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2023-05-23 | Current-driven motion of magnetic topological defects in ferromagnetic superconductors | Recent years have seen a number of instances where magnetism and
superconductivity intrinsically coexist. Our focus is on the case where
spin-triplet superconductivity arises out of ferromagnetism, and we make a
hydrodynamic analysis of the effect of a charge supercurrent on magnetic
topological defects like domain walls and merons. We find that the emergent
electromagnetic field that arises out of the superconducting order parameter
provides a description for not only the physical quantities such as the local
energy flux density and the interaction between current and defects but also
the energy dissipation through magnetic dynamics of the Gilbert damping, which
becomes more prominent compared to the normal state as superconductivity
attenuates the energy dissipation through the charge sector. In particular, we
reveal that the current-induced dynamics of domain walls and merons in the
presence of the Gilbert damping give rise to the nonsingular $4\pi$ and $2\pi$
phase slips, respectively, revealing the intertwined dynamics of spin and
charge degrees of freedom in ferromagnetic superconductors. | 2305.13564v1 |
2023-07-03 | Magnetic lump motion in saturated ferromagnetic films | In this paper, we study in detail the nonlinear propagation of magnetic
soliton in a ferromagnetic film. The sample is magnetized to saturation by an
external field perpendicular to film plane. A new generalized (2+1)-dimensional
short-wave asymptotic model is derived. The bilinear-like forms of this
equation are constructed, and exact magnetic line soliton solutions are
exhibited. It is observed that a series of stable lumps can be generated by an
unstable magnetic soliton under Gaussian disturbance. Such magnetic lumps are
highly stable and can maintain their shapes and velocities during evolution or
collision. The interaction between lump and magnetic soliton, as well as
interaction between two lumps, are numerically investigated. We further discuss
the nonlinear motion of lumps in ferrites with Gilbert-damping and
inhomogeneous exchange effects. The results show that the Gilbert-damping
effects make the amplitude and velocity of the magnetic lump decay
exponentially during propagation. And the shock waves are generated from a lump
when quenching the strength of inhomogeneous exchange. | 2307.00903v1 |
2005-03-24 | Fast magnetization switching of Stoner particles: A nonlinear dynamics picture | The magnetization reversal of Stoner particles is investigated from the point
of view of nonlinear dynamics within the Landau-Lifshitz-Gilbert formulation.
The following results are obtained. 1) We clarify that the so-called
Stoner-Wohlfarth (SW) limit becomes exact when damping constant is infinitely
large. Under the limit, the magnetization moves along the steepest energy
descent path. The minimal switching field is the one at which there is only one
stable fixed point in the system. 2) For a given magnetic anisotropy, there is
a critical value for the damping constant, above which the minimal switching
field is the same as that of the SW-limit. 3) We illustrate how fixed points
and their basins change under a field along different directions. This change
explains well why a non-parallel field gives a smaller minimal switching field
and a short switching time. 4) The field of a ballistic magnetization reversal
should be along certain direction window in the presence of energy dissipation.
The width of the window depends on both of the damping constant and the
magnetic anisotropy. The upper and lower bounds of the direction window
increase with the damping constant. The window width oscillates with the
damping constant for a given magnetic anisotropy. It is zero for both zero and
infinite damping. Thus, the perpendicular field configuration widely employed
in the current experiments is not the best one since the damping constant in a
real system is far from zero. | 0503594v1 |
2022-03-03 | Stability results of locally coupled wave equations with local Kelvin-Voigt damping: Cases when the supports of damping and coupling coefficients are disjoint | In this paper, we study the direct/indirect stability of locally coupled wave
equations with local Kelvin-Voigt dampings/damping and by assuming that the
supports of the dampings and the coupling coefficients are disjoint. First, we
prove the well-posedness, strong stability, and polynomial stability for some
one dimensional coupled systems. Moreover, under some geometric control
condition, we prove the well-posedness and strong stability in the
multi-dimensional case. | 2203.01632v1 |
2020-09-16 | Fast convex optimization via inertial dynamics combining viscous and Hessian-driven damping with time rescaling | In a Hilbert setting, we develop fast methods for convex unconstrained
optimization. We rely on the asymptotic behavior of an inertial system
combining geometric damping with temporal scaling. The convex function to
minimize enters the dynamic via its gradient. The dynamic includes three
coefficients varying with time, one is a viscous damping coefficient, the
second is attached to the Hessian-driven damping, the third is a time scaling
coefficient. We study the convergence rate of the values under general
conditions involving the damping and the time scale coefficients. The obtained
results are based on a new Lyapunov analysis and they encompass known results
on the subject. We pay particular attention to the case of an asymptotically
vanishing viscous damping, which is directly related to the accelerated
gradient method of Nesterov. The Hessian-driven damping significantly reduces
the oscillatory aspects. As a main result, we obtain an exponential rate of
convergence of values without assuming the strong convexity of the objective
function. The temporal discretization of these dynamics opens the gate to a
large class of inertial optimization algorithms. | 2009.07620v1 |
2021-08-04 | Nonlinear fluid damping of elastically mounted pitching wings in quiescent water | We experimentally study the nonlinear fluid damping of a rigid but
elastically mounted pitching wing in the absence of a freestream flow. The
dynamics of the elastic mount are simulated using a cyber-physical system. We
perturb the wing and measure the fluid damping coefficient from damped
oscillations over a large range of pitching frequencies, pitching amplitudes,
pivot locations and sweep angles. A universal fluid damping scaling is proposed
to incorporate all these parameters. Flow fields obtained using particle image
velocimetry are analyzed to explain the nonlinear behaviors of the fluid
damping. | 2108.02090v1 |
2023-07-05 | Optimal damping of vibrating systems: dependence on initial conditions | Common criteria used for measuring performance of vibrating systems have one
thing in common: they do not depend on initial conditions of the system. In
some cases it is assumed that the system has zero initial conditions, or some
kind of averaging is used to get rid of initial conditions. The aim of this
paper is to initiate rigorous study of the dependence of vibrating systems on
initial conditions in the setting of optimal damping problems. We show that,
based on the type of initial conditions, especially on the ratio of potential
and kinetic energy of the initial conditions, the vibrating system will have
quite different behavior and correspondingly the optimal damping coefficients
will be quite different. More precisely, for single degree of freedom systems
and the initial conditions with mostly potential energy, the optimal damping
coefficient will be in the under-damped regime, while in the case of the
predominant kinetic energy the optimal damping coefficient will be in the
over-damped regime. In fact, in the case of pure kinetic initial energy, the
optimal damping coefficient is $+\infty$! Qualitatively, we found the same
behavior in multi degree of freedom systems with mass proportional damping. We
also introduce a new method for determining the optimal damping of vibrating
systems, which takes into account the peculiarities of initial conditions and
the fact that, although in theory these systems asymptotically approach
equilibrium and never reach it exactly, in nature and in experiments they
effectively reach equilibrium in some finite time. | 2307.02352v2 |
2021-06-25 | Perturbed primal-dual dynamics with damping and time scaling coefficients for affine constrained convex optimization problems | In Hilbert space, we propose a family of primal-dual dynamical system for
affine constrained convex optimization problem. Several damping coefficients,
time scaling coefficients, and perturbation terms are thus considered. By
constructing the energy functions, we investigate the convergence rates with
different choices of the damping coefficients and time scaling coefficients.
Our results extend the inertial dynamical approaches for unconstrained convex
optimization problems to affine constrained convex optimization problems. | 2106.13702v1 |
2020-06-24 | Stability of a star-shaped network with local Kelvin-Voigt damping and non-smooth coefficient at interface | In this paper, we study the stability problem of a star-shaped network of
elastic strings with a local Kelvin-Voigt damping. Under the assumption that
the damping coefficients have some singularities near the transmission point,
we prove that the semigroup corresponding to the system is polynomially stable
and the decay rates depends on the speed of the degeneracy. This result
improves the decay rate of the semigroup associated to the system on an earlier
result of Z.~Liu and Q.~Zhang in \cite{LZ} involving the wave equation with
local Kelvin-Voigt damping and non-smooth coefficient at interface. | 2006.14949v1 |
2008-05-07 | Comparison Between Damping Coefficients of Measured Perforated Micromechanical Test Structures and Compact Models | Measured damping coefficients of six different perforated micromechanical
test structures are compared with damping coefficients given by published
compact models. The motion of the perforated plates is almost translational,
the surface shape is rectangular, and the perforation is uniform validating the
assumptions made for compact models. In the structures, the perforation ratio
varies from 24% - 59%. The study of the structure shows that the
compressibility and inertia do not contribute to the damping at the frequencies
used (130kHz - 220kHz). The damping coefficients given by all four compact
models underestimate the measured damping coefficient by approximately 20%. The
reasons for this underestimation are discussed by studying the various flow
components in the models. | 0805.0893v1 |
2003-02-17 | Magnetization dynamics with a spin-transfer torque | The magnetization reversal and dynamics of a spin valve pillar, whose lateral
size is 64$\times$64 nm$^2$, are studied by using micromagnetic simulation in
the presence of spin transfer torque. Spin torques display both characteristics
of magnetic damping (or anti-damping) and of an effective magnetic field. For a
steady-state current, both M-I and M-H hysteresis loops show unique features,
including multiple jumps, unusual plateaus and precessional states. These
states originate from the competition between the energy dissipation due to
Gilbert damping and the energy accumulation due to the spin torque supplied by
the spin current. The magnetic energy oscillates as a function of time even for
a steady-state current. For a pulsed current, the minimum width and amplitude
of the spin torque for achieving current-driven magnetization reversal are
quantitatively determined. The spin torque also shows very interesting thermal
activation that is fundamentally different from an ordinary damping effect. | 0302337v1 |
2003-10-13 | Domain wall mobility in nanowires: transverse versus vortex walls | The motion of domain walls in ferromagnetic, cylindrical nanowires is
investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a
classical spin model in which energy contributions from exchange, crystalline
anisotropy, dipole-dipole interaction, and a driving magnetic field are
considered. Depending on the diameter, either transverse domain walls or vortex
walls are found. The transverse domain wall is observed for diameters smaller
than the exchange length of the given material. Here, the system behaves
effectively one-dimensional and the domain wall mobility agrees with a result
derived for a one-dimensional wall by Slonczewski. For low damping the domain
wall mobility decreases with decreasing damping constant. With increasing
diameter, a crossover to a vortex wall sets in which enhances the domain wall
mobility drastically. For a vortex wall the domain wall mobility is described
by the Walker-formula, with a domain wall width depending on the diameter of
the wire. The main difference is the dependence on damping: for a vortex wall
the domain wall mobility can be drastically increased for small values of the
damping constant up to a factor of $1/\alpha^2$. | 0310277v1 |
2013-10-29 | Observational Study of Large Amplitude Longitudinal Oscillations in a Solar Filament | On 20 August 2010 an energetic disturbance triggered damped large-amplitude
longitudinal (LAL) oscillations in almost an entire filament. In the present
work we analyze this periodic motion in the filament to characterize the
damping and restoring mechanism of the oscillation. Our method involves placing
slits along the axis of the filament at different angles with respect to the
spine of the filament, finding the angle at which the oscillation is clearest,
and fitting the resulting oscillation pattern to decaying sinusoidal and Bessel
functions. These functions represent the equations of motion of a pendulum
damped by mass accretion. With this method we determine the period and the
decaying time of the oscillation. Our preliminary results support the theory
presented by Luna and Karpen (2012) that the restoring force of LAL
oscillations is solar gravity in the tubes where the threads oscillate, and the
damping mechanism is the ongoing accumulation of mass onto the oscillating
threads. Following an earlier paper, we have determined the magnitude and
radius of curvature of the dipped magnetic flux tubes hosting a thread along
the filament, as well as the mass accretion rate of the filament threads, via
the fitted parameters. | 1310.7657v1 |
2014-12-08 | Magnetization Dynamics driven by Non-equilibrium Spin-Orbit Coupled Electron Gas | The dynamics of magnetization coupled to an electron gas via s-d exchange
interaction is investigated by using density matrix technique. Our theory shows
that non-equilibrium spin accumulation induces a spin torque and the electron
bath leads to a damping of the magnetization. For the two-dimensional
magnetization thin film coupled to the electron gas with Rashba spin-orbit
coupling, the result for the spin-orbit torques is consistent with the previous
semi-classical theory. Our theory predicts a damping of the magnetization,
which is absent in the semi-classical theory. The magnitude of the damping due
to the electron bath is comparable to the intrinsic Gilbert damping and may be
important in describing the magnetization dynamics of the system. | 1412.2479v1 |
2017-03-06 | Damping dependence of spin-torque effects in thermally assisted magnetization reversal | Thermal fluctuations of nanomagnets driven by spin-polarized currents are
treated via the Landau-Lifshitz-Gilbert equation as generalized to include both
the random thermal noise field and Slonczewski spin-transfer torque terms. The
magnetization reversal time of such a nanomagnet is then evaluated for wide
ranges of damping by using a method which generalizes the solution of the
so-called Kramers turnover problem for mechanical Brownian particles, thereby
bridging the very low damping and intermediate damping Kramers escape rates, to
the analogous magnetic turnover problem. The reversal time is then evaluated
for a nanomagnet with the free energy density given in the standard form of
superimposed easy-plane and in-plane easy-axis anisotropies with the dc bias
field along the easy axis. | 1703.01879v5 |
2017-05-09 | Low spin wave damping in the insulating chiral magnet Cu$_{2}$OSeO$_{3}$ | Chiral magnets with topologically nontrivial spin order such as Skyrmions
have generated enormous interest in both fundamental and applied sciences. We
report broadband microwave spectroscopy performed on the insulating chiral
ferrimagnet Cu$_{2}$OSeO$_{3}$. For the damping of magnetization dynamics we
find a remarkably small Gilbert damping parameter of about $1\times10^{-4}$ at
5 K. This value is only a factor of 4 larger than the one reported for the best
insulating ferrimagnet yttrium iron garnet. We detect a series of sharp
resonances and attribute them to confined spin waves in the mm-sized samples.
Considering the small damping, insulating chiral magnets turn out to be
promising candidates when exploring non-collinear spin structures for high
frequency applications. | 1705.03416v1 |
2018-09-04 | Separation of the two-magnon scattering contribution to damping for the determination of the spin mixing conductance | We present angle dependent measurements of the damping properties of
epitaxial Fe layers with MgO, Al and Pt capping layers. Based on the
preferential distribution of lattice defects following the crystal symmetry, we
make use of a model of the defect density to separate the contribution of
two-magnon scattering to the damping from the isotropic contribution
originating in the spin pumping effect, the viscous Gilbert damping and the
magnetic proximity effect. The separation of the two-magnon contribution, which
depends strongly on the defect density, allows for the measurement of a value
of the effective spin mixing conductance which is closer to the value
exclusively due to spin pumping. The influence of the defect density for
bilayers systems due to the different capping layers and to the unavoidable
spread in defect density from sample to sample is thus removed. This shows the
potential of studying spin pumping phenomena in fully ordered systems in which
this separation is possible, contrary to polycrystalline or amorphous metallic
thin films. | 1809.01042v1 |
2011-11-27 | A two-stage approach to relaxation in billiard systems of locally confined hard spheres | We consider the three-dimensional dynamics of systems of many interacting
hard spheres, each individually confined to a dispersive environment, and show
that the macroscopic limit of such systems is characterized by a coefficient of
heat conduction whose value reduces to a dimensional formula in the limit of
vanishingly small rate of interaction. It is argued that this limit arises from
an effective loss of memory. Similarities with the diffusion of a tagged
particle in binary mixtures are emphasized. | 1111.6272v1 |
2014-03-16 | Interpolating local constants in families | We extend the theory of local constants to l-adic families of representations
of GL_n(F) where F is a p-adic field with l not equal to p. We construct zeta
integrals and gamma factors for representations coming from the conjectural
"local Langlands correspondence in families" of Emerton-Helm, proving a
rationality result and functional equation. We also construct a universal gamma
factor with coefficients in the integral Bernstein center. | 1403.3914v2 |
2014-08-02 | Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards | We study diffusion on a periodic billiard table with infinite horizon in the
limit of narrow corridors. An effective trapping mechanism emerges according to
which the process can be modeled by a L\'evy walk combining
exponentially-distributed trapping times with free propagation along paths
whose precise probabilities we compute. This description yields an
approximation of the mean squared displacement of infinite-horizon billiards in
terms of two transport coefficients which generalizes to this anomalous regime
the Machta-Zwanzig approximation of normal diffusion in finite-horizon
billiards [Phys. Rev. Lett. 50, 1959 (1983)]. | 1408.0349v1 |
2022-12-22 | Novel Bottomonium Results | We present the latest results from the use of the Backus-Gilbert method for
reconstructing the spectra of NRQCD bottomonium mesons using anisotropic
FASTSUM ensembles at non-zero temperature. We focus in particular on results
from the $\eta_b$, $\Upsilon$, $\chi_{b1}$ and $h_b$ generated from
Tikhonov-regularized Backus-Gilbert coefficient sets. We extend previous work
on the Laplace shifting theorem as a means of resolution improvement and
present new results from its use. We conclude with a discussion of the
limitations of the improvement routine and elucidate a connection with
Parisi-Lepage statistical scaling. | 2212.12016v1 |
2023-11-29 | Bayesian interpretation of Backus-Gilbert methods | The extraction of spectral densities from Euclidean correlators evaluated on
the lattice is an important problem, as these quantities encode physical
information on scattering amplitudes, finite-volume spectra, inclusive decay
rates, and transport coefficients. In this contribution, we show that the
Bayesian approach to this "inverse" problem, based on Gaussian processes, can
be reformulated in a way that yields a solution equivalent, up to statistical
uncertainties, to the one obtained in a Backus-Gilbert approach. After
discussing this equivalence, we point out its implications for a reliable
determination of spectral densities from lattice simulations. | 2311.18125v1 |
2006-02-09 | Magnetization damping in polycrystalline Co ultra-thin films: Evidence for non-local effects | The magnetic properties and magnetization dynamics of polycrystalline
ultra-thin Co layers were investigated using a broadband ferromagnetic
resonance (FMR) technique at room temperature. A variable thickness (1 nm $\leq
t \leq$ 10 nm) Co layer is sandwiched between 10 nm thick Cu layers (10 nm Cu|
t Co|10 nm Cu), while materials in contact with the Cu outer interfaces are
varied to determine their influence on the magnetization damping. The resonance
field and the linewidth were studied for in-plane magnetic fields in field
swept experiments at a fixed frequency, from 4 to 25 GHz. The Co layers have a
lower magnetization density than the bulk, and an interface contribution to the
magnetic anisotropy normal to the film plane. The Gilbert damping, as
determined from the frequency dependence of the linewidth, increases with
decreasing Co layer thickness for films with outer Pt layers. This enhancement
is not observed in structures without Pt layers. The result can be understood
in terms of a non-local contribution to the damping due to spin pumping from Co
through the Cu layer and spin relaxation in Pt layers. Pt layers just 1.5 nm
thick are found to be sufficient to enhance the damping and thus act as
efficient "spin-sinks". In structures with Pt outer layers, this non-local
contribution to the damping becomes predominant when the Co layer is thinner
than 4 nm. | 0602243v2 |
2020-04-09 | Magnetic Damping in Epitaxial Fe Alloyed with Vanadium and Aluminum | To develop low-moment, low-damping metallic ferromagnets for power-efficient
spintronic devices, it is crucial to understand how magnetic relaxation is
impacted by the addition of nonmagnetic elements. Here, we compare magnetic
relaxation in epitaxial Fe films alloyed with light nonmagnetic elements of V
and Al. FeV alloys exhibit lower intrinsic damping compared to pure Fe, reduced
by nearly a factor of 2, whereas damping in FeAl alloys increases with Al
content. Our experimental and computational results indicate that reducing the
density of states at the Fermi level, rather than the average atomic number,
has a more significant impact in lowering damping in Fe alloyed with light
elements. Moreover, FeV is confirmed to exhibit an intrinsic Gilbert damping
parameter of $\simeq$0.001, among the lowest ever reported for ferromagnetic
metals. | 2004.04840v3 |
2016-05-17 | Simultaneous Identification of Damping Coefficient and Initial Value in PDEs from boundary measurement | In this paper, the simultaneous identification of damping or anti-damping
coefficient and initial value for some PDEs is considered. An identification
algorithm is proposed based on the fact that the output of system happens to be
decomposed into a product of an exponential function and a periodic function.
The former contains information of the damping coefficient, while the latter
does not. The convergence and error analysis are also developed. Three
examples, namely an anti-stable wave equation with boundary anti-damping, the
Schr\"odinger equation with internal anti-damping, and two connected strings
with middle joint anti-damping, are investigated and demonstrated by numerical
simulations to show the effectiveness of the proposed algorithm. | 1605.05063v1 |
2020-03-13 | Anharmonic phonon damping enhances the $T_c$ of BCS-type superconductors | A theory of superconductivity is presented where the effect of anharmonicity,
as entailed in the acoustic, or optical, phonon damping, is explicitly
considered in the pairing mechanism. The gap equation is solved including
diffusive Akhiezer damping for longitudinal acoustic phonons or Klemens damping
for optical phonons, with a damping coefficient which, in either case, can be
directly related to the Gruneisen parameter and hence to the anharmonic
coefficients in the interatomic potential. The results show that the increase
of anharmonicity has a strikingly non-monotonic effect on the critical
temperature $T_{c}$. The optimal damping coefficient yielding maximum $T_c$ is
set by the velocity of the bosonic mediator. This theory may open up
unprecedented opportunities for material design where $T_{c}$ may be tuned via
the anharmonicity of the interatomic potential, and presents implications for
the superconductivity in the recently discovered hydrides, where anharmonicity
is very strong and for which the anharmonic damping is especially relevant. | 2003.06220v2 |
2014-05-19 | Comparison of micromagnetic parameters of ferromagnetic semiconductors (Ga,Mn)(As,P) and (Ga,Mn)As | We report on the determination of micromagnetic parameters of epilayers of
the ferromagnetic semiconductor (Ga,Mn)As, which has easy axis in the sample
plane, and (Ga,Mn)(As,P) which has easy axis perpendicular to the sample plane.
We use an optical analog of ferromagnetic resonance where the
laser-pulse-induced precession of magnetization is measured directly in the
time domain. By the analysis of a single set of pump-and-probe magneto-optical
data we determined the magnetic anisotropy fields, the spin stiffness and the
Gilbert damping constant in these two materials. We show that incorporation of
10% of phosphorus in (Ga,Mn)As with 6% of manganese leads not only to the
expected sign change of the perpendicular to plane anisotropy field but also to
an increase of the Gilbert damping and to a reduction of the spin stiffness.
The observed changes in the micromagnetic parameters upon incorporating P in
(Ga,Mn)As are consistent with the reduced hole density, conductivity, and Curie
temperature of the (Ga,Mn)(As,P) material. We report that the magnetization
precession damping is stronger for the n = 1 spin wave resonance mode than for
the n = 0 uniform magnetization precession mode. | 1405.4677v1 |
2015-03-24 | Spin dynamics and frequency dependence of magnetic damping study in soft ferromagnetic FeTaC film with a stripe domain structure | Perpendicular magnetic anisotropy (PMA) and low magnetic damping are the key
factors for the free layer magnetization switching by spin transfer torque
technique in magnetic tunnel junction devices. The magnetization precessional
dynamics in soft ferromagnetic FeTaC thin film with a stripe domain structure
was explored in broad band frequency range by employing micro-strip
ferromagnetic resonance technique. The polar angular variation of resonance
field and linewidth at different frequencies have been analyzed numerically
using Landau-Lifshitz-Gilbert equation by taking into account the total free
energy density of the film. The numerically estimated parameters Land\'{e}
$g$-factor, PMA constant, and effective magnetization are found to be 2.1,
2$\times10^{5}$ erg/cm$^{3}$ and 7145 Oe, respectively. The frequency
dependence of Gilbert damping parameter ($\alpha$) is evaluated by considering
both intrinsic and extrinsic effects into the total linewidth analysis. The
value of $\alpha$ is found to be 0.006 at 10 GHz and it increases with
decreasing precessional frequency. | 1503.07043v5 |
2016-05-22 | Low Gilbert damping in Co2FeSi and Fe2CoSi films | Thin highly textured Fe$_{\mathrm{1+x}}$Co$_{\mathrm{2-x}}$Si ($0 \leq$ x
$\leq 1$) films were prepared on MgO (001) substrates by magnetron
co-sputtering. The magneto-optic Kerr effect (MOKE) and ferromagnetic resonance
(FMR) measurements were used to investigate the composition dependence of the
magnetization, the magnetic anisotropy, the gyromagnetic ratio and the
relaxation of the films. The effective magnetization for the thin
Fe$_{\mathrm{1+x}}$Co$_{\mathrm{2-x}}$Si films, determined by FMR measurements,
are consistent with the Slater Pauling prediction. Both MOKE and FMR
measurements reveal a pronounced fourfold anisotropy distribution for all
films. In addition we found a strong influence of the stoichiometry on the
anisotropy as the cubic anisotropy strongly increases with increasing Fe
concentration. The gyromagnetic ratio is only weakly dependent on the
composition. We find low Gilbert damping parameters for all films with values
down to $0.0012\pm0.00012$ for Fe$_{1.75}$Co$_{1.25}$Si. The effective damping
parameter for Co$_2$FeSi is found to be $0.0018\pm 0.0004$. We also find a
pronounced anisotropic relaxation, which indicates significant contributions of
two-magnon scattering processes that is strongest along the easy axes of the
films. This makes thin Fe$_{\mathrm{1+x}}$Co$_{\mathrm{2-x}}$Si films ideal
materials for the application in STT-MRAM devices. | 1605.06797v1 |
2017-09-21 | Low Gilbert Damping Constant in Perpendicularly Magnetized W/CoFeB/MgO Films with High Thermal Stability | Perpendicular magnetic materials with low damping constant and high thermal
stability have great potential for realizing high-density, non-volatile, and
low-power consumption spintronic devices, which can sustain operation
reliability for high processing temperatures. In this work, we study the
Gilbert damping constant ({\alpha}) of perpendicularly magnetized W/CoFeB/MgO
films with a high perpendicular magnetic anisotropy (PMA) and superb thermal
stability. The {\alpha} of these PMA films annealed at different temperatures
is determined via an all-optical Time-Resolved Magneto-Optical Kerr Effect
method. We find that {\alpha} of these W/CoFeB/MgO PMA films decreases with
increasing annealing temperature, reaches a minimum of {\alpha} = 0.016 at an
annealing temperature of 350 {\deg}C, and then increases to 0.024 after
post-annealing at 400 {\deg}C. The minimum {\alpha} observed at 350 {\deg}C is
rationalized by two competing effects as the annealing temperature becomes
higher: the enhanced crystallization of CoFeB and dead-layer growth occurring
at the two interfaces of the CoFeB layer. We further demonstrate that {\alpha}
of the 400 {\deg}C-annealed W/CoFeB/MgO film is comparable to that of a
reference Ta/CoFeB/MgO PMA film annealed at 300 {\deg}C, justifying the
enhanced thermal stability of the W-seeded CoFeB films. | 1709.07483v1 |
2022-02-06 | Enhancing Perpendicular Magnetic Anisotropy in Garnet Ferrimagnet by Interfacing with Few-Layer WTe2 | Engineering magnetic anisotropy in a ferro- or ferrimagnetic (FM) thin film
is crucial in spintronic device. One way to modify the magnetic anisotropy is
through the surface of the FM thin film. Here, we report the emergence of a
perpendicular magnetic anisotropy (PMA) induced by interfacial interactions in
a heterostructure comprised of a garnet ferrimagnet, Y3Fe5O12 (YIG), and the
low-symmetry, high spin orbit coupling (SOC) transition metal dichalcogenide,
WTe2. At the same time, we also observed an enhancement in Gilbert damping in
the WTe2 covered YIG area. Both the magnitude of interface-induced PMA and the
Gilbert damping enhancement have no observable WTe2 thickness dependence down
to single quadruple-layer, indicating that the interfacial interaction plays a
critical role. The ability of WTe2 to enhance the PMA in FM thin film, combined
with its previously reported capability to generate out-of-plane damping like
spin torque, makes it desirable for magnetic memory applications. | 2202.02834v1 |
2022-05-27 | Scalar field damping at high temperatures | The motion of a scalar field that interacts with a hot plasma, like the
inflaton during reheating, is damped, which is a dissipative process. At high
temperatures the damping can be described by a local term in the effective
equation of motion. The damping coefficient is sensitive to multiple
scattering. In the loop expansion its computation would require an all-order
resummation. Instead we solve an effective Boltzmann equation, similarly to the
computation of transport coefficients. For an interaction with another scalar
field we obtain a simple relation between the damping coefficient and the bulk
viscosity, so that one can make use of known results for the latter. The
numerical prefactor of the damping coefficient turns out to be rather large, of
order $ 10 ^ 4 $. | 2205.14166v2 |
2022-12-02 | Equivalence between the energy decay of fractional damped Klein-Gordon equations and geometric conditions for damping coefficients | We consider damped $s$-fractional Klein--Gordon equations on $\mathbb{R}^d$,
where $s$ denotes the order of the fractional Laplacian. In the one-dimensional
case $d = 1$, Green (2020) established that the exponential decay for $s \geq
2$ and the polynomial decay of order $s/(4-2s)$ hold if and only if the damping
coefficient function satisfies the so-called geometric control condition. In
this note, we show that the $o(1)$ energy decay is also equivalent to these
conditions in the case $d=1$. Furthermore, we extend this result to the
higher-dimensional case: the logarithmic decay, the $o(1)$ decay, and the
thickness of the damping coefficient are equivalent for $s \geq 2$. In
addition, we also prove that the exponential decay holds for $0 < s < 2$ if and
only if the damping coefficient function has a positive lower bound, so in
particular, we cannot expect the exponential decay under the geometric control
condition. | 2212.01029v4 |
2017-06-13 | Uniform energy decay for wave equations with unbounded damping coefficients | We consider the Cauchy problem for wave equations with unbounded damping
coefficients in the whole space. For a general class of unbounded damping
coefficients, we derive uniform total energy decay estimates together with a
unique existence result of a weak solution. In this case we never impose strong
assumptions such as compactness of the support of the initial data. This means
that we never rely on the finite propagation speed property of the solution,
and we try to deal with an essential unbounded coefficient case. | 1706.03942v1 |
2021-06-09 | Grammage of cosmic rays in the proximity of supernova remnants embedded in a partially ionized medium | We investigate the damping of Alfv\'en waves generated by the cosmic ray
resonant streaming instability in the context of the cosmic ray escape and
propagation in the proximity of supernova remnants. We consider ion-neutral
damping, turbulent damping and non linear Landau damping in the warm ionized
and warm neutral phases of the interstellar medium. For the ion-neutral
damping, up-to-date damping coefficients are used. We investigate in particular
whether the self-confinement of cosmic rays nearby sources can appreciably
affect the grammage. We show that the ion-neutral damping and the turbulent
damping effectively limit the residence time of cosmic rays in the source
proximity, so that the grammage accumulated near sources is found to be
negligible. Contrary to previous results, this also happens in the most extreme
scenario where ion-neutral damping is less effective, namely in a medium with
only neutral helium and fully ionized hydrogen. Therefore, the standard
picture, in which CR secondaries are produced during the whole time spent by
cosmic rays throughout the Galactic disk, need not to be deeply revisited. | 2106.04948v1 |
2023-02-23 | Buckling Metamaterials for Extreme Vibration Damping | Damping mechanical resonances is a formidable challenge in an increasing
number of applications. Many of the passive damping methods rely on using low
stiffness dissipative elements, complex mechanical structures or electrical
systems, while active vibration damping systems typically add an additional
layer of complexity. However, in many cases, the reduced stiffness or
additional complexity and mass render these vibration damping methods
unfeasible. Here, we introduce a method for passive vibration damping by
allowing buckling of the primary load path, which sets an upper limit for
vibration transmission: the transmitted acceleration saturates at a maximum
value, no matter what the input acceleration is. This nonlinear mechanism leads
to an extreme damping coefficient tan delta ~0.23 in our metal
metamaterial|orders of magnitude larger than the linear damping of traditional
lightweight structural materials. We demonstrate this principle experimentally
and numerically in free-standing rubber and metal mechanical metamaterials over
a range of accelerations, and show that bi-directional buckling can further
improve its performance. Buckling metamaterials pave the way towards extreme
vibration damping without mass or stiffness penalty, and as such could be
applicable in a multitude of high-tech applications, including aerospace
structures, vehicles and sensitive instruments. | 2302.11968v1 |
2014-03-19 | The effects of time-dependent dissipation on the basins of attraction for the pendulum with oscillating support | We consider a pendulum with vertically oscillating support and time-dependent
damping coefficient which varies until reaching a finite final value. The sizes
of the corresponding basins of attraction are found to depend strongly on the
full evolution of the dissipation. In order to predict the behaviour of the
system, it is essential to understand how the sizes of the basins of attraction
for constant dissipation depend on the damping coefficient. For values of the
parameters in the perturbation regime, we characterise analytically the
conditions under which the attractors exist and study numerically how the sizes
of their basins of attraction depend on the damping coefficient. Away from the
perturbation regime, a numerical study of the attractors and the corresponding
basins of attraction for different constant values of the damping coefficient
produces a much more involved scenario: changing the magnitude of the
dissipation causes some attractors to disappear either leaving no trace or
producing new attractors by bifurcation, such as period doubling and
saddle-node bifurcation. For an initially non-constant damping coefficient,
both increasing and decreasing to some finite final value, we numerically
observe that, when the damping coefficient varies slowly from a finite initial
value to a different final value, without changing the set of attractors, the
slower the variation the closer the sizes of the basins of attraction are to
those they have for constant damping coefficient fixed at the initial value. If
during the variation of the damping coefficient attractors appear or disappear,
remarkable additional phenomena may occur. For instance, a fixed point
asymptotically may attract the entire phase space, up to a zero measure set,
even though no attractor with such a property exists for any value of the
damping coefficient between the extreme values. | 1403.4996v1 |
2016-08-14 | Mechanical energy and mean equivalent viscous damping for SDOF fractional oscillators | This paper addresses the total mechanical energy of a single degree of
freedom fractional oscillator. Based on the energy storage and dissipation
properties of the Caputo fractional derivatives, the expression for total
mechanical energy in the single degree of freedom fractional oscillator is
firstly presented. The energy regeneration due to the external exciting force
and the energy loss due to the fractional damping force during the vibratory
motion are analyzed. Furthermore, based on the mean energy dissipation of the
fractional damping element in steady-state vibration, a new concept of mean
equivalent viscous damping is suggested and the value of the damping
coefficient is evaluated. | 1608.04071v1 |
2023-09-26 | Qualitative properties of solutions to a nonlinear transmission problem for an elastic Bresse beam | We consider a nonlinear transmission problem for a Bresse beam, which
consists of two parts, damped and undamped. The mechanical damping in the
damped part is present in the shear angle equation only, and the damped part
may be of arbitrary positive length. We prove well-posedness of the
corresponding PDE system in energy space and establish existence of a regular
global attractor under certain conditions on nonlinearities and coefficients of
the damped part only. Moreover, we study singular limits of the problem when
$l\to 0$ or $l\to 0$ simultaneously with $k_i\to +\infty$ and perform numerical
modelling for these processes. | 2309.15171v2 |
2016-09-05 | Remarks on an elliptic problem arising in weighted energy estimates for wave equations with space-dependent damping term in an exterior domain | This paper is concerned with weighted energy estimates and diffusion
phenomena for the initial-boundary problem of the wave equation with
space-dependent damping term in an exterior domain. In this analysis, an
elliptic problem was introduced by Todorova and Yordanov. This attempt was
quite useful when the coefficient of the damping term is radially symmetric. In
this paper, by modifying their elliptic problem, we establish weighted energy
estimates and diffusion phenomena even when the coefficient of the damping term
is not radially symmetric. | 1609.01063v2 |
2017-03-09 | Long-time dynamics of the strongly damped semilinear plate equation in $\mathbb{R}^{n}$ | We investigate the initial-value problem for the semilinear plate equation
containing localized strong damping, localized weak damping and nonlocal
nonlinearity. We prove that if nonnegative damping coefficients are strictly
positive almost everywhere in the exterior of some ball and the sum of these
coefficients is positive a.e. in $%
\mathbb{R}
^{n}$, then the semigroup generated by the considered problem possesses a
global attractor in $H^{2}\left(
\mathbb{R}
^{n}\right) \times L^{2}\left(
\mathbb{R}
^{n}\right) $. We also establish boundedness of this attractor in $
H^{3}\left(
\mathbb{R}
^{n}\right) \times H^{2}\left(
\mathbb{R} ^{n}\right) $. | 1703.03485v2 |
2020-11-06 | A generalized finite element method for the strongly damped wave equation with rapidly varying data | We propose a generalized finite element method for the strongly damped wave
equation with highly varying coefficients. The proposed method is based on the
localized orthogonal decomposition introduced and is designed to handle
independent variations in both the damping and the wave propagation speed
respectively. The method does so by automatically correcting for the damping in
the transient phase and for the propagation speed in the steady state phase.
Convergence of optimal order is proven in $L_2(H^1)$-norm, independent of the
derivatives of the coefficients. We present numerical examples that confirm the
theoretical findings. | 2011.03311v1 |
2022-10-30 | Intrinsic polynomial squeezing for Balakrishnan-Taylor beam models | We explore the energy decay properties related to a model in extensible beams
with the so-called energy damping. We investigate the influence of the
nonloncal damping coefficient in the stability of the model. We prove, for the
first time, that the corresponding energy functional is squeezed by
polynomial-like functions involving the power of the damping coefficient, which
arises intrinsically from the Balakrishnan-Taylor beam models. As a
consequence, it is shown that such models with nonlocal energy damping are
never exponentially stable in its essence. | 2210.16931v1 |
2020-11-16 | Technology to Counter Online Flaming Based on the Frequency-Dependent Damping Coefficient in the Oscillation Model | Online social networks, which are remarkably active, often experience
explosive user dynamics such as online flaming, which can significantly impact
the real world. However, countermeasures based on social analyses of the
individuals causing flaming are too slow to be effective because of the
rapidity with which the influence of online user dynamics propagates. A
countermeasure technology for the flaming phenomena based on the oscillation
model, which describes online user dynamics, has been proposed; it is an
immediate solution as it does not depend on social analyses of individuals.
Conventional countermeasures based on the oscillation model assume that the
damping coefficient is a constant regardless of the eigenfrequency. This
assumption is, however, problematic as the damping coefficients are, in
general, inherently frequency-dependent; the theory underlying the dependence
is being elucidated. This paper discusses a design method that uses the damping
coefficient to prevent flaming under general conditions considering the
frequency-dependence of the damping coefficient and proposes a countermeasure
technology for the flaming phenomena. | 2011.08117v1 |
2018-10-25 | Time-retarded damping and magnetic inertia in the Landau-Lifshitz-Gilbert equation self-consistently coupled to electronic time-dependent nonequilibrium Green functions | The conventional Landau-Lifshitz-Gilbert (LLG) equation is a widely used tool
to describe dynamics of local magnetic moments, viewed as classical vectors of
fixed length, with their change assumed to take place simultaneously with the
cause. Here we demonstrate that recently developed [M. D. Petrovi\'{c} {\em et
al.}, {\tt arXiv:1802.05682}] self-consistent coupling of the LLG equation to
time-dependent quantum-mechanical description of electrons microscopically
generates time-retarded damping in the LLG equation described by a memory
kernel which is also spatially dependent. For sufficiently slow dynamics of
local magnetic moments, the memory kernel can be expanded to extract the
Gilbert damping (proportional to first time derivative of magnetization) and
magnetic inertia (proportional to second time derivative of magnetization)
terms whose parameters, however, are time-dependent in contrast to
time-independent parameters used in the conventional LLG equation. We use
examples of single or multiple magnetic moments precessing in an external
magnetic field, as well as field-driven motion of a magnetic domain wall (DW),
to quantify the difference in their time evolution computed from conventional
LLG equation vs. TDNEGF+LLG quantum-classical hybrid approach. The faster DW
motion predicted by TDNEGF+LLG approach reveals that important quantum effects,
stemming from finite amount of time which it takes for conduction electron spin
to react to the motion of classical local magnetic moments, are missing from
conventional classical micromagnetics simulations. We also demonstrate large
discrepancy between TDNEGF+LLG-computed numerically exact and, therefore,
nonperturbative result for charge current pumped by a moving DW and the same
quantity computed by perturbative spin motive force formula combined with the
conventional LLG equation. | 1810.11016v2 |
2019-08-08 | Annihilation of topological solitons in magnetism with spin wave burst finale: The role of nonequilibrium electrons causing nonlocal damping and spin pumping over ultrabroadband frequency range | We not only reproduce burst of short-wavelength spin waves (SWs) observed in
recent experiment [S. Woo et al., Nat. Phys. 13, 448 (2017)] on
magnetic-field-driven annihilation of two magnetic domain walls (DWs) but,
furthermore, we predict that this setup additionally generates highly unusual}
pumping of electronic spin currents in the absence of any bias voltage. Prior
to the instant of annihilation, their power spectrum is ultrabroadband, so they
can be converted into rapidly changing in time charge currents, via the inverse
spin Hall effect, as a source of THz radiation of bandwidth $\simeq 27$ THz
where the lowest frequency is controlled by the applied magnetic field. The
spin pumping stems from time-dependent fields introduced into the quantum
Hamiltonian of electrons by the classical dynamics of localized magnetic
moments (LMMs) comprising the domains. The pumped currents carry spin-polarized
electrons which, in turn, exert backaction on LMMs in the form of nonlocal
damping which is more than twice as large as conventional local Gilbert
damping. The nonlocal damping can substantially modify the spectrum of emitted
SWs when compared to widely-used micromagnetic simulations where conduction
electrons are completely absent. Since we use fully microscopic (i.e.,
Hamiltonian-based) framework, self-consistently combining time-dependent
electronic nonequilibrium Green functions with the Landau-Lifshitz-Gilbert
equation, we also demonstrate that previously derived phenomenological formulas
miss ultrabroadband spin pumping while underestimating the magnitude of
nonlocal damping due to nonequilibrium electrons. | 1908.03194v5 |
2020-09-23 | Remark on the exponential decay of the solutions of the damped wave equation | A condition which guaranties the exponential decay of the solutions of the
initial-boundary value problem for the damped wave equation is proved. A method
for the effective computability of the coefficient of exponential decay is also
presented. | 2009.11244v1 |
2021-06-22 | Choice of Damping Coefficient in Langevin Dynamics | This article considers the application of Langevin dynamics to sampling and
investigates how to choose the damping parameter in Langevin dynamics for the
purpose of maximizing thoroughness of sampling. Also, it considers the
computation of measures of sampling thoroughness. | 2106.11597v1 |
2004-03-12 | Factorization of damped wave equations with cubic nonlinearities | The recent factorization scheme that we introduced for nonlinear polynomial
ODEs in math-ph/0401040 is applied to the interesting case of damped wave
equations with cubic nonlinearities. Traveling kink solutions are possible in
the plane defined by the kink velocity versus the damping coefficient only
along hyperbolas that are plotted herein | 0403022v1 |
2002-08-07 | Toward a Universal Model of Damping--Modified Coulomb Friction | A modification of Coulomb's law of friction uses a variable coefficient of
friction that depends on a power law in the energy of mechanical oscillation.
Through the use of three different exponents: 0, 1/2 and 1; all commonly
encountered non-viscous forms of damping are accommodated. The nonlinear model
appears to yield good agreement with experiment in cases of surface, internal,
and amplitude dependent damping. | 0208025v1 |
2012-12-08 | A note on the lifespan of solutions to the semilinear damped wave equation | This paper concerns estimates of the lifespan of solutions to the semilinear
damped wave equation. We give upper estimates of the lifespan for the
semilinear damped wave equation with variable coefficients in all space
dimensions. | 1212.1772v3 |
2018-03-20 | Stability of the wave equations on a tree with local Kelvin-Voigt damping | In this paper we study the stability problem of a tree of elastic strings
with local Kelvin-Voigt damping on some of the edges. Under the compatibility
condition of displacement and strain and continuity condition of damping
coefficients at the vertices of the tree, exponential/polynomial stability are
proved. | 1803.07280v1 |
2021-08-17 | Spectral enclosures for the damped elastic wave equation | In this paper we investigate spectral properties of the damped elastic wave
equation. Deducing a correspondence between the eigenvalue problem of this
model and the one of Lam\'e operators with non self-adjoint perturbations, we
provide quantitative bounds on the location of the point spectrum in terms of
suitable norms of the damping coefficient. | 2108.07676v1 |
2022-05-26 | Ergodic results for the stochastic nonlinear Schrödinger equation with large damping | We study the nonlinear Schr\"odinger equation with linear damping, i.e. a
zero order dissipation, and additive noise. Working in $R^d$ with d = 2 or d =
3, we prove the uniqueness of the invariant measure when the damping
coefficient is sufficiently large. | 2205.13364v1 |
2016-08-30 | Optimal damping ratios of multi-axial perfectly matched layers for elastic-wave modeling in general anisotropic media | The conventional Perfectly Matched Layer (PML) is unstable for certain kinds
of anisotropic media. This instability is intrinsic and independent of PML
formulation or implementation. The Multi-axial PML (MPML) removes such
instability using a nonzero damping coefficient in the direction parallel with
the interface between a PML and the investigated domain. The damping ratio of
MPML is the ratio between the damping coefficients along the directions
parallel with and perpendicular to the interface between a PML and the
investigated domain. No quantitative approach is available for obtaining these
damping ratios for general anisotropic media. We develop a quantitative
approach to determining optimal damping ratios to not only stabilize PMLs, but
also minimize the artificial reflections from MPMLs. Numerical tests based on
finite-difference method show that our new method can effectively provide a set
of optimal MPML damping ratios for elastic-wave propagation in 2D and 3D
general anisotropic media. | 1608.08326v3 |
2017-10-13 | Mode-Dependent Damping in Metallic Antiferromagnets Due to Inter-Sublattice Spin Pumping | Damping in magnetization dynamics characterizes the dissipation of magnetic
energy and is essential for improving the performance of spintronics-based
devices. While the damping of ferromagnets has been well studied and can be
artificially controlled in practice, the damping parameters of
antiferromagnetic materials are nevertheless little known for their physical
mechanisms or numerical values. Here we calculate the damping parameters in
antiferromagnetic dynamics using the generalized scattering theory of
magnetization dissipation combined with the first-principles transport
computation. For the PtMn, IrMn, PdMn and FeMn metallic antiferromagnets, the
damping coefficient associated with the motion of magnetization ($\alpha_m$) is
one to three orders of magnitude larger than the other damping coefficient
associated with the variation of the N\'eel order ($\alpha_n$), in sharp
contrast to the assumptions made in the literature. | 1710.04766v1 |
2020-03-29 | Stability results for an elastic-viscoelastic waves interaction systems with localized Kelvin-Voigt damping and with an internal or boundary time delay | We investigate the stability of a one-dimensional wave equation with non
smooth localized internal viscoelastic damping of Kelvin-Voigt type and with
boundary or localized internal delay feedback. The main novelty in this paper
is that the Kelvin-Voigt and the delay damping are both localized via non
smooth coefficients. In the case that the Kelvin-Voigt damping is localized
faraway from the tip and the wave is subjected to a locally distributed
internal or boundary delay feedback, we prove that the energy of the system
decays polynomially of type t^{-4}. However, an exponential decay of the energy
of the system is established provided that the Kelvin-Voigt damping is
localized near a part of the boundary and a time delay damping acts on the
second boundary. While, when the Kelvin-Voigt and the internal delay damping
are both localized via non smooth coefficients near the tip, the energy of the
system decays polynomially of type t^{-4}. Frequency domain arguments combined
with piecewise multiplier techniques are employed. | 2003.12967v1 |
2023-09-15 | On the formation of singularities for the slightly supercritical NLS equation with nonlinear damping | We consider the focusing, mass-supercritical NLS equation augmented with a
nonlinear damping term. We provide sufficient conditions on the nonlinearity
exponents and damping coefficients for finite-time blow-up. In particular,
singularities are formed for focusing and dissipative nonlinearities of the
same power, provided that the damping coefficient is sufficiently small. Our
result thus rigorously proves the non-regularizing effect of nonlinear damping
in the mass-supercritical case, which was suggested by previous numerical and
formal results.
We show that, under our assumption, the damping term may be controlled in
such a way that the self-similar blow-up structure for the focusing NLS is
approximately retained even within the dissipative evolution. The nonlinear
damping contributes as a forcing term in the equation for the perturbation
around the self-similar profile, that may produce a growth over finite time
intervals. We estimate the error terms through a modulation analysis and a
careful control of the time evolution of total momentum and energy functionals. | 2309.08281v1 |
2006-06-05 | Phenomenological theory of current driven exchange switching in ferromagnetic nanojunctions | Phenomenological approach is developed in the theory of spin-valve type
ferromagnetic junctions to describe exchange switching by current flowing
perpendicular to interfaces. Forward and backward current switching effects are
described and they may be principally different in nature. Mobile electron
spins are considered as being free in all the contacting ferromagnetic layers.
Joint action of the following two current effects is investigated: the
nonequilibrium longitudinal spin-injection effective field and the transverse
spin-transfer surface torque. Dispersion relation for fluctuations is derived
and solved for a junction model having spatially localized spin transfer
torque: depth of the torque penetration into the free layer is assumed much
smaller than the total free layer thickness. Some critical value of the well
known Gilbert damping constant is established for the first time. Spin transfer
torque dominates in the instability threshold determination for small enough
damping constants, while the spin-injection effective field dominates for high
damping. Fine interplay between spin transfer torque and spin injection is
necessary to provide a hysteretic behavior of the resistance versus current
dependence. The state diagram building up shows the possibility of
non-stationary (time dependent) nonlinear states arising due to instability
development. Calculations lead to the instability rise time values of the order
of 0.1 ns. Spin wave resonance frequency spectrum softening occurs under the
current growing to the instability threshold. Magnetization fluctuations above
the threshold rise oscillating with time for low damping, but rise
aperiodically and much more rapid for high damping. | 0606102v2 |
2015-07-29 | Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau-Lifschitz-Gilbert equation | The real-time dynamics of a classical spin in an external magnetic field and
locally exchange coupled to an extended one-dimensional system of
non-interacting conduction electrons is studied numerically. Retardation
effects in the coupled electron-spin dynamics are shown to be the source for
the relaxation of the spin in the magnetic field. Total energy and spin is
conserved in the non-adiabatic process. Approaching the new local ground state
is therefore accompanied by the emission of dispersive wave packets of
excitations carrying energy and spin and propagating through the lattice with
Fermi velocity. While the spin dynamics in the regime of strong exchange
coupling J is rather complex and governed by an emergent new time scale, the
motion of the spin for weak J is regular and qualitatively well described by
the Landau-Lifschitz-Gilbert (LLG) equation. Quantitatively, however, the full
quantum-classical hybrid dynamics differs from the LLG approach. This is
understood as a breakdown of weak-coupling perturbation theory in J in the
course of time. Furthermore, it is shown that the concept of the Gilbert
damping parameter is ill-defined for the case of a one-dimensional system. | 1507.08227v2 |
2008-09-26 | Damping and magnetic anisotropy of ferromagnetic GaMnAs thin films | The magnetic properties of annealed, epitaxial Ga0.93Mn0.07As layers under
tensile and compressive stress have been investigated by X-band (9GHz) and
Q-band (35GHz) ferromagnetic resonance (FMR) spectroscopy. From the analysis of
the linewidths of the uniform mode spectra the FMR Gilbert damping factor
"alpha" has been determined. At T=4K we obtain a minimum damping factor of
"alpha" = 0.003 for the compressively stressed layer. Its value is not
isotropic. It has a minimum value for the easy axes orientations of the
magnetic field and increases with the measuring temperature. Its average value
is for both type of films of the order of 0.01 in spite of strong differences
in the inhomogeneous linewidth which vary between 20 Oe and 600 Oe for the
layers grown on GaAs and GaInAs substrates respectively. | 0809.4644v2 |
2013-08-02 | Spin pumping damping and magnetic proximity effect in Pd and Pt spin-sink layers | We investigated the spin pumping damping contributed by paramagnetic layers
(Pd, Pt) in both direct and indirect contact with ferromagnetic
Ni$_{81}$Fe$_{19}$ films. We find a nearly linear dependence of the
interface-related Gilbert damping enhancement $\Delta\alpha$ on the heavy-metal
spin-sink layer thicknesses t$_\textrm{N}$ in direct-contact
Ni$_{81}$Fe$_{19}$/(Pd, Pt) junctions, whereas an exponential dependence is
observed when Ni$_{81}$Fe$_{19}$ and (Pd, Pt) are separated by \unit[3]{nm} Cu.
We attribute the quasi-linear thickness dependence to the presence of induced
moments in Pt, Pd near the interface with Ni$_{81}$Fe$_{19}$, quantified using
X-ray magnetic circular dichroism (XMCD) measurements. Our results show that
the scattering of pure spin current is configuration-dependent in these systems
and cannot be described by a single characteristic length. | 1308.0450v2 |
2015-02-05 | Nonlinear analysis of magnetization dynamics excited by spin Hall effect | We investigate the possibility of exciting self-oscillation in a
perpendicular ferromagnet by the spin Hall effect on the basis of a nonlinear
analysis of the Landau-Lifshitz-Gilbert (LLG) equation. In the self-oscillation
state, the energy supplied by the spin torque during a precession on a constant
energy curve should equal the dissipation due to damping. Also, the current to
balance the spin torque and the damping torque in the self-oscillation state
should be larger than the critical current to destabilize the initial state. We
find that the second condition in the spin Hall system is not satisfied by
deriving analytical solutions of the energy supplied by the spin transfer
effect and the dissipation due to the damping from the nonlinear LLG equation.
This indicates that the self-oscillation of a perpendicular ferromagnet cannot
be excited solely by the spin Hall torque. | 1502.01420v2 |
2015-03-04 | Critical current destabilizing perpendicular magnetization by the spin Hall effect | The critical current needed to destabilize the magnetization of a
perpendicular ferromagnet via the spin Hall effect is studied. Both the
dampinglike and fieldlike torques associated with the spin current generated by
the spin Hall effect is included in the Landau-Lifshitz-Gilbert equation to
model the system. In the absence of the fieldlike torque, the critical current
is independent of the damping constant and is much larger than that of
conventional spin torque switching of collinear magnetic systems, as in
magnetic tunnel junctions. With the fieldlike torque included, we find that the
critical current scales with the damping constant as $\alpha^{0}$ (i.e.,
damping independent),$\alpha$, and $\alpha^{1/2}$ depending on the sign of the
fieldlike torque and other parameters such as the external field. Numerical and
analytical results show that the critical current can be significantly reduced
when the fieldlike torque possesses the appropriate sign, i.e. when the
effective field associated with the fieldlike torque is pointing opposite to
the spin direction of the incoming electrons. These results provide a pathway
to reducing the current needed to switch magnetization using the spin Hall
effect. | 1503.01478v2 |
2015-10-23 | Laser-induced THz magnetization precession for a tetragonal Heusler-like nearly compensated ferrimagnet | Laser-induced magnetization precessional dynamics was investigated in
epitaxial films of Mn$_3$Ge, which is a tetragonal Heusler-like nearly
compensated ferrimagnet. The ferromagnetic resonance (FMR) mode was observed,
the precession frequency for which exceeded 0.5 THz and originated from the
large magnetic anisotropy field of approximately 200 kOe for this ferrimagnet.
The effective damping constant was approximately 0.03. The corresponding
effective Landau-Lifshitz constant of approximately 60 Mrad/s and is comparable
to those of the similar Mn-Ga materials. The physical mechanisms for the
Gilbert damping and for the laser-induced excitation of the FMR mode were also
discussed in terms of the spin-orbit-induced damping and the laser-induced
ultrafast modulation of the magnetic anisotropy, respectively. | 1510.06793v1 |
2017-04-11 | CoFeAlB alloy with low damping and low magnetization for spin transfer torque switching | We investigate the effect of Al doping on the magnetic properties of the
alloy CoFeB. Comparative measurements of the saturation magnetization, the
Gilbert damping parameter $\alpha$ and the exchange constant as a function of
the annealing temperature for CoFeB and CoFeAlB thin films are presented. Our
results reveal a strong reduction of the magnetization for CoFeAlB in
comparison to CoFeB. If the prepared CoFeAlB films are amorphous, the damping
parameter $\alpha$ is unaffected by the Al doping in comparison to the CoFeB
alloy. In contrast, in the case of a crystalline CoFeAlB film, $\alpha$ is
found to be reduced. Furthermore, the x-ray characterization and the evolution
of the exchange constant with the annealing temperature indicate a similar
crystallization process in both alloys. The data proves the suitability of
CoFeAlB for spin torque switching properties where a reduction of the switching
current in comparison with CoFeB is expected. | 1704.03326v1 |
2018-09-25 | Theory of damping in magnetization dynamics, dispelling a myth and pointing a way forward | There is a widely-held belief amongst theoreticians that the Gilbert damping
parameter {\alpha} in magnetization dynamics is infinite for a pure metal at
T=0. The basic error leading to this belief is pointed out explicitly and the
various methods of calculation used are viewed in a unified way based on the
Lorentzian lineshape of ferromagnetic resonance spectra. A general torque
formula for {\alpha} is proposed as a good starting-point for treating
inhomogeneous materials such as alloys, compounds and layered structures. Local
spin density functional theory provides a simple physical picture, in terms of
a non-uniform precessional cone angle in ferromagnetic resonance, of how such
inhomogeneity contributes to the damping. In a complementary many-body theory
this contribution is given by a vertex correction to the torque-torque response
function. | 1809.09429v1 |
2018-10-31 | Anisotropic and controllable Gilbert-Bloch dissipation in spin valves | Spin valves form a key building block in a wide range of spintronic concepts
and devices from magnetoresistive read heads to spin-transfer-torque
oscillators. We elucidate the dependence of the magnetic damping in the free
layer on the angle its equilibrium magnetization makes with that in the fixed
layer. The spin pumping-mediated damping is anisotropic and tensorial, with
Gilbert- and Bloch-like terms. Our investigation reveals a mechanism for tuning
the free layer damping in-situ from negligible to a large value via the
orientation of fixed layer magnetization, especially when the magnets are
electrically insulating. Furthermore, we expect the Bloch contribution that
emerges from the longitudinal spin accumulation in the non-magnetic spacer to
play an important role in a wide range of other phenomena in spin valves. | 1811.00020v2 |
2019-07-27 | Two improved Gauss-Seidel projection methods for Landau-Lifshitz-Gilbert equation | In this paper, we present two improved Gauss-Seidel projection methods with
unconditional stability. The first method updates the gyromagnetic term and the
damping term simultaneously and follows by a projection step. The second method
introduces two sets of approximate solutions, where we update the gyromagnetic
term and the damping term simultaneously for one set of approximate solutions
and apply the projection step to the other set of approximate solutions in an
alternating manner. Compared to the original Gauss-Seidel projection method
which has to solve heat equations $7$ times at each time step, the improved
methods solve heat equations $5$ times and $3$ times, respectively. First-order
accuracy in time and second-order accuracy in space are verified by examples in
both 1D and 3D. In addition, unconditional stability with respect to both the
grid size and the damping parameter is confirmed numerically. Application of
both methods to a realistic material is also presented with hysteresis loops
and magnetization profiles. Compared with the original method, the recorded
running times suggest that savings of both methods are about $2/7$ and $4/7$
for the same accuracy requirement, respectively. | 1907.11853v1 |
2020-10-01 | Modeling coupled spin and lattice dynamics | A unified model of molecular and atomistic spin dynamics is presented
enabling simulations both in microcanonical and canonical ensembles without the
necessity of additional phenomenological spin damping. Transfer of energy and
angular momentum between the lattice and the spin systems is achieved by a
coupling term based upon the spin-orbit interaction. The characteristic spectra
of the spin and phonon systems are analyzed for different coupling strength and
temperatures. The spin spectral density shows magnon modes together with the
uncorrelated noise induced by the coupling to the lattice. The effective
damping parameter is investigated showing an increase with both coupling
strength and temperature. The model paves the way to understanding magnetic
relaxation processes beyond the phenomenological approach of the Gilbert
damping and the dynamics of the energy transfer between lattice and spins. | 2010.00642v1 |
2021-04-22 | Impact of Fe$_{80}$B$_{20}$ insertion on the properties of dual-MgO perpendicular magnetic tunnel junctions | We explore the impact of Fe80B20 inserted at both
Co$_{20}$Fe$_{80}$B$_{20}$/MgO interfaces of dual-MgO free layers (FLs) in
bottom-pinned magnetic tunnel junctions (MTJs). MTJ stacks are annealed for 30
min at 350 $^\circ$C and 400 $^\circ$C in a vacuum after film deposition.
Current-in-plane tunneling measurements are carried out to characterize
magnetotransport properties of the MTJs. Conventional magnetometry measurements
and ferromagnetic resonance are conducted to estimate the saturation
magnetization, the effective perpendicular anisotropy field and the Gilbert
damping of dual-MgO FLs as a function of the Fe$_{80}$B$_{20}$ thickness and
annealing temperatures. With ultrathin Fe$_{80}$B$_{20}$ (0.2 - 0.4 nm)
inserted, perpendicular magnetic anisotropy (PMA) of FLs increases with similar
tunnel magneto-resistance (TMR) and low damping values. As Fe$_{80}$B$_{20}$
layer thickness further increases (0.6 - 1.2 nm), both TMR and PMA degrade, and
damping increases dramatically. This study demonstrates a novel approach to
tune properties of MTJ stacks with dual-MgO FLs up to 400 $^\circ$C annealing,
which enables MTJ stacks for various applications. | 2104.10918v1 |
2021-09-24 | Damping in yttrium iron garnet film with an interface | We report strong damping enhancement in a 200 nm thick yttrium iron garnet
(YIG) film due to spin inhomogeneity at the interface. The growth-induced thin
interfacial gadolinium iron garnet (GdIG) layer antiferromagnetically (AFM)
exchange couples with the rest of the YIG layer. The out-of-plane angular
variation of ferromagnetic resonance (FMR) linewidth $\Delta H$ reflects a
large inhomogeneous distribution of effective magnetization $\Delta 4 \pi
M_{eff}$ due to the presence of an exchange springlike moments arrangement in
YIG. We probe the spin inhomogeneity at the YIG-GdIG interface by performing an
in-plane angular variation of resonance field $H_{r}$, leading to a
unidirectional feature. The large extrinsic $\Delta 4\pi M_{eff}$ contribution,
apart from the inherent intrinsic Gilbert contribution, manifests enhanced
precessional damping in YIG film. | 2109.12071v1 |
2019-01-29 | Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients | A key quantity that occurs in the error analysis of several numerical methods
for eigenvalue problems is the distance between the eigenvalue of interest and
the next nearest eigenvalue. When we are interested in the smallest or
fundamental eigenvalue, we call this the spectral or fundamental gap. In a
recent manuscript [Gilbert et al., arXiv:1808.02639], the current authors,
together with Frances Kuo, studied an elliptic eigenvalue problem with
homogeneous Dirichlet boundary conditions, and with coefficients that depend on
an infinite number of uniformly distributed stochastic parameters. In this
setting, the eigenvalues, and in turn the eigenvalue gap, also depend on the
stochastic parameters. Hence, for a robust error analysis one needs to be able
to bound the gap over all possible realisations of the parameters, and because
the gap depends on infinitely-many random parameters, this is not trivial. This
short note presents, in a simplified setting, an important result that was
shown in the paper above. Namely, that, under certain decay assumptions on the
coefficient, the spectral gap of such a random elliptic eigenvalue problem can
be bounded away from 0, uniformly over the entire infinite-dimensional
parameter space. | 1901.10470v1 |
2003-09-11 | Theory of Current-Induced Magnetization Precession | We solve appropriate drift-diffusion and Landau-Lifshitz-Gilbert equations to
demonstrate that unpolarized current flow from a non-magnet into a ferromagnet
can produce a precession-type instability of the magnetization. The fundamental
origin of the instability is the difference in conductivity between majority
spins and minority spins in the ferromagnet. This leads to spin accumulation
and spin currents that carry angular momentum across the interface. The
component of this angular momentum perpendicular to the magnetization drives
precessional motion that is opposed by Gilbert damping. Neglecting magnetic
anisotropy and magnetostatics, our approximate analytic and exact numerical
solutions using realistic values for the material parameters show (for both
semi-infinite and thin film geometries) that a linear instability occurs when
both the current density and the excitation wave vector parallel to the
interface are neither too small nor too large. For many aspects of the problem,
the variation of the magnetization in the direction of the current flows makes
an important contribution. | 0309289v1 |
2005-07-20 | All-optical probe of precessional magnetization dynamics in exchange biased NiFe/FeMn bilayers | An internal anisotropy pulse field is launched by an 8.3 ps short laser
excitation, which triggers precessional magnetization dynamics of a
polycrystalline NiFe/FeMn exchange bias system on the picosecond timescale. Due
to the excitation the unidirectional anisotropy and, thus, the exchange
coupling across the interface between the ferromagnetic and the
antiferromagnetic layer is reduced, leading to a fast reduction of the exchange
bias field and to a dramatic increase of the zero-field susceptibility. The
fast optical unpinning is followed by a slower recovery of the interfacial
exchange coupling dominated by spin-lattice and heat flow relaxation with a
time constant of the order of 160 ps. The measured picosecond time evolution of
the exchange decoupling and restoration is interpreted as an anisotropy pulse
field giving rise to fast precessional magnetization dynamics of the
ferromagnetic layer. The strength of the internal pulse field and even the
initial magnetization deflection direction from the equilibrium orientation can
be controlled by the absorbed photons. The dependence of the effective Gilbert
damping on both small and large angle precessional motion was studied, yielding
that both cases can be modeled with reasonable accuracy within the
Landau-Lifshitz and Gilbert framework. | 0507475v1 |
2009-05-28 | Hydrodynamic theory of coupled current and magnetization dynamics in spin-textured ferromagnets | We develop the hydrodynamical theory of collinear spin currents coupled to
magnetization dynamics in metallic ferromagnets. The collective spin density
couples to the spin current through a U(1) Berry-phase gauge field determined
by the local texture and dynamics of the magnetization. We determine
phenomenologically the dissipative corrections to the equation of motion for
the electronic current, which consist of a dissipative spin-motive force
generated by magnetization dynamics and a magnetic texture-dependent
resistivity tensor. The reciprocal dissipative, adiabatic spin torque on the
magnetic texture follows from the Onsager principle. We investigate the effects
of thermal fluctuations and find that electronic dynamics contribute to a
nonlocal Gilbert damping tensor in the Landau-Lifshitz-Gilbert equation for the
magnetization. Several simple examples, including magnetic vortices, helices,
and spirals, are analyzed in detail to demonstrate general principles. | 0905.4544v2 |
2010-11-26 | Dependence of nonlocal Gilbert damping on the ferromagnetic layer type in FM/Cu/Pt heterostructures | We have measured the size effect in nonlocal Gilbert relaxation rate in
FM(t$_{FM}$) / Cu (5nm) [/ Pt (2nm)] / Al(2nm) heterostructures, FM = \{
Ni$_{81}$Fe$_{19}$, Co$_{60}$Fe$_{20}$B$_{20}$, pure Co\}. Common behavior is
observed for three FM layers, where the additional relaxation obeys both a
strict inverse power law dependence $\Delta G =K \:t^{n}$,
$n=-\textrm{1.04}\pm\textrm{0.06}$ and a similar magnitude
$K=\textrm{224}\pm\textrm{40 Mhz}\cdot\textrm{nm}$. As the tested FM layers
span an order of magnitude in spin diffusion length $\lambda_{SDL}$, the
results are in support of spin diffusion, rather than nonlocal resistivity, as
the origin of the effect. | 1011.5868v1 |
2012-06-21 | Fast domain wall propagation in uniaxial nanowires with transverse fields | Under a magnetic field along its axis, domain wall motion in a uniaxial
nanowire is much slower than in the fully anisotropic case, typically by
several orders of magnitude (the square of the dimensionless Gilbert damping
parameter). However, with the addition of a magnetic field transverse to the
wire, this behaviour is dramatically reversed; up to a critical field strength,
analogous to the Walker breakdown field, domain walls in a uniaxial wire
propagate faster than in a fully anisotropic wire (without transverse field).
Beyond this critical field strength, precessional motion sets in, and the mean
velocity decreases. Our results are based on leading-order analytic
calculations of the velocity and critical field as well as numerical solutions
of the Landau-Lifshitz-Gilbert equation. | 1206.4819v2 |
2013-03-05 | Angle-Dependent Spin-Wave Resonance Spectroscopy of (Ga,Mn)As Films | A modeling approach for standing spin-wave resonances based on a
finite-difference formulation of the Landau-Lifshitz-Gilbert equation is
presented. In contrast to a previous study [Bihler et al., Phys. Rev. B 79,
045205 (2009)], this formalism accounts for elliptical magnetization precession
and magnetic properties arbitrarily varying across the layer thickness,
including the magnetic anisotropy parameters, the exchange stiffness, the
Gilbert damping, and the saturation magnetization. To demonstrate the
usefulness of our modeling approach, we experimentally study a set of (Ga,Mn)As
samples grown by low-temperature molecular-beam epitaxy by means of
electrochemical capacitance-voltage measurements and angle-dependent standing
spin-wave resonance spectroscopy. By applying our modeling approach, the angle
dependence of the spin-wave resonance data can be reproduced in a simulation
with one set of simulation parameters for all external field orientations. We
find that the approximately linear gradient in the out-of-plane magnetic
anisotropy is related to a linear gradient in the hole concentrations of the
samples. | 1303.1192v1 |
2013-04-26 | Landau-Lifshitz theory of the longitudinal spin Seebeck effect | Thermal-bias-induced spin angular momentum transfer between a paramagnetic
metal and ferromagnetic insulator is studied theoretically based on the
stochastic Landau-Lifshitz-Gilbert (LLG) phenomenology. Magnons in the
ferromagnet establish a nonequilibrium steady state by equilibrating with
phonons via bulk Gilbert damping and electrons in the paramagnet via spin
pumping, according to the fluctuation-dissipation theorem. Subthermal magnons
and the associated spin currents are treated classically, while the appropriate
quantum crossover is imposed on high-frequency magnetic fluctuations. We
identify several length scales in the ferromagnet, which govern qualitative
changes in the dependence of the thermally-induced spin current on the magnetic
film thickness. | 1304.7295v2 |
2013-09-21 | Patterns formation in axially symmetric Landau-Lifshitz-Gilbert-Slonczewski equations | The Landau-Lifshitz-Gilbert-Slonczewski equation describes magnetization
dynamics in the presence of an applied field and a spin polarized current. In
the case of axial symmetry and with focus on one space dimension, we
investigate the emergence of space-time patterns in the form of wavetrains and
coherent structures, whose local wavenumber varies in space. A major part of
this study concerns existence and stability of wavetrains and of front- and
domain wall-type coherent structures whose profiles asymptote to wavetrains or
the constant up-/down-magnetizations. For certain polarization the Slonczewski
term can be removed which allows for a more complete charaterization, including
soliton-type solutions. Decisive for the solution structure is the polarization
parameter as well as size of anisotropy compared with the difference of field
intensity and current intensity normalized by the damping. | 1309.5523v4 |
2014-02-27 | On the longitudinal spin current induced by a temperature gradient in a ferromagnetic insulator | Based on the solution of the stochastic Landau-Lifshitz-Gilbert equation
discretized for a ferromagnetic chain subject to a uniform temperature
gradient, we present a detailed numerical study of the spin dynamics with a
focus particularly on finite-size effects. We calculate and analyze the net
longitudinal spin current for various temperature gradients, chain lengths, and
external static magnetic fields. In addition, we model an interface formed by a
nonuniformly magnetized finite-size ferromagnetic insulator and a normal metal
and inspect the effects of enhanced Gilbert damping on the formation of the
space-dependent spin current within the chain. A particular aim of this study
is the inspection of the spin Seebeck effect beyond the linear response regime.
We find that within our model the microscopic mechanism of the spin Seebeck
current is the magnon accumulation effect quantified in terms of the exchange
spin torque. According to our results, this effect drives the spin Seebeck
current even in the absence of a deviation between the magnon and phonon
temperature profiles. Our theoretical findings are in line with the recently
observed experimental results by M. Agrawal et al., Phys. Rev. Lett. 111,
107204 (2013). | 1402.6899v1 |
2015-01-19 | Effect of Exchange Interaction on Magnetic Thermal Fluctuation and Spin Susceptibility | The expression of the thermal fluctuation parameter in the stochastic
Landau-Lifshitz-Gilbert equation has been derived from a fundamental quantum
theory of spins and phonons, in which the exchange interaction between nearest
atoms has been included. Our studies show that the thermal fluctuation
decreases exponentially with increasing exchange interaction. The non-uniform
fluctuation of local spins make the spin susceptibility much different from the
result derived by the macro-spin model or single spin model. The related spin
susceptibility depends not only on the strength of exchange interaction, but
also on the lattice structure. The non-uniform fluctuation can lead to an extra
broadening of the resonance line width along with the broadening arisen from
the Gilbert damping. | 1501.04503v2 |
2015-07-23 | Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor | The precessing magnetization of a magnetic islands coupled to a quantum spin
Hall edge pumps charge along the edge. Conversely, a bias voltage applied to
the edge makes the magnetization precess. We point out that this device
realizes an adiabatic quantum motor and discuss the efficiency of its operation
based on a scattering matrix approach akin to Landauer-B"uttiker theory.
Scattering theory provides a microscopic derivation of the
Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device,
including spin-transfer torque, Gilbert damping, and Langevin torque. We find
that the device can be viewed as a Thouless motor, attaining unit efficiency
when the chemical potential of the edge states falls into the
magnetization-induced gap. For more general parameters, we characterize the
device by means of a figure of merit analogous to the ZT value in
thermoelectrics. | 1507.06505v2 |
2017-03-28 | Temperature dependent magnetic damping of yttrium iron garnet spheres | We investigate the temperature dependent microwave absorption spectrum of an
yttrium iron garnet sphere as a function of temperature (5 K to 300 K) and
frequency (3 GHz to 43.5 GHz). At temperatures above 100 K, the magnetic
resonance linewidth increases linearly with temperature and shows a
Gilbert-like linear frequency dependence. At lower temperatures, the
temperature dependence of the resonance linewidth at constant external magnetic
fields exhibits a characteristic peak which coincides with a non-Gilbert-like
frequency dependence. The complete temperature and frequency evolution of the
linewidth can be modeled by the phenomenology of slowly relaxing rare-earth
impurities and either the Kasuya-LeCraw mechanism or the scattering with
optical magnons. Furthermore, we extract the temperature dependence of the
saturation magnetization, the magnetic anisotropy and the g-factor. | 1703.09444v2 |
2017-12-10 | Magnetic field gradient driven dynamics of isolated skyrmions and antiskyrmions in frustrated magnets | The study of skyrmion/antiskyrmion motion in magnetic materials is very
important in particular for the spintronics applications. In this work, we
study the dynamics of isolated skyrmions and antiskyrmions in frustrated
magnets driven by magnetic field gradient, using the Landau-Lifshitz-Gilbert
simulations on the frustrated classical Heisenberg model on the triangular
lattice. A Hall-like motion induced by the gradient is revealed in bulk system,
similar to that in the well-studied chiral magnets. More interestingly, our
work suggests that the lateral confinement in nano-stripes of the frustrated
system can completely suppress the Hall motion and significantly speed up the
motion along the gradient direction. The simulated results are well explained
by the Thiele theory. It is demonstrated that the acceleration of the motion is
mainly determined by the Gilbert damping constant, which provides useful
information for finding potential materials for skyrmion-based spintronics. | 1712.03550v1 |
2018-02-28 | Roles of chiral renormalization on magnetization dynamics in chiral magnets | In metallic ferromagnets, the interaction between local magnetic moments and
conduction electrons renormalizes parameters of the Landau-Lifshitz-Gilbert
equation such as the gyromagnetic ratio and the Gilbert damping, and makes them
dependent on the magnetic configurations. Although the effects of the
renormalization for nonchiral ferromagnets are usually minor and hardly
detectable, we show that the renormalization does play a crucial role for
chiral magnets. Here the renormalization is chiral and as such we predict
experimentally identifiable effects on the phenomenology of magnetization
dynamics. In particular, our theory for the self-consistent magnetization
dynamics of chiral magnets allows for a concise interpretation of domain wall
creep motion. We also argue that the conventional creep theory of the domain
wall motion, which assumes Markovian dynamics, needs critical reexamination
since the gyromagnetic ratio makes the motion non-Markovian. The non-Markovian
nature of the domain wall dynamics is experimentally checkable by the chirality
of the renormalization. | 1803.00017v2 |
2018-12-20 | Laser Controlled Spin Dynamics of Ferromagnetic Thin Film from Femtosecond to Nanosecond Timescale | Laser induced modulation of the magnetization dynamics occurring over various
time-scales have been unified here for a Ni80Fe20 thin film excited by
amplified femtosecond laser pulses. The weak correlation between
demagnetization time and pump fluence with substantial enhancement in
remagnetization time is demonstrated using three-temperature model considering
the temperatures of electron, spin and lattice. The picosecond magnetization
dynamics is modeled using the Landau-Lifshitz-Gilbert equation. With increasing
pump fluence the Gilbert damping parameter shows significant enhancement from
its intrinsic value due to increment in the ratio of electronic temperature to
Curie temperature within very short time scale. The precessional frequency
experiences noticeable red shift with increasing pump fluence. The changes in
the local magnetic properties due to accumulation and dissipation of thermal
energy within the probed volume are described by the evolution of temporal
chirp parameter in a comprehensive manner. A unification of ultrafast magnetic
processes and its control over broad timescale would enable the integration of
various magnetic processes in a single device and use one effect to control
another. | 1812.08404v1 |
2019-03-13 | Higher-order linearly implicit full discretization of the Landau--Lifshitz--Gilbert equation | For the Landau--Lifshitz--Gilbert (LLG) equation of micromagnetics we study
linearly implicit backward difference formula (BDF) time discretizations up to
order $5$ combined with higher-order non-conforming finite element space
discretizations, which are based on the weak formulation due to Alouges but use
approximate tangent spaces that are defined by $L^2$-averaged instead of nodal
orthogonality constraints. We prove stability and optimal-order error bounds in
the situation of a sufficiently regular solution. For the BDF methods of orders
$3$ to~$5$, this requires %a mild time step restriction $\tau \leqslant ch$ and
that the damping parameter in the LLG equations be above a positive threshold;
this condition is not needed for the A-stable methods of orders $1$ and $2$,
for which furthermore a discrete energy inequality irrespective of solution
regularity is proved. | 1903.05415v2 |
2019-12-01 | Coarse-graining in micromagnetic simulations of dynamic hysteresis loops | Micromagnetic simulations based on the stochastic Landau-Lifshitz-Gilbert
equation are used to calculate dynamic magnetic hysteresis loops relevant to
magnetic hyperthermia. With the goal to effectively simulate room-temperature
loops for large iron-oxide-based systems at relatively slow sweep rates on the
order of 1 Oe/ns or less, a previously derived renormalization group approach
for coarse-graining (Grinstein and Koch, Phys. Rev. Lett. 20, 207201, 2003) is
modified and applied to calculating loops for a magnetite nanorod. The nanorod
modelled is the building block for larger nanoparticles that were employed in
preclinical studies (Dennis et al., Nanotechnology 20, 395103, 2009). The
scaling algorithm is shown to produce nearly identical loops over several
decades in the model grain size. Sweep-rate scaling involving the Gilbert
damping parameter is also demonstrated to allow orders of magnitude speed-up of
the loop calculations. | 1912.00310v3 |
2020-02-17 | Self-similar shrinkers of the one-dimensional Landau-Lifshitz-Gilbert equation | The main purpose of this paper is the analytical study of self-shrinker
solutions of the one-dimensional Landau-Lifshitz-Gilbert equation (LLG), a
model describing the dynamics for the spin in ferromagnetic materials. We show
that there is a unique smooth family of backward self-similar solutions to the
LLG equation, up to symmetries, and we establish their asymptotics. Moreover,
we obtain that in the presence of damping, the trajectories of the self-similar
profiles converge to great circles on the sphere $\mathbb{S}^2$, at an
exponential rate. In particular, the results presented in this paper provide
examples of blow-up in finite time, where the singularity develops due to rapid
oscillations forming limit circles. | 2002.06858v2 |
2021-02-20 | Fast magnetization reversal of a magnetic nanoparticle induced by cosine chirp microwave field pulse | We investigate the magnetization reversal of single-domain magnetic
nanoparticle driven by the circularly polarized cosine chirp microwave pulse
(CCMP). The numerical findings, based on the Landau-Lifshitz-Gilbert equation,
reveal that the CCMP is by itself capable of driving fast and energy-efficient
magnetization reversal. The microwave field amplitude and initial frequency
required by a CCMP are much smaller than that of the linear down-chirp
microwave pulse. This is achieved as the frequency change of the CCMP closely
matches the frequency change of the magnetization precession which leads to an
efficient stimulated microwave energy absorption (emission) by (from) the
magnetic particle before (after) it crosses over the energy barrier. We further
find that the enhancement of easy-plane shape anisotropy significantly reduces
the required microwave amplitude and the initial frequency of CCMP. We also
find that there is an optimal Gilbert damping for fast magnetization reversal.
These findings may provide a pathway to realize the fast and low-cost memory
device. | 2102.10394v2 |
2021-07-24 | Electron-Phonon Scattering governs both Ultrafast and Precessional Magnetization Dynamics in Co-Fe Alloys | Recent investigations have advanced the understanding of how
structure-property relationships in ferromagnetic metal alloys affect the
magnetization dynamics on nanosecond time-scales. A similar understanding for
magnetization dynamics on femto- to pico-second time-scales does not yet exist.
To address this, we perform time-resolved magneto optic Kerr effect (TRMOKE)
measurements of magnetization dynamics in Co-Fe alloys on femto- to nano-second
regimes. We show that Co-Fe compositions that exhibit low Gilbert damping
parameters also feature prolonged ultrafast demagnetization upon
photoexcitation. We analyze our experimental TR-MOKE data with the
three-temperature-model (3TM) and the Landau-Lifshitz-Gilbert equation. These
analyses reveal a strong compositional dependence of the dynamics across all
time-scales on the strength of electron-phonon interactions. Our findings are
beneficial to the spintronics and magnonics community, and will aid in the
quest for energy-efficient magnetic storage applications. | 2107.11699v1 |
2022-09-07 | Convergence analysis of an implicit finite difference method for the inertial Landau-Lifshitz-Gilbert equation | The Landau-Lifshitz-Gilbert (LLG) equation is a widely used model for fast
magnetization dynamics in ferromagnetic materials. Recently, the inertial LLG
equation, which contains an inertial term, has been proposed to capture the
ultra-fast magnetization dynamics at the sub-picosecond timescale.
Mathematically, this generalized model contains the first temporal derivative
and a newly introduced second temporal derivative of magnetization.
Consequently, it produces extra difficulties in numerical analysis due to the
mixed hyperbolic-parabolic type of this equation with degeneracy. In this work,
we propose an implicit finite difference scheme based on the central difference
in both time and space. A fixed point iteration method is applied to solve the
implicit nonlinear system. With the help of a second order accurate constructed
solution, we provide a convergence analysis in $H^1$ for this numerical scheme,
in the $\ell^\infty (0, T; H_h^1)$ norm. It is shown that the proposed method
is second order accurate in both time and space, with unconditional stability
and a natural preservation of the magnetization length. In the hyperbolic
regime, significant damping wave behaviors of magnetization at a shorter
timescale are observed through numerical simulations. | 2209.02914v2 |
2022-09-16 | Pseudo-PT symmetric Dirac equation : effect of a new mean spin angular momentum operator on Gilbert damping | The pseudo-PT symmetric Dirac equation is proposed and analyzed by using a
non-unitary Foldy-Wouthuysen transformations. A new spin operator PT symmetric
expectation value (called the mean spin operator) for an electron interacting
with a time-dependent electromagnetic field is obtained. We show that spin
magnetization - which is the quantity usually measured experimentally - is not
described by the standard spin operator but by this new mean spin operator to
properly describe magnetization dynamics in ferromagnetic materials and the
corresponding equation of motion is compatible with the phenomenological model
of the Landau-Lifshitz-Gilbert equation (LLG). | 2209.07908v1 |
2022-11-15 | Nonlinear sub-switching regime of magnetization dynamics in photo-magnetic garnets | We analyze, both experimentally and numerically, the nonlinear regime of the
photo-induced coherent magnetization dynamics in cobalt-doped yttrium iron
garnet films. Photo-magnetic excitation with femtosecond laser pulses reveals a
strongly nonlinear response of the spin subsystem with a significant increase
of the effective Gilbert damping. By varying both laser fluence and the
external magnetic field, we show that this nonlinearity originates in the
anharmonicity of the magnetic energy landscape. We numerically map the
parameter workspace for the nonlinear photo-induced spin dynamics below the
photo-magnetic switching threshold. Corroborated by numerical simulations of
the Landau-Lifshitz-Gilbert equation, our results highlight the key role of the
cubic symmetry of the magnetic subsystem in reaching the nonlinear spin
precession regime. These findings expand the fundamental understanding of
laser-induced nonlinear spin dynamics as well as facilitate the development of
applied photo-magnetism. | 2211.08048v2 |
2023-08-16 | Discovery and regulation of chiral magnetic solitons: Exact solution from Landau-Lifshitz-Gilbert equation | The Landau-Lifshitz-Gilbert (LLG) equation has emerged as a fundamental and
indispensable framework within the realm of magnetism. However, solving the LLG
equation, encompassing full nonlinearity amidst intricate complexities,
presents formidable challenges. In this context, we develop a precise mapping
through geometric representation, establishing a direct linkage between the LLG
equation and an integrable generalized nonlinear Schr\"odinger equation. This
novel mapping provides accessibility towards acquiring a great number of exact
spatiotemporal solutions. Notably, exact chiral magnetic solitons, critical for
stability and controllability in propagation with and without damping effects
are discovered. Our formulation provides exact solutions for the long-standing
fully nonlinear problem, facilitating practical control through spin current
injection in magnetic memory applications. | 2308.08331v1 |
1997-07-20 | Effects of gluon damping rate on the viscosity coefficient of the quark-gluon plasma at finite chemical potential | By considering the Debye screening and damping rate of gluons, the viscosity
coefficient of the quark-gluon plasma was evaluated via real-time finite
temperature QCD in the relaxation time approximation at finite temperature and
chemical potential . The results show that both the damping rate and the
chemical potential cause considerable enhancements to the viscosity coefficient
of hot dense quark-gluon plasma. | 9707033v1 |
2015-07-04 | Comments on turbulence theory by Qian and by Edwards and McComb | We reexamine Liouville equation based turbulence theories proposed by Qian
{[}Phys. Fluids \textbf{26}, 2098 (1983){]} and Edwards and McComb {[}J. Phys.
A: Math. Gen. \textbf{2}, 157 (1969){]}, which are compatible with Kolmogorov
spectrum. These theories obtained identical equation for spectral density
$q(k)$ and different results for damping coefficient. Qian proposed variational
approach and Edwards and McComb proposed maximal entropy principle to obtain
equation for the damping coefficient. We show that assumptions used in these
theories to obtain damping coefficient correspond to unphysical conditions. | 1507.01124v1 |
2018-10-14 | Critical exponent for nonlinear damped wave equations with non-negative potential in 3D | We are studying possible interaction of damping coefficients in the
subprincipal part of the linear 3D wave equation and their impact on the
critical exponent of the corresponding nonlinear Cauchy problem with small
initial data. The main new phenomena is that certain relation between these
coefficients may cause very strong jump of the critical Strauss exponent in 3D
to the critical 5D Strauss exponent for the wave equation without damping
coefficients. | 1810.05956v1 |
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