to elastic spin-flipping is
strongly enhanced by the vertex correction when the ratio of the two spin-orbit
interactions is near a special value at which the spin relaxation time diverges
while that due to magnon absorption shows only small modification. We also show
that the shift in the resonant frequency due to elastic spin-flipping is
strongly enhanced in a similar way as the Gilbert damping.
|
2201.11498v3
|
2016-02-22
|
Effects of Landau-Lifshitz-Gilbert damping on domain growth
|
Domain patterns are simulated by the Landau-Lifshitz-Gilbert (LLG) equation
with an easy-axis anisotropy. If the Gilbert damping is removed from the LLG
equation, it merely describes the precession of magnetization with a
ferromagnetic interaction. However, even without the damping, domains that look
similar to those of scalar fields are formed, and they grow with time. It is
demonstrated that the damping has no significant effects on domain growth laws
and large-scale domain structure. In contrast, small-scale domain structure is
affected by the damping. The difference in small-scale structure arises from
energy dissipation due to the damping.
|
1602.06673v3
|
2018-06-13
|
Low magnetic damping of ferrimagnetic GdFeCo alloys
|
We investigate the Gilbert damping parameter for rare earth (RE)-transition
metal (TM) ferrimagnets over a wide temperature range. Extracted from the
field-driven magnetic domain-wall mobility, the Gilbert damping parameter was
as low as 0.0072 and was almost constant across the angular momentum
compensation temperature, starkly contrasting previous predictions that the
Gilbert damping parameter should diverge at the angular momentum compensation
temperature due to vanishing total angular momentum. Thus, magnetic damping of
RE-TM ferrimagnets is not related to the total angular momentum but is
dominated by electron scattering at the Fermi level where the TM has a dominant
damping role.
|
1806.04881v1
|
2023-06-22
|
Gilbert damping in metallic ferromagnets from Schwinger-Keldysh field theory: Intrinsically nonlocal and nonuniform, and made anisotropic by spin-orbit coupling
|
Understanding the origin of damping mechanisms in magnetization dynamics of
metallic ferromagnets is a fundamental problem for nonequilibrium many-body
physics of systems where quantum conduction electrons interact with localized
spins assumed to be governed by the classical Landau-Lifshitz-Gilbert (LLG)
equation. It is also of critical importance for applications, as damping
affects energy consumption and speed of spintronic and magnonic devices. Since
the 1970s, a variety of linear-response and scattering theory approaches have
been developed to produce widely used formulas for computation of
spatially-independent Gilbert scalar parameter as the magnitude of the Gilbert
damping term in the LLG equation. The largely unexploited for this purpose
Schwinger-Keldysh field theory (SKFT) offers additional possibilities, such as
to rigorously derive an extended LLG equation by integrating quantum electrons
out. Here we derive such equation whose Gilbert damping for metallic
ferromagnets is nonlocal, i.e., dependent on all localized spins at a given
time, and nonuniform, even if all localized spins are collinear and spin-orbit
coupling (SOC) is absent. This is in sharp contrast to standard lore, where
nonlocal damping is considered to emerge only if localized spins are
noncollinear; for such situations, direct comparison on the example of magnetic
domain wall shows that SKFT-derived nonlocal damping is an order of magnitude
larger than the previously considered one. Switching on SOC makes such nonlocal
damping anisotropic, in contrast to standard lore where SOC is usually
necessary to obtain nonzero Gilbert damping scalar parameter. Our analytical
formulas, with their nonlocality being more prominent in low spatial
dimensions, are fully corroborated by numerically exact quantum-classical
simulations.
|
2306.13013v4
|
2018-07-20
|
Another view on Gilbert damping in two-dimensional ferromagnets
|
A keen interest towards technological implications of spin-orbit driven
magnetization dynamics requests a proper theoretical description, especially in
the context of a microscopic framework, to be developed. Indeed, magnetization
dynamics is so far approached within Landau-Lifshitz-Gilbert equation which
characterizes torques on magnetization on purely phenomenological grounds.
Particularly, spin-orbit coupling does not respect spin conservation, leading
thus to angular momentum transfer to lattice and damping as a result. This
mechanism is accounted by the Gilbert damping torque which describes relaxation
of the magnetization to equilibrium. In this study we work out a microscopic
Kubo-St\v{r}eda formula for the components of the Gilbert damping tensor and
apply the elaborated formalism to a two-dimensional Rashba ferromagnet in the
weak disorder limit. We show that an exact analytical expression corresponding
to the Gilbert damping parameter manifests linear dependence on the scattering
rate and retains the constant value up to room temperature when no vibrational
degrees of freedom are present in the system. We argue that the methodology
developed in this paper can be safely applied to bilayers made of non- and
ferromagnetic metals, e.g., CoPt.
|
1807.07897v2
|
2017-05-21
|
Dynamical depinning of chiral domain walls
|
The domain wall depinning field represents the minimum magnetic field needed
to move a domain wall, typically pinned by samples' disorder or patterned
constrictions. Conventionally, such field is considered independent on the
Gilbert damping since it is assumed to be the field at which the Zeeman energy
equals the pinning energy barrier (both damping independent). Here, we analyse
numerically the domain wall depinning field as function of the Gilbert damping
in a system with perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya
interaction. Contrary to expectations, we find that the depinning field depends
on the Gilbert damping and that it strongly decreases for small damping
parameters. We explain this dependence with a simple one-dimensional model and
we show that the reduction of the depinning field is related to the internal
domain wall dynamics, proportional to the Dzyaloshinskii-Moriya interaction,
and the finite size of the pinning barriers.
|
1705.07489v2
|
2019-01-07
|
Giant anisotropy of Gilbert damping in epitaxial CoFe films
|
Tailoring Gilbert damping of metallic ferromagnetic thin films is one of the
central interests in spintronics applications. Here we report a giant Gilbert
damping anisotropy in epitaxial Co$_{50}$Fe$_{50}$ thin film with a
maximum-minimum damping ratio of 400 \%, determined by broadband spin-torque as
well as inductive ferromagnetic resonance. We conclude that the origin of this
damping anisotropy is the variation of the spin orbit coupling for different
magnetization orientations in the cubic lattice, which is further corroborate
from the magnitude of the anisotropic magnetoresistance in Co$_{50}$Fe$_{50}$.
|
1901.01941v1
|
2019-11-02
|
Tuning Non-Gilbert-type damping in FeGa films on MgO(001) via oblique deposition
|
The ability to tailor the damping factor is essential for spintronic and
spin-torque applications. Here, we report an approach to manipulate the damping
factor of FeGa/MgO(001) films by oblique deposition. Owing to the defects at
the surface or interface in thin films, two-magnon scattering (TMS) acts as a
non-Gilbert damping mechanism in magnetization relaxation. In this work, the
contribution of TMS was characterized by in-plane angular dependent
ferromagnetic resonance (FMR). It is demonstrated that the intrinsic Gilbert
damping is isotropic and invariant, while the extrinsic mechanism related to
TMS is anisotropic and can be tuned by oblique deposition. Furthermore, the two
and fourfold TMS related to the uniaxial magnetic anisotropy (UMA) and
magnetocrystalline anisotropy were discussed. Our results open an avenue to
manipulate magnetization relaxation in spintronic devices.
|
1911.00728v1
|
2001-10-11
|
Enhanced Gilbert Damping in Thin Ferromagnetic Films
|
Using a scattering matrix approach, the precession of the magnetization of a
ferromagnet is shown to transfer spins into adjacent normal metal layers. This
``pumping'' of spins slows down the precession corresponding to an enhanced
Gilbert damping factor in the Landau-Lifshitz equation. The damping is
expressed in terms of the scattering matrix of the ferromagnet-normal metal
interface, which is accessible to model and first-principles calculations. Our
estimates for permalloy thin films explain the trends observed in recent
experiments.
|
0110247v2
|
2002-02-11
|
Radiation Induced Landau-Lifshitz-Gilbert Damping in Ferromagnets
|
The Landau-Lifshitz-Gilbert damping coefficient employed in the analysis of
spin wave ferromagnetic resonance is related to the electrical conductivity of
the sample. The changing magnetization (with time) radiates electromagnetic
fields. The electromagnetic energy is then absorbed by the sample and the
resulting heating effect describes magnetic dissipative damping. The
ferromagnetic resonance relaxation rate theoretically depends on the geometry
(shape and size) of the sample as well as temperature in agreement with
experiment.
|
0202181v1
|
2006-01-10
|
Voltage dependence of Landau-Lifshitz-Gilbert damping of a spin in a current driven tunnel junction
|
We present a theory of Landau-Lifshitz-Gilbert damping $\alpha$ for a
localized spin ${\vec S}$ in the junction coupled to the conduction electrons
in both leads under an applied volatege $V$. We find the voltage dependence of
the damping term reflecting the energy dependence of the density of states. We
find the effect is linear in the voltage and cotrolled by particle-hole
asymmetry of the leads.
|
0601185v1
|
2015-02-06
|
Microscopic theory of Gilbert damping in metallic ferromagnets
|
We present a microscopic theory for magnetization relaxation in metallic
ferromagnets of nanoscopic dimensions that is based on the dynamic spin
response matrix in the presence of spin-orbit coupling. Our approach allows the
calculation of the spin excitation damping rate even for perfectly crystalline
systems, where existing microscopic approaches fail. We demonstrate that the
relaxation properties are not completely determined by the transverse
susceptibility alone, and that the damping rate has a non-negligible frequency
dependence in experimentally relevant situations. Our results indicate that the
standard Landau-Lifshitz-Gilbert phenomenology is not always appropriate to
describe spin dynamics of metallic nanostructure in the presence of strong
spin-orbit coupling.
|
1502.02068v1
|
2018-05-03
|
Exact Intrinsic Localized Excitation of an Anisotropic Ferromagnetic Spin Chain in External Magnetic Field with Gilbert Damping, Spin Current and PT-Symmetry
|
We obtain the exact one-spin intrinsic localized excitation in an anisotropic
Heisenberg ferromagnetic spin chain in a constant/variable external magnetic
field with Gilbert damping included. We also point out how an appropriate
magnitude spin current term in a spin transfer nano-oscillator (STNO) can
stabilize the tendency towards damping. Further, we show how this excitation
can be sustained in a recently suggested PT-symmetric magnetic nanostructure.
We also briefly consider more general spin excitations.
|
1805.01230v1
|
2011-09-22
|
Hole spin relaxation and coefficients in Landau-Lifshitz-Gilbert equation in ferromagnetic GaMnAs
|
We investigate the temperature dependence of the coefficients in the
Landau-Lifshitz-Gilbert equation in ferromagnetic GaMnAs by employing the Zener
model. We first calculate the hole spin relaxation time based on the
microscopic kinetic equation. We find that the hole spin relaxation time is
typically several tens femtoseconds and can present a nonmonotonic temperature
dependence due to the variation of the interband spin mixing, influenced by the
temperature related Zeeman splitting. With the hole spin relaxation time, we
are able to calculate the coefficients in the Landau-Lifshitz-Gilbert equation,
such as the Gilbert damping, nonadiabatic spin torque, spin stiffness and
vertical spin stiffness coefficients. We find that the nonadiabatic spin torque
coefficient $\beta$ is around $0.1\sim 0.3$ at low temperature, which is
consistent with the experiment [Adam {\em et al.}, Phys. Rev. B {\bf 80},
193204 (2009)]. As the temperature increases, $\beta$ monotonically increases
and can exceed one in the vicinity of the Curie temperature. In the low
temperature regime with $\beta<1$, the Gilbert damping coefficient $\alpha$
increases with temperature, showing good agreement with the experiments [Sinova
{\em et al.}, Phys. Rev. B {\bf 69}, 085209 (2004); Khazen {\em et al.}, {\em
ibid.} {\bf 78}, 195210 (2008)]. Furthermore, we predict that $\alpha$
decreases with increasing temperature once $\beta>1$ near the Curie
temperature. We also find that the spin stiffness decreases with increasing
temperature, especially near the Curie temperature due to the modification of
the finite $\beta$. Similar to the Gilbert damping, the vertical spin stiffness
coefficient is also found to be nonmonotonically dependent on the temperature.
|
1109.4964v1
|
2011-04-08
|
Magnetization Dissipation in Ferromagnets from Scattering Theory
|
The magnetization dynamics of ferromagnets are often formulated in terms of
the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation
describes the response of the magnetization in terms of effective fields,
whereas the dissipative part is parameterized by the Gilbert damping tensor. We
formulate a scattering theory for the magnetization dynamics and map this
description on the linearized LLG equation by attaching electric contacts to
the ferromagnet. The reactive part can then be expressed in terms of the static
scattering matrix. The dissipative contribution to the low-frequency
magnetization dynamics can be described as an adiabatic energy pumping process
to the electronic subsystem by the time-dependent magnetization. The Gilbert
damping tensor depends on the time derivative of the scattering matrix as a
function of the magnetization direction. By the fluctuation-dissipation
theorem, the fluctuations of the effective fields can also be formulated in
terms of the quasistatic scattering matrix. The theory is formulated for
general magnetization textures and worked out for monodomain precessions and
domain wall motions. We prove that the Gilbert damping from scattering theory
is identical to the result obtained by the Kubo formalism.
|
1104.1625v1
|
2022-02-12
|
Generalization of the Landau-Lifshitz-Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets
|
We propose a systematic and sequential expansion of the
Landau-Lifshitz-Gilbert equation utilizing the dependence of the Gilbert
damping tensor on the angle between magnetic moments, which arises from
multi-body scattering processes. The tensor consists of a damping-like term and
a correction to the gyromagnetic ratio. Based on electronic structure theory,
both terms are shown to depend on e.g. the scalar, anisotropic, vector-chiral
and scalar-chiral products of magnetic moments: $\vec{e}_i\cdot\vec{e}_j$,
$(\vec{n}_{ij}\cdot\vec{e}_i)(\vec{n}_{ij}\cdot\vec{e}_j)$,
$\vec{n}_{ij}\cdot(\vec{e}_i\times\vec{e}_j)$, $(\vec{e}_i\cdot\vec{e}_j)^2$,
$\vec{e}_i\cdot(\vec{e}_j\times\vec{e}_k)$..., where some terms are subjected
to the spin-orbit field $\vec{n}_{ij}$ in first and second order. We explore
the magnitude of the different contributions using both the Alexander-Anderson
model and time-dependent density functional theory in magnetic adatoms and
dimers deposited on Au(111) surface.
|
2202.06154v1
|
2022-11-23
|
The fractional Landau-Lifshitz-Gilbert equation
|
The dynamics of a magnetic moment or spin are of high interest to
applications in technology. Dissipation in these systems is therefore of
importance for improvement of efficiency of devices, such as the ones proposed
in spintronics. A large spin in a magnetic field is widely assumed to be
described by the Landau-Lifshitz-Gilbert (LLG) equation, which includes a
phenomenological Gilbert damping. Here, we couple a large spin to a bath and
derive a generic (non-)Ohmic damping term for the low-frequency range using a
Caldeira-Leggett model. This leads to a fractional LLG equation, where the
first-order derivative Gilbert damping is replaced by a fractional derivative
of order $s \ge 0$. We show that the parameter $s$ can be determined from a
ferromagnetic resonance experiment, where the resonance frequency and linewidth
no longer scale linearly with the effective field strength.
|
2211.12889v1
|
2018-05-04
|
Effective damping enhancement in noncollinear spin structures
|
Damping mechanisms in magnetic systems determine the lifetime, diffusion and
transport properties of magnons, domain walls, magnetic vortices, and
skyrmions. Based on the phenomenological Landau-Lifshitz-Gilbert equation, here
the effective damping parameter in noncollinear magnetic systems is determined
describing the linewidth in resonance experiments or the decay parameter in
time-resolved measurements. It is shown how the effective damping can be
calculated from the elliptic polarization of magnons, arising due to the
noncollinear spin arrangement. It is concluded that the effective damping is
larger than the Gilbert damping, and it may significantly differ between
excitation modes. Numerical results for the effective damping are presented for
the localized magnons in isolated skyrmions, with parameters based on the
Pd/Fe/Ir(111) model-type system.
|
1805.01815v2
|
2023-12-14
|
Nonlocal damping of spin waves in a magnetic insulator induced by normal, heavy, or altermagnetic metallic overlayer: a Schwinger-Keldysh field theory approach
|
Understanding spin wave (SW) damping, and how to control it to the point of
being able to amplify SW-mediated signals, is one of the key requirements to
bring the envisaged magnonic technologies to fruition. Even widely used
magnetic insulators with low magnetization damping in their bulk, such as
yttrium iron garnet, exhibit 100-fold increase in SW damping due to inevitable
contact with metallic layers in magnonic circuits, as observed in very recent
experiments [I. Bertelli et al., Adv. Quantum Technol. 4, 2100094 (2021)]
mapping SW damping in spatially-resolved fashion. Here, we provide microscopic
and rigorous understanding of wavevector-dependent SW damping using extended
Landau-Lifshitz-Gilbert equation with nonlocal damping tensor, instead of
conventional local scalar Gilbert damping, as derived from Schwinger-Keldysh
nonequilibrium quantum field theory. In this picture, the origin of nonlocal
magnetization damping and thereby induced wavevector-dependent SW damping is
interaction of localized magnetic moments of magnetic insulator with conduction
electrons from the examined three different types of metallic overlayers --
normal, heavy, and altermagnetic. Due to spin-split energy-momentum dispersion
of conduction electrons in the latter two cases, the nonlocal damping is
anisotropic in spin and space, and it can be dramatically reduced by changing
the relative orientation of the two layers when compared to the usage of normal
metal overlayer.
|
2312.09140v1
|
2017-03-20
|
Relativistic theory of magnetic inertia in ultrafast spin dynamics
|
The influence of possible magnetic inertia effects has recently drawn
attention in ultrafast magnetization dynamics and switching. Here we derive
rigorously a description of inertia in the Landau-Lifshitz-Gilbert equation on
the basis of the Dirac-Kohn-Sham framework. Using the Foldy-Wouthuysen
transformation up to the order of $1/c^4$ gives the intrinsic inertia of a pure
system through the 2$^{\rm nd}$ order time-derivative of magnetization in the
dynamical equation of motion. Thus, the inertial damping $\mathcal{I}$ is a
higher order spin-orbit coupling effect, $\sim 1/c^4$, as compared to the
Gilbert damping $\Gamma$ that is of order $1/c^2$. Inertia is therefore
expected to play a role only on ultrashort timescales (sub-picoseconds). We
also show that the Gilbert damping and inertial damping are related to one
another through the imaginary and real parts of the magnetic susceptibility
tensor respectively.
|
1704.01559v1
|
2019-07-10
|
The superior role of the Gilbert damping on the signal-to-noise ratio in heat-assisted magnetic recording
|
In magnetic recording the signal-to-noise ratio (SNR) is a good indicator for
the quality of written bits. However, a priori it is not clear which parameters
have the strongest influence on the SNR. In this work, we investigate the role
of the Gilbert damping on the SNR. Grains consisting of FePt like hard magnetic
material with two different grain sizes $d_1=5\,$nm and $d_2=7\,$nm are
considered and simulations of heat-assisted magnetic recording (HAMR) are
performed with the atomistic simulation program VAMPIRE. The simulations
display that the SNR saturates for damping constants larger or equal than 0.1.
Additionally, we can show that the Gilbert damping together with the bit length
have a major effect on the SNR whereas other write head and material parameters
only have a minor relevance on the SNR.
|
1907.04577v2
|
2019-10-24
|
Spin waves in ferromagnetic thin films
|
A spin wave is the disturbance of intrinsic spin order in magnetic materials.
In this paper, a spin wave in the Landau-Lifshitz-Gilbert equation is obtained
based on the assumption that the spin wave maintains its shape while it
propagates at a constant velocity. Our main findings include: (1) in the
absence of Gilbert damping, the spin wave propagates at a constant velocity
with the increment proportional to the strength of the magnetic field; (2) in
the absence of magnetic field, at a given time the spin wave converges
exponentially fast to its initial profile as the damping parameter goes to zero
and in the long time the relaxation dynamics of the spin wave converges
exponentially fast to the easy-axis direction with the exponent proportional to
the damping parameter; (3) in the presence of both Gilbert damping and magnetic
field, the spin wave converges to the easy-axis direction exponentially fast at
a small timescale while propagates at a constant velocity beyond that. These
provides a comprehensive understanding of spin waves in ferromagnetic
materials.
|
1910.11200v1
|
2020-06-30
|
Negative Gilbert damping in cavity optomagnonics
|
Exceptional point (EP) associated with the parity-time (PT) symmetry breaking
is receiving considerable recent attention by the broad physics community. By
introducing balanced gain and loss, it has been realized in photonic, acoustic,
and electronic structures. However, the observation of magnonic EP remains
elusive. The major challenge is to experimentally generate the negative Gilbert
damping, which was thought to be highly unlikely but is demanded by the PT
symmetry. In this work, we study the magneto-optical interaction of
circularly-polarized lasers with a submicron magnet placed in an optical
cavity. We show that the off-resonant coupling between the driving laser and
cavity photon in the far-blue detuning can induce the magnetic gain (or
negative damping) exactly of the Gilbert type. A hyperbolic-tangent function
ansatz is found to well describe the time-resolved spin switching as the
intrinsic magnetization dissipation is overcome. When the optically pumped
magnet interacts with a purely lossy one, we observe a phase transition from
the imbalanced to passive PT symmetries by varying the detuning coeffcient. Our
findings provide a feasible way to manipulate the sign of the magnetic damping
parameter and to realize the EP in cavity optomagnonics.
|
2006.16510v1
|
2017-11-20
|
Spin Pumping in Ion-beam Sputtered Co_{2}FeAl/Mo Bilayers:Interfacial Gilbert Damping
|
The spin pumping mechanism and associated interfacial Gilbert damping are
demonstrated in ion-beam sputtered Co2FeAl (CFA) /Mo bilayer thin films
employing ferromagnetic resonance spectroscopy. The dependence of the net spin
current transportation on Mo layer thickness, 0 to 10 nm, and the enhancement
of the net effective Gilbert damping are reported. The experimental data has
been analyzed using spin pumping theory in terms of spin current pumped through
the ferromagnet /nonmagnetic metal interface to deduce the effective spin
mixing conductance and the spin-diffusion length, which are estimated to be
1.16(0.19)x10^19 m^-2 and 3.50(0.35)nm, respectively. The damping constant is
found to be 8.4(0.3)x10^-3 in the Mo(3.5nm) capped CFA(8nm) sample
corresponding to a ~42% enhancement of the original Gilbert damping
(6.0(0.3)x10^-3) in the uncapped CFA layer. This is further confirmed by
inserting a Cu dusting layer which reduces the spin transport across the CFA
/Mo interface. The Mo layer thickness dependent net spin current density is
found to lie in the range of 1-3 MAm^-2, which also provides additional
quantitative evidence of spin pumping in this bilayer thin film system.
|
1711.07455v1
|
2014-04-05
|
Gilbert damping in noncollinear ferromagnets
|
The precession and damping of a collinear magnetization displaced from its
equilibrium are described by the Landau-Lifshitz-Gilbert equation. For a
noncollinear magnetization, it is not known how the damping should be
described. We use first-principles scattering theory to investigate the damping
in one-dimensional transverse domain walls (DWs) of the important ferromagnetic
alloy Ni$_{80}$Fe$_{20}$ and interpret the results in terms of phenomenological
models. The damping is found to depend not only on the magnetization texture
but also on the specific dynamic modes of Bloch and N\'eel DWs. Even in the
highly disordered Ni$_{80}$Fe$_{20}$ alloy, the damping is found to be
remarkably nonlocal.
|
1404.1488v2
|
2003-04-04
|
Dynamic exchange coupling and Gilbert damping in magnetic multilayers
|
We theoretically study dynamic properties of thin ferromagnetic films in
contact with normal metals. Moving magnetizations cause a flow of spins into
adjacent conductors, which relax by spin flip, scatter back into the
ferromagnet, or are absorbed by another ferromagnet. Relaxation of spins
outside the moving magnetization enhances the overall damping of the
magnetization dynamics in accordance with the Gilbert phenomenology. Transfer
of spins between different ferromagnets by these nonequilibrium spin currents
leads to a long-ranged dynamic exchange interaction and novel collective
excitation modes. Our predictions agree well with recent
ferromagnetic-resonance experiments on ultrathin magnetic films.
|
0304116v1
|
2008-08-09
|
Gilbert Damping in Conducting Ferromagnets I: Kohn-Sham Theory and Atomic-Scale Inhomogeneity
|
We derive an approximate expression for the Gilbert damping coefficient
\alpha_G of itinerant electron ferromagnets which is based on their description
in terms of spin-density-functional-theory (SDFT) and Kohn-Sham quasiparticle
orbitals. We argue for an expression in which the coupling of magnetization
fluctuations to particle-hole transitions is weighted by the spin-dependent
part of the theory's exchange-correlation potential, a quantity which has large
spatial variations on an atomic length scale. Our SDFT result for \alpha_G is
closely related to the previously proposed spin-torque correlation-function
expression.
|
0808.1373v1
|
2012-03-03
|
Scaling of intrinsic Gilbert damping with spin-orbital coupling strength
|
We have experimentally and theoretically investigated the dependence of the
intrinsic Gilbert damping parameter $\alpha_0$ on the spin-orbital coupling
strength $\xi$ by using L1$_{\mathrm{0}}$ ordered
FePd$_{\mathrm{1-x}}$Pt$_{\mathrm{x}}$ ternary alloy films with perpendicular
magnetic anisotropy. With the time-resolved magneto-optical Kerr effect,
$\alpha_0$ is found to increase by more than a factor of ten when $x$ varies
from 0 to 1.0. Since changes of other leading parameters are found to be
neglected, the $\alpha_0$ has for the first time been proven to be proportional
to $\xi^2$.
|
1203.0607v1
|
2013-03-20
|
Spin-pumping and Enhanced Gilbert Damping in Thin Magnetic Insulator Films
|
Precessing magnetization in a thin film magnetic insulator pumps spins into
adjacent metals; however, this phenomenon is not quantitatively understood. We
present a theory for the dependence of spin-pumping on the transverse mode
number and in-plane wave vector. For long-wavelength spin waves, the enhanced
Gilbert damping for the transverse mode volume waves is twice that of the
macrospin mode, and for surface modes, the enhancement can be ten or more times
stronger. Spin-pumping is negligible for short-wavelength exchange spin waves.
We corroborate our analytical theory with numerical calculations in agreement
with recent experimental results.
|
1303.4922v1
|
2022-06-10
|
Spin Pumping into Anisotropic Dirac Electrons
|
We study spin pumping into an anisotropic Dirac electron system induced by
microwave irradiation to an adjacent ferromagnetic insulator theoretically. We
formulate the Gilbert damping enhancement due to the spin current flowing into
the Dirac electron system using second-order perturbation with respect to the
interfacial exchange coupling. As an illustration, we consider the anisotropic
Dirac system realized in bismuth to show that the Gilbert damping varies
according to the magnetization direction in the ferromagnetic insulator. Our
results indicate that this setup can provide helpful information on the
anisotropy of the Dirac electron system.
|
2206.04899v1
|
2023-03-02
|
Spin Pumping into Carbon Nanotubes
|
We theoretically study spin pumping from a ferromagnetic insulator (FI) into
a carbon nanotube (CNT). By employing the bosonization method, we formulate the
Gilbert damping induced by the FI/CNT junction, which can be measured by
ferromagnetic resonance. We show that the increase in the Gilbert damping has a
temperature dependence characteristic of a Luttinger liquid and is highly
sensitive to the Luttinger parameter of the spin sector for a clean interface.
We also discuss the experimental relevance of our findings based on numerical
estimates, using realistic parameters.
|
2303.01343v2
|
2019-08-29
|
Enhancement of ultrafast demagnetization rate and Gilbert damping driven by femtosecond laser-induced spin currents in Fe81Ga19/Ir20Mn80 bilayers
|
In spintronics applications, ultrafast spin dynamics have to be controlled at
femtosecond (fs) timescales via fs-laser radiation. At such ultrafast
timescales, the effect of the Gilbert damping factor {\alpha} on ultrafast
demagnetization time should be considered. In previous explorations for the
relationship between these two parameters, it was found that the theoretical
calculations based on the local spin-flip scattering model do not agree with
the experimental results. Here, we find that in Fe81Ga19(FeGa)/Ir20Mn80(IrMn)
bilayers, the unconventional IrMn thickness dependence of {\alpha} results from
the competition between spin currents pumped from the ferromagnetic (FM) FeGa
layer to the antiferromagnetic (AFM) IrMn layer and those pumped from the AFM
layer to the FM layer. More importantly, we establish a proportional
relationship between the change of the ultrafast demagnetization rate and the
enhancement of Gilbert damping induced by the spin currents via interfacial
spin chemical potential . Our work builds a bridge to connect the ultrafast
demagnetization time and Gilbert damping in ultrafast photo-induced spin
currents dominated systems, which not only explains the disagreement between
experimental and theoretical results in the relation of {\tau}_M with {\alpha},
but provides further insight into ultrafast spin dynamics as well.
|
1908.11084v1
|
2021-09-08
|
Room-Temperature Intrinsic and Extrinsic Damping in Polycrystalline Fe Thin Films
|
We examine room-temperature magnetic relaxation in polycrystalline Fe films.
Out-of-plane ferromagnetic resonance (FMR) measurements reveal Gilbert damping
parameters of $\approx$ 0.0024 for Fe films with thicknesses of 4-25 nm,
regardless of their microstructural properties. The remarkable invariance with
film microstructure strongly suggests that intrinsic Gilbert damping in
polycrystalline metals at room temperature is a local property of nanoscale
crystal grains, with limited impact from grain boundaries and film roughness.
By contrast, the in-plane FMR linewidths of the Fe films exhibit distinct
nonlinear frequency dependences, indicating the presence of strong extrinsic
damping. To fit our in-plane FMR data, we have used a grain-to-grain two-magnon
scattering model with two types of correlation functions aimed at describing
the spatial distribution of inhomogeneities in the film. However, neither of
the two correlation functions is able to reproduce the experimental data
quantitatively with physically reasonable parameters. Our findings advance the
fundamental understanding of intrinsic Gilbert damping in structurally
disordered films, while demonstrating the need for a deeper examination of how
microstructural disorder governs extrinsic damping.
|
2109.03684v2
|
2006-06-09
|
Spin wave dynamics and the determination of intrinsic Gilbert damping in locally-excited Permalloy thin films
|
Time-resolved scanning Kerr effect microscopy has been used to study
magnetization dynamics in Permalloy thin films excited by transient magnetic
pulses generated by a micrometer-scale transmission line structure. The results
are consistent with magnetostatic spin wave theory and are supported by
micromagnetic simulations. Magnetostatic volume and surface spin waves are
measured for the same specimen using different bias field orientations and can
be accurately calculated by k-space integrations over all excited plane wave
components. A single damping constant of Gilbert form is sufficient to describe
both scenarios. The nonuniform pulsed field plays a key role in the spin wave
dynamics, with its Fourier transform serving as a weighting function for the
participating modes. The intrinsic Gilbert damping parameter $\alpha$ is most
conveniently measured when the spin waves are effectively stationary.
|
0606235v3
|
2007-05-10
|
Effective temperature and Gilbert damping of a current-driven localized spin
|
Starting from a model that consists of a semiclassical spin coupled to two
leads we present a microscopic derivation of the Langevin equation for the
direction of the spin. For slowly-changing direction it takes on the form of
the stochastic Landau-Lifschitz-Gilbert equation. We give expressions for the
Gilbert damping parameter and the strength of the fluctuations, including their
bias-voltage dependence. At nonzero bias-voltage the fluctuations and damping
are not related by the fluctuation-dissipation theorem. We find, however, that
in the low-frequency limit it is possible to introduce a voltage-dependent
effective temperature that characterizes the fluctuations in the direction of
the spin, and its transport-steady-state probability distribution function.
|
0705.1432v3
|
2012-11-15
|
Spin transport and tunable Gilbert damping in a single-molecule magnet junction
|
We study time-dependent electronic and spin transport through an electronic
level connected to two leads and coupled with a single-molecule magnet via
exchange interaction. The molecular spin is treated as a classical variable and
precesses around an external magnetic field. We derive expressions for charge
and spin currents by means of the Keldysh non-equilibrium Green's functions
technique in linear order with respect to the time-dependent magnetic field
created by this precession. The coupling between the electronic spins and the
magnetization dynamics of the molecule creates inelastic tunneling processes
which contribute to the spin currents. The inelastic spin currents, in turn,
generate a spin-transfer torque acting on the molecular spin. This back-action
includes a contribution to the Gilbert damping and a modification of the
precession frequency. The Gilbert damping coefficient can be controlled by the
bias and gate voltages or via the external magnetic field and has a
non-monotonic dependence on the tunneling rates.
|
1211.3611v2
|
2014-12-05
|
Calculating linear response functions for finite temperatures on the basis of the alloy analogy model
|
A scheme is presented that is based on the alloy analogy model and allows to
account for thermal lattice vibrations as well as spin fluctuations when
calculating response quantities in solids. Various models to deal with spin
fluctuations are discussed concerning their impact on the resulting temperature
dependent magnetic moment, longitudinal conductivity and Gilbert damping
parameter. It is demonstrated that using the Monte Carlo (MC) spin
configuration as an input, the alloy analogy model is capable to reproduce
results of MC simulations on the average magnetic moment within all spin
fluctuation models under discussion. On the other hand, response quantities are
much more sensitive to the spin fluctuation model. Separate calculations
accounting for either the thermal effect due to lattice vibrations or spin
fluctuations show their comparable contributions to the electrical conductivity
and Gilbert damping. However, comparison to results accounting for both thermal
effects demonstrate violation of Matthiessen's rule, showing the non-additive
effect of lattice vibrations and spin fluctuations. The results obtained for
bcc Fe and fcc Ni are compared with the experimental data, showing rather good
agreement for the temperature dependent electrical conductivity and Gilbert
damping parameter.
|
1412.1988v1
|
2015-10-13
|
Nonlocal torque operators in ab initio theory of the Gilbert damping in random ferromagnetic alloys
|
We present an ab initio theory of the Gilbert damping in substitutionally
disordered ferromagnetic alloys. The theory rests on introduced nonlocal
torques which replace traditional local torque operators in the well-known
torque-correlation formula and which can be formulated within the atomic-sphere
approximation. The formalism is sketched in a simple tight-binding model and
worked out in detail in the relativistic tight-binding linear muffin-tin
orbital (TB-LMTO) method and the coherent potential approximation (CPA). The
resulting nonlocal torques are represented by nonrandom, non-site-diagonal and
spin-independent matrices, which simplifies the configuration averaging. The
CPA-vertex corrections play a crucial role for the internal consistency of the
theory and for its exact equivalence to other first-principles approaches based
on the random local torques. This equivalence is also illustrated by the
calculated Gilbert damping parameters for binary NiFe and FeCo random alloys,
for pure iron with a model atomic-level disorder, and for stoichiometric FePt
alloys with a varying degree of L10 atomic long-range order.
|
1510.03571v2
|
2016-12-07
|
Gilbert damping of magnetostatic modes in a yttrium iron garnet sphere
|
The magnetostatic mode (MSM) spectrum of a 300$\mu$m diameter single
crystalline sphere of yttrium iron garnet is investigated using broadband
ferromagnetic resonance (FMR). The individual MSMs are identified via their
characteristic dispersion relations and the corresponding mode number tuples
$(nmr)$ are assigned. Taking FMR data over a broad frequency and magnetic field
range allows to analyze both the Gilbert damping parameter~$\alpha$ and the
inhomogeneous line broadening contribution to the total linewidth of the MSMs
separately. The linewidth analysis shows that all MSMs share the same Gilbert
damping parameter $\alpha=2.7(5) \times 10^{-5}$ irrespective of their mode
index. In contrast, the inhomogeneous line broadening shows a pronounced mode
dependence. This observation is modeled in terms of two-magnon scattering
processes of the MSMs into the spin-wave manifold, mediated by surface and
volume defects.
|
1612.02360v1
|
2018-05-29
|
Gilbert damping in non-collinear magnetic system
|
The modification of the magnetization dissipation or Gilbert damping caused
by an inhomogeneous magnetic structure and expressed in terms of a wave vector
dependent tensor $\underline{\alpha}(\vec{q})$ is investigated by means of
linear response theory. A corresponding expression for
$\underline{\alpha}(\vec{q})$ in terms of the electronic Green function has
been developed giving in particular the leading contributions to the Gilbert
damping linear and quadratic in $q$. Numerical results for realistic systems
are presented that have been obtained by implementing the scheme within the
framework of the fully relativistic KKR (Korringa-Kohn-Rostoker) band structure
method. Using the multilayered system (Cu/Fe$_{1-x}$Co$_x$/Pt)$_n$ as an
example for systems without inversion symmetry we demonstrate the occurrence of
non-vanishing linear contributions. For the alloy system bcc Fe$_{1-x}$Co$_x$
having inversion symmetry, on the other hand, only the quadratic contribution
is non-zero. As it is shown, this quadratic contribution does not vanish even
if the spin-orbit coupling is suppressed, i.e.\ it is a direct consequence of
the non-collinear spin configuration.
|
1805.11468v1
|
2018-10-15
|
Localized spin waves in isolated $kπ$ skyrmions
|
The localized magnon modes of isolated $k\pi$ skyrmions on a field-polarized
background are analyzed based on the Landau-Lifshitz-Gilbert equation within
the terms of an atomistic classical spin model, with system parameters based on
the Pd/Fe biatomic layer on Ir(111). For increasing skyrmion order $k$ a higher
number of excitation modes are found, including modes with nodes in the radial
eigenfunctions. It is shown that at low fields $2\pi$ and $3\pi$ skyrmions are
destroyed via a burst instability connected to a breathing mode, while $1\pi$
skyrmions undergo an elliptic instability. At high fields all $k\pi$ skyrmions
collapse due to the instability of a breathing mode. The effective damping
parameters of the spin waves are calculated in the low Gilbert damping limit,
and they are found to diverge in the case of the lowest-lying modes at the
burst and collapse instabilities, but not at the elliptic instability. It is
shown that the breathing modes of $k\pi$ skyrmions may become overdamped at
higher Gilbert damping values.
|
1810.06471v1
|
2018-10-24
|
Nearly isotropic spin-pumping related Gilbert damping in Pt/Ni$_{81}$Fe$_{19}$/Pt
|
A recent theory by Chen and Zhang [Phys. Rev. Lett. 114, 126602 (2015)]
predicts strongly anisotropic damping due to interfacial spin-orbit coupling in
ultrathin magnetic films. Interfacial Gilbert-type relaxation, due to the spin
pumping effect, is predicted to be significantly larger for magnetization
oriented parallel to compared with perpendicular to the film plane. Here, we
have measured the anisotropy in the Pt/Ni$_{81}$Fe$_{19}$/Pt system via
variable-frequency, swept-field ferromagnetic resonance (FMR). We find a very
small anisotropy of enhanced Gilbert damping with sign opposite to the
prediction from the Rashba effect at the FM/Pt interface. The results are
contrary to the predicted anisotropy and suggest that a mechanism separate from
Rashba spin-orbit coupling causes the rapid onset of spin-current absorption in
Pt.
|
1810.10595v4
|
2019-11-08
|
Giant anisotropy of Gilbert damping in a Rashba honeycomb antiferromagnet
|
Giant Gilbert damping anisotropy is identified as a signature of strong
Rashba spin-orbit coupling in a two-dimensional antiferromagnet on a honeycomb
lattice. The phenomenon originates in spin-orbit induced splitting of
conduction electron subbands that strongly suppresses certain spin-flip
processes. As a result, the spin-orbit interaction is shown to support an
undamped non-equilibrium dynamical mode that corresponds to an ultrafast
in-plane N\'eel vector precession and a constant perpendicular-to-the-plane
magnetization. The phenomenon is illustrated on the basis of a two dimensional
$s$-$d$ like model. Spin-orbit torques and conductivity are also computed
microscopically for this model. Unlike Gilbert damping these quantities are
shown to reveal only a weak anisotropy that is limited to the semiconductor
regime corresponding to the Fermi energy staying in a close vicinity of
antiferromagnetic gap.
|
1911.03408v1
|
2005-05-10
|
Fluctuation-dissipation considerations and damping models for ferromagnetic materials
|
The role of fluctuation-dissipation relations (theorems) for the
magnetization dynamics with Landau-Lifshitz-Gilbert and Bloch-Bloembergen
damping terms are discussed. We demonstrate that the use of the Callen-Welton
fluctuation-dissipation theorem that was proven for Hamiltonian systems can
give an inconsistent result for magnetic systems with dissipation.
|
0505259v1
|
2018-07-13
|
Gilbert damping of high anisotropy Co/Pt multilayers
|
Using broadband ferromagnetic resonance, we measure the damping parameter of
[Co(5 \r{A})/Pt(3 \r{A})]${\times 6}$ multilayers whose growth was optimized to
maximize the perpendicular anisotropy. Structural characterizations indicate
abrupt interfaces essentially free of intermixing despite the miscible
character of Co and Pt. Gilbert damping parameters as low as 0.021 can be
obtained despite a magneto-crystalline anisotropy as large as
$10^6~\textrm{J/m}^3$. The inhomogeneous broadening accounts for part of the
ferromagnetic resonance linewidth, indicating some structural disorder leading
to a equivalent 20 mT of inhomogenity of the effective field. The unexpectedly
relatively low damping factor indicates that the presence of the Pt heavy metal
within the multilayer may not be detrimental to the damping provided that
intermixing is avoided at the Co/Pt interfaces.
|
1807.04977v1
|
2019-08-23
|
Damping enhancement in coherent ferrite/insulating-paramagnet bilayers
|
High-quality epitaxial ferrites, such as low-damping MgAl-ferrite (MAFO), are
promising nanoscale building blocks for all-oxide heterostructures driven by
pure spin current. However, the impact of oxide interfaces on spin dynamics in
such heterostructures remains an open question. Here, we investigate the spin
dynamics and chemical and magnetic depth profiles of 15-nm-thick MAFO
coherently interfaced with an isostructural $\approx$1-8-nm-thick overlayer of
paramagnetic CoCr$_2$O$_4$ (CCO) as an all-oxide model system. Compared to MAFO
without an overlayer, effective Gilbert damping in MAFO/CCO is enhanced by a
factor of $>$3, irrespective of the CCO overlayer thickness. We attribute this
damping enhancement to spin scattering at the $\sim$1-nm-thick chemically
disordered layer at the MAFO/CCO interface, rather than spin pumping or
proximity-induced magnetism. Our results indicate that damping in ferrite-based
heterostructures is strongly influenced by interfacial chemical disorder, even
if the thickness of the disordered layer is a small fraction of the ferrite
thickness.
|
1908.08629v2
|
2021-05-08
|
A second-order numerical method for Landau-Lifshitz-Gilbert equation with large damping parameters
|
A second order accurate numerical scheme is proposed and implemented for the
Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in
ferromagnetic materials, with large damping parameters. The main advantages of
this method are associated with the following features: (1) It only solves
linear systems of equations with constant coefficients where fast solvers are
available, so that the numerical efficiency has been greatly improved, in
comparison with the existing Gauss-Seidel project method. (2) The second-order
accuracy in time is achieved, and it is unconditionally stable for large
damping parameters. Moreover, both the second-order accuracy and the great
efficiency improvement will be verified by several numerical examples in the 1D
and 3D simulations. In the presence of large damping parameters, it is observed
that this method is unconditionally stable and finds physically reasonable
structures while many existing methods have failed. For the domain wall
dynamics, the linear dependence of wall velocity with respect to the damping
parameter and the external magnetic field will be obtained through the reported
simulations.
|
2105.03576v1
|
2006-11-23
|
Analytical solutions for two-level systems with damping
|
A method is proposed to transform any analytic solution of the Bloch equation
into an analytic solution of the Landau-Lifshitz-Gilbert equation. This allows
for the analytical description of the dynamics of a two level system with
damping. This method shows that damping turns the linear Schr\"{o}dinger
equation of a two-level system into a nonlinear Schr\"{o}dinger equation. As
applications, it is shown that damping has a relatively mild influence on
self-induced transparency but destroys dynamical localization.
|
0611238v1
|
2017-01-10
|
Magnetic properties in ultra-thin 3d transition metal alloys II: Experimental verification of quantitative theories of damping and spin-pumping
|
A systematic experimental study of Gilbert damping is performed via
ferromagnetic resonance for the disordered crystalline binary 3d transition
metal alloys Ni-Co, Ni-Fe and Co-Fe over the full range of alloy compositions.
After accounting for inhomogeneous linewidth broadening, the damping shows
clear evidence of both interfacial damping enhancement (by spin pumping) and
radiative damping. We quantify these two extrinsic contributions and thereby
determine the intrinsic damping. The comparison of the intrinsic damping to
multiple theoretical calculations yields good qualitative and quantitative
agreement in most cases. Furthermore, the values of the damping obtained in
this study are in good agreement with a wide range of published experimental
and theoretical values. Additionally, we find a compositional dependence of the
spin mixing conductance.
|
1701.02475v1
|
2004-12-18
|
Fluctuations of the Magnetization in Thin Films due to Conduction Electrons
|
A detailed analysis of damping and noise due to a {\it sd}-interaction in a
thin ferromagnetic film sandwiched between two large normal metal layers is
carried out. The magnetization is shown to obey in general a non-local equation
of motion which differs from the the Gilbert equation and is extended to the
non-adiabatic regime. To lowest order in the exchange interaction and in the
limit where the Gilbert equation applies, we show that the damping term is
enhanced due to interfacial effects but it also shows oscillations as a
function of the film thickness. The noise calculation is however carried out to
all orders in the exchange coupling constant. The ellipticity of the precession
of the magnetization is taken into account. The damping is shown to have a
Gilbert form only in the adiabatic limit while the relaxation time becomes
strongly dependent on the geometry of the thin film. It is also shown that the
induced noise characteristic of sd-exchange is inherently colored in character
and depends on the symmetry of the Hamiltonian of the magnetization in the
film. We show that the sd-noise can be represented in terms of an external
stochastic field which is white only in the adiabatic regime. The temperature
is also renormalized by the spin accumulation in the system. For large
intra-atomic exchange interactions, the Gilbert-Brown equation is no longer
valid.
|
0412510v1
|
2014-07-02
|
Spin Waves in Ferromagnetic Insulators Coupled via a Normal Metal
|
Herein, we study the spin-wave dispersion and dissipation in a ferromagnetic
insulator--normal metal--ferromagnetic insulator system. Long-range dynamic
coupling because of spin pumping and spin transfer lead to collective magnetic
excitations in the two thin-film ferromagnets. In addition, the dynamic dipolar
field contributes to the interlayer coupling. By solving the
Landau-Lifshitz-Gilbert-Slonczewski equation for macrospin excitations and the
exchange-dipole volume as well as surface spin waves, we compute the effect of
the dynamic coupling on the resonance frequencies and linewidths of the various
modes. The long-wavelength modes may couple acoustically or optically. In the
absence of spin-memory loss in the normal metal, the spin-pumping-induced
Gilbert damping enhancement of the acoustic mode vanishes, whereas the optical
mode acquires a significant Gilbert damping enhancement, comparable to that of
a system attached to a perfect spin sink. The dynamic coupling is reduced for
short-wavelength spin waves, and there is no synchronization. For intermediate
wavelengths, the coupling can be increased by the dipolar field such that the
modes in the two ferromagnetic insulators can couple despite possible small
frequency asymmetries. The surface waves induced by an easy-axis surface
anisotropy exhibit much greater Gilbert damping enhancement. These modes also
may acoustically or optically couple, but they are unaffected by thickness
asymmetries.
|
1407.0635v1
|
2009-04-21
|
Tensor damping in metallic magnetic multilayers
|
The mechanism of spin-pumping, described by Tserkovnyak et al., is formally
analyzed in the general case of a magnetic multilayer consisting of two or more
metallic ferromagnetic (FM) films separated by normal metal (NM) layers. It is
shown that the spin-pumping-induced dynamic coupling between FM layers modifies
the linearized Gilbert equations in a way that replaces the scalar Gilbert
damping constant with a nonlocal matrix of Cartesian damping tensors. The
latter are shown to be methodically calculable from a matrix algebra solution
of the Valet-Fert transport equations. As an example, explicit analytical
results are obtained for a 5-layer (spin-valve) of form NM/FM/NM'/FM/NM.
Comparisons with earlier well known results of Tserkovnyak et al. for the
related 3-layer FM/NM/FM indicate that the latter inadvertently hid the tensor
character of the damping, and instead singled out the diagonal element of the
local damping tensor along the axis normal to the plane of the two
magnetization vectors. For spin-valve devices of technological interest, the
influence of the tensor components of the damping on thermal noise or
spin-torque critical currents are strongly weighted by the relative magnitude
of the elements of the nonlocal, anisotropic stiffness-field tensor-matrix, and
for in-plane magnetized spin-valves are generally more sensitive to the
in-plane element of the damping tensor.
|
0904.3150v2
|
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
|
2003-09-29
|
Damping rates of the atomic velocity in Sisyphus cooling
|
We present a theoretical and experimental study of the damping process of the
atomic velocity in Sisyphus cooling. The relaxation rates of the atomic kinetic
temperature are determined for a 3D lin$\perp$lin optical lattice. We find that
the damping rates of the atomic temperature depend linearly on the optical
pumping rate, for a given depth of the potential wells. This is at variance
with the behavior of the friction coefficient as calculated from the spatial
diffusion coefficients within a model of Brownian motion. The origin of this
different behavior is identified by distinguishing the role of the trapped and
traveling atoms.
|
0309209v1
|
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
|
2008-07-18
|
Current-induced dynamics of spiral magnet
|
We study the dynamics of the spiral magnet under the charge current by
solving the Landau-Lifshitz-Gilbert equation numerically. In the steady state,
the current ${\vec j}$ induces (i) the parallel shift of the spiral pattern
with velocity $v=(\beta/\alpha)j$ ($\alpha$, $\beta$: the Gilbert damping
coefficients), (ii) the uniform magnetization $M$ parallel or anti-parallel to
the current depending on the chirality of the spiral and the ratio $\beta /
\alpha $, and (iii) the change in the wavenumber $k$ of the spiral. These are
analyzed by the continuum effective theory using the scaling argument, and the
various nonequilibrium phenomena such as the chaotic behavior and
current-induced annealing are also discussed.
|
0807.2901v1
|
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
|
2010-03-19
|
Dynamics of magnetization on the topological surface
|
We investigate theoretically the dynamics of magnetization coupled to the
surface Dirac fermions of a three dimensional topological insulator, by
deriving the Landau-Lifshitz-Gilbert (LLG) equation in the presence of charge
current. Both the inverse spin-Galvanic effect and the Gilbert damping
coefficient $\alpha$ are related to the two-dimensional diagonal conductivity
$\sigma_{xx}$ of the Dirac fermion, while the Berry phase of the ferromagnetic
moment to the Hall conductivity $\sigma_{xy}$. The spin transfer torque and the
so-called $\beta$-terms are shown to be negligibly small. Anomalous behaviors
in various phenomena including the ferromagnetic resonance are predicted in
terms of this LLG equation.
|
1003.3769v1
|
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
|
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
|
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