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2017-06-14
|
Temperature-dependent Gilbert damping of Co2FeAl thin films with different degree of atomic order
|
Half-metallicity and low magnetic damping are perpetually sought for in
spintronics materials and full Heusler alloys in this respect provide
outstanding properties. However, it is challenging to obtain the well-ordered
half-metallic phase in as-deposited full Heusler alloys thin films and theory
has struggled to establish a fundamentals understanding of the temperature
dependent Gilbert damping in these systems. Here we present a study of the
temperature dependent Gilbert damping of differently ordered as-deposited
Co2FeAl full Heusler alloy thin films. The sum of inter- and intraband electron
scattering in conjunction with the finite electron lifetime in Bloch states
govern the Gilbert damping for the well-ordered phase in contrast to the
damping of partially-ordered and disordered phases which is governed by
interband electronic scattering alone. These results, especially the ultralow
room temperature intrinsic damping observed for the well-ordered phase provide
new fundamental insights to the physical origin of the Gilbert damping in full
Heusler alloy thin films.
|
1706.04670v2
|
2023-11-27
|
Gilbert damping in two-dimensional metallic anti-ferromagnets
|
A finite spin life-time of conduction electrons may dominate Gilbert damping
of two-dimensional metallic anti-ferromagnets or anti-ferromagnet/metal
heterostructures. We investigate the Gilbert damping tensor for a typical
low-energy model of a metallic anti-ferromagnet system with honeycomb magnetic
lattice and Rashba spin-orbit coupling for conduction electrons. We distinguish
three regimes of spin relaxation: exchange-dominated relaxation for weak
spin-orbit coupling strength, Elliot-Yafet relaxation for moderate spin-orbit
coupling, and Dyakonov-Perel relaxation for strong spin-orbit coupling. We
show, however, that the latter regime takes place only for the in-plane Gilbert
damping component. We also show that anisotropy of Gilbert damping persists for
any finite spin-orbit interaction strength provided we consider no spatial
variation of the N\'eel vector. Isotropic Gilbert damping is restored only if
the electron spin-orbit length is larger than the magnon wavelength. Our theory
applies to MnPS3 monolayer on Pt or to similar systems.
|
2311.16268v2
|
2013-08-01
|
Inverse Spin Hall Effect in nanometer-thick YIG/Pt system
|
High quality nanometer-thick (20 nm, 7 nm and 4 nm) epitaxial YIG films have
been grown on GGG substrates using pulsed laser deposition. The Gilbert damping
coefficient for the 20 nm thick films is 2.3 x 10-4 which is the lowest value
reported for sub-micrometric thick films. We demonstrate Inverse spin Hall
effect (ISHE) detection of propagating spin waves using Pt. The amplitude and
the lineshape of the ISHE voltage correlate well to the increase of the Gilbert
damping when decreasing thickness of YIG. Spin Hall effect based
loss-compensation experiments have been conducted but no change in the
magnetization dynamics could be detected.
|
1308.0192v1
|
2020-08-14
|
Large enhancement of spin pumping due to the surface bound states in normal metal/superconductor structures
|
We show that the spin pumping from ferromagnetic insulator into the adjacent
metallic spin sink can be strongly stimulated by the superconducting
correlations.
The key physical mechanism responsible for this effect is the presence of
quasiparticle surface states at the ferromagnetic insulator/superconductor
interface. We consider the minimal model when these states appear because of
the suppressed pairing constant within the interfacial normal layer. For thin
normal layers we obtain a strongly peaked temperature dependence of the Gilbert
damping coefficient which has been recently observed in such systems. For
thicker normal layers the Gilbert damping monotonically increases down to the
temperatures much smaller than the critical one. The suggested model paves the
way to controlling the temperature dependence of the spin pumping by
fabricating hybrid normal metal/superconductor spin sinks.
|
2008.06253v1
|
2012-07-28
|
Ultrafast optical control of magnetization in EuO thin films
|
All-optical pump-probe detection of magnetization precession has been
performed for ferromagnetic EuO thin films at 10 K. We demonstrate that the
circularly-polarized light can be used to control the magnetization precession
on an ultrafast time scale. This takes place within the 100 fs duration of a
single laser pulse, through combined contribution from two nonthermal
photomagnetic effects, i.e., enhancement of the magnetization and an inverse
Faraday effect. From the magnetic field dependences of the frequency and the
Gilbert damping parameter, the intrinsic Gilbert damping coefficient is
evaluated to be {\alpha} \approx 3\times10^-3.
|
1207.6686v1
|
2015-01-02
|
Inertia, diffusion and dynamics of a driven skyrmion
|
Skyrmions recently discovered in chiral magnets are a promising candidate for
magnetic storage devices because of their topological stability, small size
($\sim 3-100$nm), and ultra-low threshold current density ($\sim
10^{6}$A/m$^2$) to drive their motion. However, the time-dependent dynamics has
hitherto been largely unexplored. Here we show, by combining the numerical
solution of the Landau-Lifshitz-Gilbert equation and the analysis of a
generalized Thiele's equation, that inertial effects are almost completely
absent in skyrmion dynamics driven by a time-dependent current. In contrast,
the response to time-dependent magnetic forces and thermal fluctuations depends
strongly on frequency and is described by a large effective mass and a (anti-)
damping depending on the acceleration of the skyrmion. Thermal diffusion is
strongly suppressed by the cyclotron motion and is proportional to the Gilbert
damping coefficient $\alpha$. This indicates that the skyrmion position is
stable, and its motion responds to the time-dependent current without delay or
retardation even if it is fast. These findings demonstrate the advantages of
skyrmions as information carriers.
|
1501.00444v1
|
2008-07-31
|
Scattering Theory of Gilbert Damping
|
The magnetization dynamics of a single domain ferromagnet in contact with a
thermal bath is studied by scattering theory. We recover the
Landau-Liftshitz-Gilbert equation and express the effective fields and Gilbert
damping tensor in terms of the scattering matrix. Dissipation of magnetic
energy equals energy current pumped out of the system by the time-dependent
magnetization, with separable spin-relaxation induced bulk and spin-pumping
generated interface contributions. In linear response, our scattering theory
for the Gilbert damping tensor is equivalent with the Kubo formalism.
|
0807.5009v1
|
2016-04-11
|
All-Optical Study of Tunable Ultrafast Spin Dynamics in [Co/Pd]-NiFe Systems: The Role of Spin-Twist Structure on Gilbert Damping
|
We investigate optically induced ultrafast magnetization dynamics in [Co(0.5
nm)/Pd(1 nm)]x5/NiFe(t) exchange-spring samples with tilted perpendicular
magnetic anisotropy using a time-resolved magneto-optical Kerr effect
magnetometer. The competition between the out-of-plane anisotropy of the hard
layer, the in-plane anisotropy of the soft layer and the applied bias field
reorganizes the spins in the soft layer, which are modified further with the
variation in t. The spin-wave spectrum, the ultrafast demagnetization time, and
the extracted damping coefficient all depend on the spin distribution in the
soft layer, while the latter two also depend on the spin-orbit coupling between
the Co and Pd layers. The spin-wave spectra change from multimode to
single-mode as t increases. At the maximum field reached in this study, H=2.5
kOe, the damping shows a nonmonotonic dependence on t with a minimum at t=7.5
nm. For t<7.5 nm, intrinsic effects dominate, whereas for t>7.5 nm, extrinsic
effects govern the damping mechanisms.
|
1604.02998v1
|
2024-01-18
|
Real-space nonlocal Gilbert damping from exchange torque correlation applied to bulk ferromagnets and their surfaces
|
In this work we present an ab initio scheme based on linear response theory
of exchange torque correlation, implemented into the real-space
Korringa-Kohn-Rostoker (RS-KKR) framework to calculate diagonal elements of the
atomic-site-dependent intrinsic Gilbert damping tensor. The method is first
applied to bcc iron and fcc cobalt bulk systems. Beside reproducing earlier
results from the literature for those bulk magnets, the effect of the lattice
compression is also studied for Fe bulk, and significant changes for the
Gilbert damping are found. Furthermore, (001)-oriented surfaces of Fe and Co
are also investigated. It is found that the on-site Gilbert damping increases
in the surface atomic layer and decreases in the subsurface layer, and
approaches the bulk value moving further inside the magnets. Realistic atomic
relaxation of the surface layers enhances the identified effects. The
first-neighbor damping parameters are extremely sensitive to the surface
relaxation. Despite their inhomogeneity caused by the surface, the transverse
Gilbert damping tensor components remain largely insensitive to the
magnetization direction.
|
2401.09938v2
|
2007-06-12
|
Gilbert and Landau-Lifshitz damping in the presense of spin-torque
|
A recent article by Stiles et al. (cond-mat/0702020) argued in favor of the
Landau-Lifshitz damping term in the micromagnetic equations of motion over that
of the more commonly accepted Gilbert damping form. Much of their argument
revolved around spin-torque driven domain wall motion in narrow magnetic wires,
since the presence of spin-torques can more acutely draw a distinction between
the two forms of damping. In this article, the author uses simple arguments and
examples to offer an alternative point of view favoring Gilbert.
|
0706.1736v1
|
2015-06-02
|
Current-Driven Motion of Magnetic Domain Wall with Many Bloch Lines
|
The current-driven motion of a domain wall (DW) in a ferromagnet with many
Bloch lines (BLs) via the spin transfer torque is studied theoretically. It is
found that the motion of BLs changes the current-velocity ($j$-$v$)
characteristic dramatically. Especially, the critical current density to
overcome the pinning force is reduced by the factor of the Gilbert damping
coefficient $\alpha$ even compared with that of a skyrmion. This is in sharp
contrast to the case of magnetic field driven motion, where the existence of
BLs reduces the mobility of the DW.
|
1506.00723v1
|
2023-03-13
|
Experimental investigation of the effect of topological insulator on the magnetization dynamics of ferromagnetic metal: $BiSbTe_{1.5}Se_{1.5}$ and $Ni_{80}Fe_{20}$ heterostructure
|
We have studied ferromagnetic metal/topological insulator bilayer system to
understand magnetization dynamics of ferromagnetic metal (FM) in contact with a
topological insulator (TI). At magnetic resonance condition, the precessing
magnetization in the metallic ferromagnet ($Ni_{80}Fe_{20}$) injects spin
current into the topological insulator ($BiSbTe_{1.5}Se_{1.5}$), a phenomenon
known as spin-pumping. Due to the spin pumping effect, fast relaxation in the
ferromagnet results in the broadening of ferromagnetic resonance linewidth
($\Delta H$). We evaluated the parameters like effective Gilbert damping
coefficient ($\alpha_{eff}$), spin-mixing conductance ($g_{eff}^{\uparrow
\downarrow}$) and spin current density ($j_S^0$) to confirm a successful spin
injection due to spin-pumping into the $BiSbTe_{1.5}Se_{1.5}$ layer. TIs embody
a spin-momentum locked surface state that span the bulk band-gap. It can act
differently to the FM magnetization than the other normal metals. To probe the
effect of topological surface state, a systematic low temperature study is
crucial as surface state of TI dominates at lower temperatures. The exponential
growth of $\Delta H$ for all different thickness combination of FM/TI bilayers
and effective Gilbert damping coefficient ($\alpha_{eff}$) with lowering
temperature confirms the prediction that spin chemical bias generated from
spin-pumping induces surface current in TI due to spin-momentum locking. The
hump-like feature of magnetic anisotropy field ($H_K$)of the bilayer around 60K
suggests that the decrease of interfacial in-plane magnetic anisotropy can
result from exchange coupling between the TI surface state and the local
moments of FM layer.
|
2303.07025v2
|
2021-01-07
|
Mechanisms behind large Gilbert damping anisotropies
|
A method with which to calculate the Gilbert damping parameter from a
real-space electronic structure method is reported here. The anisotropy of the
Gilbert damping with respect to the magnetic moment direction and local
chemical environment is calculated for bulk and surfaces of Fe$_{50}$Co$_{50}$
alloys from first principles electronic structure in a real space formulation.
The size of the damping anisotropy for Fe$_{50}$Co$_{50}$ alloys is
demonstrated to be significant. Depending on details of the simulations, it
reaches a maximum-minimum damping ratio as high as 200%. Several microscopic
origins of the strongly enhanced Gilbert damping anisotropy have been examined,
where in particular interface/surface effects stand out, as do local
distortions of the crystal structure. Although theory does not reproduce the
experimentally reported high ratio of 400% [Phys. Rev. Lett. 122, 117203
(2019)], it nevertheless identifies microscopic mechanisms that can lead to
huge damping anisotropies.
|
2101.02794v2
|
2018-08-13
|
Gilbert damping phenomenology for two-sublattice magnets
|
We present a systematic phenomenological description of Gilbert damping in
two-sublattice magnets. Our theory covers the full range of materials from
ferro- via ferri- to antiferromagnets. Following a Rayleigh dissipation
functional approach within a Lagrangian classical field formulation, the theory
captures intra- as well as cross-sublattice terms in the Gilbert damping,
parameterized by a 2$\times$2 matrix. When spin-pumping into an adjacent
conductor causes dissipation, we obtain the corresponding Gilbert damping
matrix in terms of the interfacial spin-mixing conductances. Our model
reproduces the experimentally observed enhancement of the ferromagnetic
resonance linewidth in a ferrimagnet close to its compensation temperature
without requiring an increased Gilbert parameter. It also predicts new
contributions to damping in an antiferromagnet and suggests the resonance
linewidths as a direct probe of the sublattice asymmetry, which may stem from
boundary or bulk.
|
1808.04385v2
|
2021-07-02
|
Anomalous Gilbert Damping and Duffing Features of the SFS {\boldmath $\varphi_0$} Josephson Junction
|
We demonstrate unusual features of phase dynamics, IV-characteristics and
magnetization dynamics of the $\varphi_0$ Josephson junction at small values of
spin-orbit interaction, ratio of Josephson to magnetic energy and Gilbert
damping. In particular, an anomalous shift of the ferromagnetic resonance
frequency with an increase of Gilbert damping is found. The ferromagnetic
resonance curves show the Duffing oscillator behaviour, reflecting the
nonlinear nature of Landau-Lifshitz-Gilbert (LLG) equation. Based on the
numerical analysis of each term in LLG equation we obtained an approximated
equation demonstrated both damping effect and Duffing oscillator features. The
resulting Duffing equation incorporates the Gilbert damping in a special way
across the dissipative term and the restoring force. A resonance method for the
determination of spin-orbit interaction in noncentrosymmetric materials which
play the role of barrier in $\varphi_0$ junctions is proposed.
|
2107.00982v3
|
2023-03-07
|
Electrically tunable Gilbert damping in van der Waals heterostructures of two-dimensional ferromagnetic metals and ferroelectrics
|
Tuning the Gilbert damping of ferromagnetic (FM) metals via a nonvolatile way
is of importance to exploit and design next-generation novel spintronic
devices. Through systematical first-principles calculations, we study the
magnetic properties of the van der Waals heterostructure of two-dimensional FM
metal CrTe2 and ferroelectric (FE) In2Te3 monolayers. The ferromagnetism of
CrTe2 is maintained in CrTe2/In2Te3 and its magnetic easy axis can be switched
from in-plane to out-of-plane by reversing the FE polarization of In2Te3.
Excitingly, we find that the Gilbert damping of CrTe2 is tunable when the FE
polarization of In2Te3 is reversed from upward to downward. By analyzing the
k-dependent contributions to the Gilbert damping, we unravel that such
tunability results from the changed intersections between the bands of CrTe2
and Fermi level on the reversal of the FE polarizations of In2Te3 in
CrTe2/In2Te3. Our work provides an appealing way to electrically tailor Gilbert
dampings of two-dimensional FM metals by contacting them with ferroelectrics.
|
2303.03852v1
|
2015-08-28
|
The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space
|
We prove that in dimensions three and higher the Landau-Lifshitz- Gilbert
equation with small initial data in the critical Besov space is globally
wellposed in a uniform way with respect to the Gilbert damping parameter. Then
we show that the global solution converges to that of the Schrodinger maps in
the natural space as the Gilbert damping term vanishes. The proof is based on
some studies on the derivative Ginzburg-Landau equations.
|
1508.07118v3
|
2023-09-20
|
Evaluating Gilbert Damping in Magnetic Insulators from First Principles
|
Magnetic damping has a significant impact on the performance of various
magnetic and spintronic devices, making it a long-standing focus of research.
The strength of magnetic damping is usually quantified by the Gilbert damping
constant in the Landau-Lifshitz-Gilbert equation. Here we propose a
first-principles based approach to evaluate the Gilbert damping constant
contributed by spin-lattice coupling in magnetic insulators. The approach
involves effective Hamiltonian models and spin-lattice dynamics simulations. As
a case study, we applied our method to Y$_3$Fe$_5$O$_{12}$, MnFe$_2$O$_4$ and
Cr$_2$O$_3$. Their damping constants were calculated to be $0.8\times10^{-4}$,
$0.2\times10^{-4}$, $2.2\times 10^{-4}$, respectively at a low temperature. The
results for Y$_3$Fe$_5$O$_{12}$ and Cr$_2$O$_3$ are in good agreement with
experimental measurements, while the discrepancy in MnFe$_2$O$_4$ can be
attributed to the inhomogeneity and small band gap in real samples. The
stronger damping observed in Cr$_2$O$_3$, compared to Y$_3$Fe$_5$O$_{12}$,
essentially results from its stronger spin-lattice coupling. In addition, we
confirmed a proportional relationship between damping constants and the
temperature difference of subsystems, which had been reported in previous
studies. These successful applications suggest that our approach serves as a
promising candidate for estimating the Gilbert damping constant in magnetic
insulators.
|
2309.11152v1
|
2008-11-25
|
The quantum-mechanical basis of an extended Landau-Lifshitz-Gilbert equation for a current-carrying ferromagnetic wire
|
An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe
the dynamics of inhomogeneous magnetization in a current-carrying wire. The
coefficients of all the terms in this equation are calculated
quantum-mechanically for a simple model which includes impurity scattering.
This is done by comparing the energies and lifetimes of a spin wave calculated
from the LLG equation and from the explicit model. Two terms are of particular
importance since they describe non-adiabatic spin-transfer torque and damping
processes which do not rely on spin-orbit coupling. It is shown that these
terms may have a significant influence on the velocity of a current-driven
domain wall and they become dominant in the case of a narrow wall.
|
0811.4118v1
|
2019-06-25
|
Conductivity-Like Gilbert Damping due to Intraband Scattering in Epitaxial Iron
|
Confirming the origin of Gilbert damping by experiment has remained a
challenge for many decades, even for simple ferromagnetic metals. In this
Letter, we experimentally identify Gilbert damping that increases with
decreasing electronic scattering in epitaxial thin films of pure Fe. This
observation of conductivity-like damping, which cannot be accounted for by
classical eddy current loss, is in excellent quantitative agreement with
theoretical predictions of Gilbert damping due to intraband scattering. Our
results resolve the longstanding question about a fundamental damping mechanism
and offer hints for engineering low-loss magnetic metals for cryogenic
spintronics and quantum devices.
|
1906.10326v2
|
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
|
2018-12-18
|
Thermal gradient driven domain wall dynamics
|
The issue of whether a thermal gradient acts like a magnetic field or an
electric current in the domain wall (DW) dynamics is investigated. Broadly
speaking, magnetization control knobs can be classified as energy-driving or
angular-momentum driving forces. DW propagation driven by a static magnetic
field is the best-known example of the former in which the DW speed is
proportional to the energy dissipation rate, and the current-driven DW motion
is an example of the latter. Here we show that DW propagation speed driven by a
thermal gradient can be fully explained as the angular momentum transfer
between thermally generated spin current and DW. We found DW-plane rotation
speed increases as DW width decreases. Both DW propagation speed along the wire
and DW-plane rotation speed around the wire decrease with the Gilbert damping.
These facts are consistent with the angular momentum transfer mechanism, but
are distinct from the energy dissipation mechanism. We further show that
magnonic spin-transfer torque (STT) generated by a thermal gradient has both
damping-like and field-like components. By analyzing DW propagation speed and
DW-plane rotation speed, the coefficient ( \b{eta}) of the field-like STT
arising from the non-adiabatic process, is obtained. It is found that \b{eta}
does not depend on the thermal gradient; increases with uniaxial anisotropy
K_(||) (thinner DW); and decreases with the damping, in agreement with the
physical picture that a larger damping or a thicker DW leads to a better
alignment between the spin-current polarization and the local magnetization, or
a better adiabaticity.
|
1812.07244v2
|
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
|
2008-06-28
|
Theory of spin magnetohydrodynamics
|
We develop a phenomenological hydrodynamic theory of coherent magnetic
precession coupled to electric currents. Exchange interaction between electron
spin and collective magnetic texture produces two reciprocal effects:
spin-transfer torque on the magnetic order parameter and the Berry-phase gauge
field experienced by the itinerant electrons. The dissipative processes are
governed by three coefficients: the ohmic resistance, Gilbert damping of the
magnetization, and the "beta coefficient" describing viscous coupling between
magnetic dynamics and electric current, which stems from spin mistracking of
the magnetic order. We develop general magnetohydrodynamic equations and
discuss the net dissipation produced by the coupled dynamics. The latter in
particular allows us to determine a lower bound on the magnetic-texture
resistivity.
|
0806.4656v2
|
2008-11-13
|
Intrinsic Coupling between Current and Domain Wall Motion in (Ga,Mn)As
|
We consider current-induced domain wall motion and, the reciprocal process,
moving domain wall-induced current. The associated Onsager coefficients are
expressed in terms of scattering matrices. Uncommonly, in (Ga,Mn)As, the
effective Gilbert damping coefficient $\alpha_w$ and the effective out-of-plane
spin transfer torque parameter $\beta_w$ are dominated by spin-orbit
interaction in combination with scattering off the domain wall, and not
scattering off extrinsic impurities. Numerical calculations give $\alpha_w \sim
0.01$ and $\beta_w \sim 1$ in dirty (Ga,Mn)As. The extraordinary large
$\beta_w$ parameter allows experimental detection of current or voltage induced
by domain wall motion in (Ga,Mn)As.
|
0811.2235v2
|
2009-05-01
|
Spin excitations in a monolayer scanned by a magnetic tip
|
Energy dissipation via spin excitations is investigated for a hard
ferromagnetic tip scanning a soft magnetic monolayer. We use the classical
Heisenberg model with Landau-Lifshitz-Gilbert (LLG)-dynamics including a
stochastic field representing finite temperatures. The friction force depends
linearly on the velocity (provided it is small enough) for all temperatures.
For low temperatures, the corresponding friction coefficient is proportional to
the phenomenological damping constant of the LLG equation. This dependence is
lost at high temperatures, where the friction coefficient decreases
exponentially. These findings can be explained by properties of the spin
polarization cloud dragged along with the tip.
|
0905.0112v2
|
2016-05-21
|
Landau-Lifshitz theory of the magnon-drag thermopower
|
Metallic ferromagnets subjected to a temperature gradient exhibit a magnonic
drag of the electric current. We address this problem by solving a stochastic
Landau-Lifshitz equation to calculate the magnon-drag thermopower. The
long-wavelength magnetic dynamics result in two contributions to the
electromotive force acting on electrons: (1) An adiabatic Berry-phase force
related to the solid angle subtended by the magnetic precession and (2) a
dissipative correction thereof, which is rooted microscopically in the
spin-dephasing scattering. The first contribution results in a net force
pushing the electrons towards the hot side, while the second contribution drags
electrons towards the cold side, i.e., in the direction of the magnonic drift.
The ratio between the two forces is proportional to the ratio between the
Gilbert damping coefficient $\alpha$ and the coefficient $\beta$ parametrizing
the dissipative contribution to the electromotive force.
|
1605.06578v1
|
2019-06-17
|
Controlling acoustic waves using magnetoelastic Fano resonances
|
We propose and analyze theoretically a class of energy-efficient
magneto-elastic devices for analogue signal processing. The signals are carried
by transverse acoustic waves while the bias magnetic field controls their
scattering from a magneto-elastic slab. By tuning the bias field, one can alter
the resonant frequency at which the propagating acoustic waves hybridize with
the magnetic modes, and thereby control transmission and reflection
coefficients of the acoustic waves. The scattering coefficients exhibit
Breit-Wigner/Fano resonant behaviour akin to inelastic scattering in atomic and
nuclear physics. Employing oblique incidence geometry, one can effectively
enhance the strength of magnetoelastic coupling, and thus countermand the
magnetic losses due to the Gilbert damping. We apply our theory to discuss
potential benefits and issues in realistic systems and suggest further routes
to enhance performance of the proposed devices.
|
1906.07297v2
|
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
|
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
|
2011-04-08
|
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
|
2008-05-21
|
Non-equilibrium thermodynamic study of magnetization dynamics in the presence of spin-transfer torque
|
The dynamics of magnetization in the presence of spin-transfer torque was
studied. We derived the equation for the motion of magnetization in the
presence of a spin current by using the local equilibrium assumption in
non-equilibrium thermodynamics. We show that, in the resultant equation, the
ratio of the Gilbert damping constant, $\alpha$, and the coefficient, $\beta$,
of the current-induced torque, called non-adiabatic torque, depends on the
relaxation time of the fluctuating field $\tau_{c}$. The equality
$\alpha=\beta$ holds when $\tau_c$ is very short compared to the time scale of
magnetization dynamics. We apply our theory to current-induced magnetization
reversal in magnetic multilayers and show that the switching time is a
decreasing function of $\tau_{c}$.
|
0805.3306v1
|
2010-08-03
|
Determination of the spin-flip time in ferromagnetic SrRuO3 from time-resolved Kerr measurements
|
We report time-resolved Kerr effect measurements of magnetization dynamics in
ferromagnetic SrRuO3. We observe that the demagnetization time slows
substantially at temperatures within 15K of the Curie temperature, which is ~
150K. We analyze the data with a phenomenological model that relates the
demagnetization time to the spin flip time. In agreement with our observations
the model yields a demagnetization time that is inversely proportional to T-Tc.
We also make a direct comparison of the spin flip rate and the Gilbert damping
coefficient showing that their ratio very close to kBTc, indicating a common
origin for these phenomena.
|
1008.0674v1
|
2015-03-26
|
Thermophoresis of an Antiferromagnetic Soliton
|
We study dynamics of an antiferromagnetic soliton under a temperature
gradient. To this end, we start by phenomenologically constructing the
stochastic Landau-Lifshitz-Gilbert equation for an antiferromagnet with the aid
of the fluctuation-dissipation theorem. We then derive the Langevin equation
for the soliton's center of mass by the collective coordinate approach. An
antiferromagentic soliton behaves as a classical massive particle immersed in a
viscous medium. By considering a thermodynamic ensemble of solitons, we obtain
the Fokker-Planck equation, from which we extract the average drift velocity of
a soliton. The diffusion coefficient is inversely proportional to a small
damping constant $\alpha$, which can yield a drift velocity of tens of m/s
under a temperature gradient of $1$ K/mm for a domain wall in an easy-axis
antiferromagnetic wire with $\alpha \sim 10^{-4}$.
|
1503.07854v2
|
2016-04-24
|
Coupled Spin-Light dynamics in Cavity Optomagnonics
|
Experiments during the past two years have shown strong resonant
photon-magnon coupling in microwave cavities, while coupling in the optical
regime was demonstrated very recently for the first time. Unlike with
microwaves, the coupling in optical cavities is parametric, akin to
optomechanical systems. This line of research promises to evolve into a new
field of optomagnonics, aimed at the coherent manipulation of elementary
magnetic excitations by optical means. In this work we derive the microscopic
optomagnonic Hamiltonian. In the linear regime the system reduces to the
well-known optomechanical case, with remarkably large coupling. Going beyond
that, we study the optically induced nonlinear classical dynamics of a
macrospin. In the fast cavity regime we obtain an effective equation of motion
for the spin and show that the light field induces a dissipative term
reminiscent of Gilbert damping. The induced dissipation coefficient however can
change sign on the Bloch sphere, giving rise to self-sustained oscillations.
When the full dynamics of the system is considered, the system can enter a
chaotic regime by successive period doubling of the oscillations.
|
1604.07053v3
|
2018-02-07
|
Breaking the current density threshold in spin-orbit-torque magnetic random access memory
|
Spin-orbit-torque magnetic random access memory (SOT-MRAM) is a promising
technology for the next generation of data storage devices. The main bottleneck
of this technology is the high reversal current density threshold. This
outstanding problem of SOT-MRAM is now solved by using a current density of
constant magnitude and varying flow direction that reduces the reversal current
density threshold by a factor of more than the Gilbert damping coefficient. The
Euler-Lagrange equation for the fastest magnetization reversal path and the
optimal current pulse are derived for an arbitrary magnetic cell. The
theoretical limit of minimal reversal current density and current density for a
GHz switching rate of the new reversal strategy for CoFeB/Ta SOT-MRAMs are
respectively of the order of $10^5$ A/cm$^2$ and $10^6$ A/cm$^2$ far below
$10^7$ A/cm$^2$ and $10^8$ A/cm$^2$ in the conventional strategy. Furthermore,
no external magnetic field is needed for a deterministic reversal in the new
strategy.
|
1802.02415v1
|
2022-04-22
|
A short-circuited coplanar waveguide for low-temperature single-port ferromagnetic resonance spectroscopy set-up to probe the magnetic properties of ferromagnetic thin films
|
A coplanar waveguide shorted in one end is proposed, designed, and
implemented successfully to measure the properties of magnetic thin films as a
part of the vector network analyzer ferromagnetic resonance (VNA-FMR)
spectroscopy set-up. Its simple structure, potential applications and easy
installation inside the cryostat chamber made it advantageous especially for
low-temperature measurements. It provides a wide band of frequencies in the
gigahertz range essential for FMR measurements. Our spectroscopy set-up with
short-circuited coplanar waveguide has been used to extract Gilbert damping
coefficient and effective magnetization values for standard ferromagnetic thin
films like Py and Co. The thickness and temperature dependent studies of those
magnetic parameters have also been done here for the afore mentioned magnetic
samples.
|
2204.10596v2
|
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
|
2019-11-21
|
Low damping and microstructural perfection of sub-40nm-thin yttrium iron garnet films grown by liquid phase epitaxy
|
The field of magnon spintronics is experiencing an increasing interest in the
development of solutions for spin-wave-based data transport and processing
technologies that are complementary or alternative to modern CMOS
architectures. Nanometer-thin yttrium iron garnet (YIG) films have been the
gold standard for insulator-based spintronics to date, but a potential process
technology that can deliver perfect, homogeneous large-diameter films is still
lacking. We report that liquid phase epitaxy (LPE) enables the deposition of
nanometer-thin YIG films with low ferromagnetic resonance losses and
consistently high magnetic quality down to a thickness of 20 nm. The obtained
epitaxial films are characterized by an ideal stoichiometry and perfect film
lattices, which show neither significant compositional strain nor geometric
mosaicity, but sharp interfaces. Their magneto-static and dynamic behavior is
similar to that of single crystalline bulk YIG. We found, that the Gilbert
damping coefficient alpha is independent of the film thickness and close to 1 x
10-4, and that together with an inhomogeneous peak-to-peak linewidth broadening
of delta H0|| = 0.4 G, these values are among the lowest ever reported for YIG
films with a thickness smaller than 40 nm. These results suggest, that
nanometer-thin LPE films can be used to fabricate nano- and micro-scaled
circuits with the required quality for magnonic devices. The LPE technique is
easily scalable to YIG sample diameters of several inches.
|
1911.09400v1
|
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
|
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
|
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
|
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
|
2023-04-19
|
Thickness-dependent magnetic properties in Pt[CoNi]n multilayers with perpendicular magnetic anisotropy
|
We systematically investigated the Ni and Co thickness-dependent
perpendicular magnetic anisotropy (PMA) coefficient, magnetic domain
structures, and magnetization dynamics of Pt(5 nm)/[Co(t_Co nm)/Ni(t_Ni
nm)]5/Pt(1 nm) multilayers by combining the four standard magnetic
characterization techniques. The magnetic-related hysteresis loops obtained
from the field-dependent magnetization M and anomalous Hall resistivity (AHR)
\r{ho}_xy found that the two serial multilayers with t_Co = 0.2 and 0.3 nm have
the optimum PMA coefficient K_U well as the highest coercivity H_C at the Ni
thickness t_Ni = 0.6 nm. Additionally, the magnetic domain structures obtained
by Magneto-optic Kerr effect (MOKE) microscopy also significantly depend on the
thickness and K_U of the films. Furthermore, the thickness-dependent linewidth
of ferromagnetic resonance is inversely proportional to K_U and H_C, indicating
that inhomogeneous magnetic properties dominate the linewidth. However, the
intrinsic Gilbert damping constant determined by a linear fitting of
frequency-dependent linewidth does not depend on Ni thickness and K_U. Our
results could help promote the PMA [Co/Ni] multilayer applications in various
spintronic and spin-orbitronic devices.
|
2304.09366v1
|
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
|
2015-05-15
|
Reliable Damping of Free Surface Waves in Numerical Simulations
|
This paper generalizes existing approaches for free-surface wave damping via
momentum sinks for flow simulations based on the Navier-Stokes equations. It is
shown in 2D flow simulations that, to obtain reliable wave damping, the
coefficients in the damping functions must be adjusted to the wave parameters.
A scaling law for selecting these damping coefficients is presented, which
enables similarity of the damping in model- and full-scale. The influence of
the thickness of the damping layer, the wave steepness, the mesh fineness and
the choice of the damping coefficients are examined. An efficient approach for
estimating the optimal damping setup is presented. Results of 3D ship
resistance computations show that the scaling laws apply to such simulations as
well, so the damping coefficients should be adjusted for every simulation to
ensure convergence of the solution in both model and full scale. Finally,
practical recommendations for the setup of reliable damping in flow simulations
with regular and irregular free surface waves are given.
|
1505.04087v2
|
2010-12-20
|
Global attractors for the one dimensional wave equation with displacement dependent damping
|
We study the long-time behavior of solutions of the one dimensional wave
equation with nonlinear damping coefficient. We prove that if the damping
coefficient function is strictly positive near the origin then this equation
possesses a global attractor.
|
1012.4455v1
|
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
|
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