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2021-04-29 | Nano-patterning of surfaces by ion sputtering: Numerical study of the anisotropic damped Kuramoto-Sivashinsky equation | Nonlinear models for pattern evolution by ion beam sputtering on a material
surface present an ongoing opportunity for new numerical simulations. A
numerical analysis of the evolution of preexisting patterns is proposed to
investigate surface dynamics, based on a 2D anisotropic damped
Kuramoto-Sivashinsky equation, with periodic boundary conditions. A
finite-difference semi-implicit time splitting scheme is employed on the
discretization of the governing equation. Simulations were conducted with
realistic coefficients related to physical parameters (anisotropies, beam
orientation, diffusion). The stability of the numerical scheme is analyzed with
time step and grid spacing tests for the pattern evolution, and the Method of
Manufactured Solutions has been used to verify the proposed scheme. Ripples and
hexagonal patterns were obtained from a monomodal initial condition for certain
values of the damping coefficient, while spatiotemporal chaos appeared for
lower values. The anisotropy effects on pattern formation were studied, varying
the angle of incidence of the ion beam with respect to the irradiated surface.
Analytical discussions are based on linear and weakly nonlinear analysis. | 2104.14104v1 |
2022-02-16 | On the strong convergence of the trajectories of a Tikhonov regularized second order dynamical system with asymptotically vanishing damping | This paper deals with a second order dynamical system with vanishing damping
that contains a Tikhonov regularization term, in connection to the minimization
problem of a convex Fr\'echet differentiable function $g$.
We show that for appropriate Tikhonov regularization parameters the value of
the objective function in a generated trajectory converges fast to the global
minimum of the objective function and a trajectory generated by the dynamical
system converges weakly to a minimizer of the objective function. We also
obtain the fast convergence of the velocities towards zero and some integral
estimates. Nevertheless, our main goal is to extend and improve some recent
results obtained in \cite{ABCR} and \cite{AL-nemkoz} concerning the strong
convergence of the generated trajectories to an element of minimal norm from
the $\argmin$ set of the objective function $g$. Our analysis also reveals that
the damping coefficient and the Tikhonov regularization coefficient are
strongly correlated. | 2202.08980v1 |
2023-05-06 | Stochastic wave equation with Hölder noise coefficient: well-posedness and small mass limit | We construct unique martingale solutions to the damped stochastic wave
equation $$ \mu \frac{\partial^2u}{\partial t^2}(t,x)=\Delta
u(t,x)-\frac{\partial u}{\partial
t}(t,x)+b(t,x,u(t,x))+\sigma(t,x,u(t,x))\frac{dW_t}{dt},$$
where $\Delta$ is the Laplacian on $[0,1]$ with Dirichlet boundary condition,
$W$ is space-time white noise, $\sigma$ is $\frac{3}{4}+\epsilon$ -H\"older
continuous in $u$ and uniformly non-degenerate, and $b$ has linear growth. The
same construction holds for the stochastic wave equation without damping term.
More generally, the construction holds for SPDEs defined on separable Hilbert
spaces with a densely defined operator $A$, and the assumed H\"older regularity
on the noise coefficient depends on the eigenvalues of $A$ in a quantitative
way. We further show the validity of the Smoluchowski-Kramers approximation:
assume $b$ is H\"older continuous in $u$, then as $\mu$ tends to $0$ the
solution to the damped stochastic wave equation converges in distribution, on
the space of continuous paths, to the solution of the corresponding stochastic
heat equation. The latter result is new even in the case of additive noise. | 2305.04068v2 |
2023-07-23 | Visco-elastic damped wave models with time-dependent coefficient | In this paper, we study the following Cauchy problem for linear visco-elastic
damped wave models with a general time-dependent coefficient $g=g(t)$:
\begin{equation} \label{EqAbstract} \tag{$\star$} \begin{cases} u_{tt}- \Delta
u + g(t)(-\Delta)u_t=0, &(t,x) \in (0,\infty) \times \mathbb{R}^n, \\ u(0,x)=
u_0(x),\quad u_t(0,x)= u_1(x), &x \in \mathbb{R}^n. \end{cases} \end{equation}
We are interested to study the influence of the damping term $g(t)(-\Delta)u_t$
on qualitative properties of solutions to \eqref{EqAbstract} as decay estimates
for energies of higher order and the parabolic effect. The main tools are
related to WKB-analysis. We apply elliptic as well as hyperbolic WKB-analysis
in different parts of the extended phase space. | 2307.12340v1 |
2024-03-10 | Linear-in-temperature resistivity and Planckian dissipation arise in a stochastic quantization model of Cooper pairs | We suppose that a Cooper pair (CP) will experience a damping force exerted by
the condensed matter. A Langevin equation of a CP in two dimensional condensed
matter is established. Following a method similar to Nelson's stochastic
mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is
derived. If the CPs move with a constant velocity, then the corresponding
direct current (DC) electrical conductivity can be calculated. Therefore, a
Drude like formula of resistivity of CPs is derived. We suppose that the
damping coefficient of CPs in two dimensional cuprate superconductors is a
linear function of temperature. Then the resistivity and scattering rate of CPs
turn out to be also linear-in-temperature. The origin of linear-in-temperature
resistivity and Planckian dissipation in cuprate superconductors may be the
linear temperature dependence of the damping coefficient of CPs. | 2403.09710v1 |
2013-08-16 | Quantum Gilbert-Varshamov Bound Through Symplectic Self-Orthogonal Codes | It is well known that quantum codes can be constructed through classical
symplectic self-orthogonal codes. In this paper, we give a kind of
Gilbert-Varshamov bound for symplectic self-orthogonal codes first and then
obtain the Gilbert-Varshamov bound for quantum codes. The idea of obtaining the
Gilbert-Varshamov bound for symplectic self-orthogonal codes follows from
counting arguments. | 1308.3578v1 |
2009-04-17 | Plasmons and polaritons in a semi-infinite plasma and a plasma slab | Plasmon and polariton modes are derived for an ideal semi-infinite
(half-space) plasma and an ideal plasma slab by using a general, unifying
procedure, based on equations of motion, Maxwell's equations and suitable
boundary conditions. Known results are re-obtained in much a more direct manner
and new ones are derived. The approach consists of representing the charge
disturbances by a displacement field in the positions of the moving particles
(electrons). The dielectric response and the electron energy loss are computed.
The surface contribution to the energy loss exhibits an oscillatory behaviour
in the transient regime near the surfaces. The propagation of an
electromagnetic wave in these plasmas is treated by using the retarded
electromagnetic potentials. The resulting integral equations are solved and the
reflected and refracted waves are computed, as well as the reflection
coefficient. For the slab we compute also the transmitted wave and the
transmission coefficient. Generalized Fresnel's relations are thereby obtained
for any incidence angle and polarization. Bulk and surface plasmon-polariton
modes are identified. As it is well known, the field inside the plasma is
either damped (evanescent) or propagating (transparency regime), and the
reflection coefficient for a semi-infinite plasma exhibits an abrupt
enhancement on passing from the propagating regime to the damped one (total
reflection). Similarly, apart from characteristic oscillations, the reflection
and transmission coefficients for a plasma slab exhibit an appreciable
enhancement in the damped regime. | 0904.2662v1 |
2012-10-25 | Molecular dissipation in the nonlinear eddy viscosity in the Navier-Stokes equations: modelling of accretion discs | Physical damping, regarding the nonlinear Navier-Stokes viscous flow
dynamics, refers to a tensorial turbulent dissipation term, attributed to
adjacent moving macroscopic flow components. Mutual dissipation among these
parts of fluid is described by a braking term in the momentum equation together
with a heating term in the energy equation, both responsible of the damping of
the momentum variation and of the viscous conversion of mechanical energy into
heat. A macroscopic mixing scale length is currently the only characteristic
length needed in the nonlinear modelling of viscous fluid dynamics describing
the nonlinear eddy viscosity through the kinematic viscosity coefficient in the
viscous stress tensor, without any reference to the chemical composition and to
the atomic dimensions. Therefore, in this paper, we write a new formulation for
the kinematic viscosity coefficient to the turbulent viscous physical
dissipation in the Navier-Stokes equations, where molecular parameters are also
included. Results of 2D tests are shown, where comparisons among flow
structures are made on 2D shockless radial viscous transport and on 2D damping
of collisional chaotic turbulence. An application to the 3D accretion disc
modelling in low mass cataclysmic variables is also discussed. Consequences of
the kinematic viscosity coefficient reformulation in a more strictly physical
terms on the thermal conductivity coefficient for dilute gases are also
discussed. The physical nature of the discussion here reported excludes any
dependence by the pure mathematical aspect of the numerical modelling. | 1210.6848v3 |
2021-01-27 | New estimations of the added mass and damping of two cylinders vibrating in a viscous fluid, from theoretical and numerical approaches | This paper deals with the small oscillations of two circular cylinders
immersed in a viscous stagnant fluid. A new theoretical approach based on an
Helmholtz expansion and a bipolar coordinate system is presented to estimate
the fluid forces acting on the two bodies. We show that these forces are linear
combinations of the {\textcolor{black}{cylinder accelerations}} and velocities,
through viscous fluid added coefficients. {\textcolor{black}{To assess the
validity of this theory, we consider the case of two equal size cylinders, one
of them being stationary while the other one is forced sinusoidally}}. The
self-added mass and damping coefficients are shown to decrease with both the
Stokes number and the separation distance. The cross-added mass and damping
coefficients tend to increase with the Stokes number and the separation
distance. Compared to the inviscid results, the effect of viscosity is to add a
correction term which scales as $Sk^{-1/2}$. When the separation distance is
sufficiently large, the two cylinders behave as if they were independent and
the Stokes predictions for an isolated cylinder are recovered. Compared to
previous works, the present theory offers a simple and flexible alternative for
an easy determination of the fluid forces and related added coefficients. To
our knowledge, this is also the first time that a numerical approach based on a
penalization method is presented in the context of fluid-structure interactions
for relatively small Stokes numbers, and successfully compared to theoretical
predictions. | 2101.11346v1 |
2022-09-18 | Design of a stiffness adjustable magnetic fluid shock absorber based on optimal stiffness coefficient | With the rapid development of aerospace technology, the vibration problem of
the spacecraft flexible structure urgently needs to be solved. Magnetic fluids
are a type of multi-functional smart materials, which can be employed in shock
absorbers to eliminate these vibrations. Referring to the calculation methods
of stiffness coefficients of other passive dampers, the stiffness coefficient
formula of magnetic fluid shock absorbers (MFSAs) was derived. Meanwhile, a
novel stiffness adjustable magnetic fluid shock absorber (SA-MFSA) was
proposed. On the basis of the second-order buoyancy principle, a series of
SA-MFSAs were fabricated. The range of stiffness coefficients covered by these
SA-MFSAs contains the optimal stiffness coefficient estimated by formulas. The
repulsive force measurement and vibration attenuation experiments were
conducted on these SA-MFSAs. In the case of small amplitude, the relationship
between the repulsive force and the offset distance was linear. The simulation
and experiment curves of repulsive forces were in good agreement. The results
of vibration attenuation experiments demonstrated that the rod length and the
magnetic fluid mass influence the damping efficiency of SA-MFSAs. In addition,
these results verified that the SA-MFSA with the optimal stiffness coefficient
performed best. Therefore, the stiffness coefficient formula can guide the
design of MFSAs. | 2209.08588v1 |
2017-02-03 | Enhanced Spin Conductance of a Thin-Film Insulating Antiferromagnet | We investigate spin transport by thermally excited spin waves in an
antiferromagnetic insulator. Starting from a stochastic Landau-Lifshitz-Gilbert
phenomenology, we obtain the out-of-equilibrium spin-wave properties. In linear
response to spin biasing and a temperature gradient, we compute the spin
transport through a normal metal$|$antiferromagnet$|$normal metal
heterostructure. We show that the spin conductance diverges as one approaches
the spin-flop transition; this enhancement of the conductance should be readily
observable by sweeping the magnetic field across the spin-flop transition. The
results from such experiments may, on the one hand, enhance our understanding
of spin transport near a phase transition, and on the other be useful for
applications that require a large degree of tunability of spin currents. In
contrast, the spin Seebeck coefficient does not diverge at the spin-flop
transition. Furthermore, the spin Seebeck coefficient is finite even at zero
magnetic field, provided that the normal metal contacts break the symmetry
between the antiferromagnetic sublattices. | 1702.00975v2 |
2022-03-09 | Finiteness for Hecke algebras of $p$-adic groups | Let $G$ be a reductive group over a non-archimedean local field $F$ of
residue characteristic $p$. We prove that the Hecke algebras of $G(F)$ with
coefficients in a ${\mathbb Z}_{\ell}$-algebra $R$ for $\ell$ not equal to $p$
are finitely generated modules over their centers, and that these centers are
finitely generated $R$-algebras. Following Bernstein's original strategy, we
then deduce that "second adjointness" holds for smooth representations of
$G(F)$ with coefficients in any ring $R$ in which $p$ is invertible. These
results had been conjectured for a long time. The crucial new tool that unlocks
the problem is the Fargues-Scholze morphism between a certain "excursion
algebra" defined on the Langlands parameters side and the Bernstein center of
$G(F)$. Using this bridge, our main results are representation theoretic
counterparts of the finiteness of certain morphisms between coarse moduli
spaces of local Langlands parameters that we also prove here, which may be of
independent interest | 2203.04929v2 |
2022-05-04 | Separations in Proof Complexity and TFNP | It is well-known that Resolution proofs can be efficiently simulated by
Sherali-Adams (SA) proofs. We show, however, that any such simulation needs to
exploit huge coefficients: Resolution cannot be efficiently simulated by SA
when the coefficients are written in unary. We also show that Reversible
Resolution (a variant of MaxSAT Resolution) cannot be efficiently simulated by
Nullstellensatz (NS).
These results have consequences for total NP search problems. First, we
characterise the classes PPADS, PPAD, SOPL by unary-SA, unary-NS, and
Reversible Resolution, respectively. Second, we show that, relative to an
oracle, PLS $\not\subseteq$ PPP, SOPL $\not\subseteq$ PPA, and EOPL
$\not\subseteq$ UEOPL. In particular, together with prior work, this gives a
complete picture of the black-box relationships between all classical TFNP
classes introduced in the 1990s. | 2205.02168v2 |
2002-04-29 | Schwarzschild black holes and propagation of electromagnetic and gravitational waves | Disturbing of a spacetime geometry may result in the appearance of an
oscillating and damped radiation - the so-called quasinormal modes. Their
periods of oscillations and damping coefficients carry unique information about
the mass and the angular momentum, that would allow one to identify the source
of the gravitational field. In this talk we present recent bounds on the
diffused energy, applicable to the Schwarzschild spacetime, that give also
rough estimates of the energy of excited quasinormal modes. | 0204086v1 |
2002-09-21 | Infrared Sensitivity in Damping Rate for Very Soft Moving Fermions in Finite Temperature QED | We calculate the fermion damping rate to second order in powers of the
external momentum $p$ in the context of QED at finite temperature using the
hard-thermal-loop (HTL) summation scheme. We find that the coefficient of order
$p^{2}$ is divergent in the infrared whereas the two others are finite. This
result suggests that the htl-based pertubation is infrared sensitive at
next-to-leading order. | 0209246v1 |
2004-10-11 | Nodal two-dimensional solitons in nonlinear parametric resonance | The parametrically driven damped nonlinear Schr\"odinger equation serves as
an amplitude equation for a variety of resonantly forced oscillatory systems on
the plane. In this note, we consider its nodal soliton solutions. We show that
although the nodal solitons are stable against radially-symmetric perturbations
for sufficiently large damping coefficients, they are always unstable to
azimuthal perturbations. The corresponding break-up scenarios are studied using
direct numerical simulations. Typically, the nodal solutions break into
symmetric "necklaces" of stable nodeless solitons. | 0410012v1 |
2006-10-22 | Response of a Magneto-Rheological Fluid Damper Subjected to Periodic Forcing in a High Frequency Limit | We explored vibrations of a single-degree of freedom oscillator with a
magneto-rheological damper subjected to kinematic excitations. Using fast and
slow scales decoupling procedure we derived an effective damping coefficient in
the limit of high frequency excitation. Damping characteristics, as functions
of velocity, change considerably especially by terminating the singular
non-smoothness points. This effect was more transparent for a larger control
parameter which was defined as the product of the excitation amplitude and its
frequency. | 0610055v1 |
2006-09-19 | Quantum master equations from classical Lagrangians with two stochastic forces | We show how a large family of master equations, describing quantum Brownian
motion of a harmonic oscillator with translationally invariant damping, can be
derived within a phenomenological approach, based on the assumption that an
environment can be simulated by two classical stochastic forces. This family is
determined by three time-dependent correlation functions (besides the frequency
and damping coefficients), and it includes as special cases the known master
equations, whose dissipative part is bilinear with respect to the operators of
coordinate and momentum. | 0609144v3 |
2007-05-31 | Stability of Solutions to Damped Equations with Negative Stiffness | This article concerns the stability of a model for mass-spring systems with
positive damping and negative stiness. It is well known that when the
coefficients are frozen in time the system is unstable. Here we find conditions
on the variable cofficients to prove stability. In particular, we disprove the
believe that if the eigenvalues of the system change slowly in time the system
remains unstable. We extend some of our results for nonlinear systems. | 0705.4670v1 |
2009-10-05 | Construction of quasi-periodic response solutions in forced strongly dissipative systems | We consider a class of ordinary differential equations describing
one-dimensional quasiperiodically forced systems in the presence of large
damping. We give a fully constructive proof of the existence of response
solutions, that is quasi-periodic solutions which have the same frequency
vector as the forcing. This requires dealing with a degenerate implicit
function equation: we prove that the latter has a unique solution, which can be
explicitly determined. As a by-product we obtain an explicit estimate of the
minimal size of the damping coefficient. | 0910.0746v1 |
2009-11-12 | A new perspective on supersymmetric inflation | We consider supersymmetric inflation with the hybrid-type potential. In the
absence of the symmetry that forbids Hubble-induced mass terms, the inflaton
mass will be as large as the Hubble scale during inflation. We consider
gravitational decay of the trigger field as the least decay mode and find that
the damping caused by the dissipation can dominate the friction of the inflaton
when the heavy trigger field is coupled to the inflaton. The dissipative
damping provides a solution to the traditional $\eta$ problem without
introducing additional symmetry and interactions. Considering the spatial
inhomogeneities of the dissipative coefficient, we find that modulated
inflation (modulation of the inflaton velocity) can create significant
curvature perturbations. | 0911.2350v1 |
2010-09-09 | The Damped String Problem Revisited | We revisit the damped string equation on a compact interval with a variety of
boundary conditions and derive an infinite sequence of trace formulas
associated with it, employing methods familiar from supersymmetric quantum
mechanics. We also derive completeness and Riesz basis results (with
parentheses) for the associated root functions under less smoothness
assumptions on the coefficients than usual, using operator theoretic methods
(rather than detailed eigenvalue and root function asymptotics) only. | 1009.1858v1 |
2012-01-26 | Inhomogeneous spin diffusion in traps with cold atoms | The spin diffusion and damped oscillations are studied in the collision of
two spin polarized clouds of cold atoms with resonant interactions. The strong
density dependence of the diffusion coefficient leads to inhomogeneous spin
diffusion that changes from central to surface spin flow as the temperature
increases. The inhomogeneity and the smaller finite trap size significantly
reduce the spin diffusion rate at low temperatures. The resulting spin
diffusion rates, spin drag and initial damped oscillations are compatible with
measurements at low to high temperatures for resonant attractive interactions
but are incompatible with a metastable ferromagnetic phase. | 1201.5526v2 |
2012-07-31 | An analytic description of the damping of gravitational waves by free streaming neutrinos | We provide an analytic solution to the general wavelength
integro-differential equation describing the damping of tensor modes of
gravitational waves due to free streaming neutrinos in the early universe. Our
result is expressed as a series of spherical Bessel functions whose
coefficients are functions of the reduced wave number $Q$. | 1207.7285v4 |
2013-07-17 | Functional inequalities on path space over a non-compact Riemannian manifold | We prove the existence of the O-U Dirichlet form and the damped O-U Dirichlet
form on path space over a general non-compact Riemannian manifold which is
complete and stochastically complete. We show a weighted log-Sobolev inequality
for the O-U Dirichlet form and the (standard) log-Sobolev inequality for the
damped O-U Dirichlet form. In particular, the Poincar\'e inequality (and the
super Poincar\'e inequality) can be established for the O-U Dirichlet form on
path space over a class of Riemannian manifolds with unbounded Ricci
curvatures. Moreover, we construct a large class of quasi-regular local
Dirichlet forms with unbounded random diffusion coefficients on the path space
over a general non-compact manifold. | 1307.4482v2 |
2016-04-27 | Temperature Dependence Calibration and Correction of the DAMPE BGO Electromagnetic Calorimeter | A BGO electromagnetic calorimeter (ECAL) is built for the DArk Matter
Particle Explorer (DAMPE) mission. The effect of temperature on the BGO ECAL
was investigated with a thermal vacuum experiment. The light output of a BGO
crystal depends on temperature significantly. The temperature coefficient of
each BGO crystal bar has been calibrated, and a correction method is also
presented in this paper. | 1604.08060v1 |
2017-11-06 | Linear inviscid damping and enhanced dissipation for the Kolmogorov flow | In this paper, we prove the linear inviscid damping and voticity depletion
phenomena for the linearized Euler equations around the Kolmogorov flow. These
results confirm Bouchet and Morita's predictions based on numerical analysis.
By using the wave operator method introduced by Li, Wei and Zhang, we solve
Beck and Wayne's conjecture on the optimal enhanced dissipation rate for the
2-D linearized Navier-Stokes equations around the bar state called Kolmogorov
flow. The same dissipation rate is proved for the Navier-Stokes equations if
the initial velocity is included in a basin of attraction of the Kolmogorov
flow with the size of $\nu^{\frac 23+}$, here $\nu$ is the viscosity
coefficient. | 1711.01822v1 |
2018-02-26 | Controllability and observability for non-autonomous evolution equations: the averaged Hautus test | We consider the observability problem for non-autonomous evolution systems
(i.e., the operators governing the system depend on time). We introduce an
averaged Hautus condition and prove that for skew-adjoint operators it
characterizes exact observability. Next, we extend this to more general class
of operators under a growth condition on the associated evolution family. We
give an application to the Schr\"odinger equation with time dependent potential
and the damped wave equation with a time dependent damping coefficient. | 1802.09224v1 |
2018-03-15 | Improving the capacity of quantum dense coding by weak measurement and reversal measurement | A protocol of quantum dense coding protection of two qubits is proposed in
amplitude damping (AD) channel using weak measurement and reversal measurement.
It is found that the capacity of quantum dense coding under the weak
measurement and reversal measurement is always greater than that without weak
measurement and reversal measurement. When the protocol is applied, for the AD
channels with different damping coefficient, the result reflects that quantum
entanglement can be protected and quantum dense coding becomes successful. | 1803.05678v1 |
2018-09-25 | On the energy decay rates for the 1D damped fractional Klein-Gordon equation | We consider the fractional Klein-Gordon equation in one spatial dimension,
subjected to a damping coefficient, which is non-trivial and periodic, or more
generally strictly positive on a periodic set. We show that the energy of the
solution decays at the polynomial rate $O(t^{-\frac{s}{4-2s}})$ for $0< s<2 $
and at some exponential rate when $s\geq 2$. Our approach is based on the
asymptotic theory of $C_0$ semigroups in which one can relate the decay rate of
the energy in terms of the resolvent growth of the semigroup generator. The
main technical result is a new observability estimate for the fractional
Laplacian, which may be of independent interest. | 1809.09531v1 |
2019-09-11 | Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping | In this paper, we consider the 1D compressible Euler equation with the
damping coefficient $\lambda/(1+t)^{\mu}$. Under the assumption that $0\leq \mu
<1$ and $\lambda >0$ or $\mu=1$ and $\lambda > 2$, we prove that solutions
exist globally in time, if initial data are small $C^1$ perturbation near
constant states. In particular, we remove the conditions on the limit
$\lim_{|x| \rightarrow \infty} (u (0,x), v (0,x))$, assumed in previous
results. | 1909.05683v1 |
2020-07-24 | Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems | In this paper, we propose a second-order continuous primal-dual dynamical
system with time-dependent positive damping terms for a separable convex
optimization problem with linear equality constraints. By the Lyapunov function
approach, we investigate asymptotic properties of the proposed dynamical system
as the time $t\to+\infty$. The convergence rates are derived for different
choices of the damping coefficients. We also show that the obtained results are
robust under external perturbations. | 2007.12428v1 |
2021-02-14 | Suppression of singularities of solutions of the Euler-Poisson system with density-dependent damping | We find a sharp condition on the density-dependent coefficient of damping of
a one-dimensional repulsive Euler-Poisson system, which makes it possible to
suppress the formation of singularities in the solution of the Cauchy problem
with arbitrary smooth data. In the context of plasma physics, this means the
possibility of suppressing the breakdown of arbitrary oscillations of cold
plasma. | 2102.07176v2 |
2021-02-28 | The influence of the physical coefficients of a Bresse system with one singular local viscous damping in the longitudinal displacement on its stabilization | In this paper, we investigate the stabilization of a linear Bresse system
with one singular local frictional damping acting in the longitudinal
displacement, under fully Dirichlet boundary conditions. First, we prove the
strong stability of our system. Next, using a frequency domain approach
combined with the multiplier method, we establish the exponential stability of
the solution if and only if the three waves have the same speed of propagation.
On the contrary, we prove that the energy of our system decays polynomially
with rates $t^{-1}$ or $t^{-\frac{1}{2}}$. | 2103.00628v2 |
2021-11-11 | Stabilization for Euler-Bernoulli beam equation with a local degenerated Kelvin-Voigt damping | We consider the Euler-Bernoulli beam equation with a local Kelvin-Voigt
dissipation type in the interval $(-1,1)$. The coefficient damping is only
effective in $(0,1)$ and is degenerating near the $0$ point with a speed at
least equal to $x^{\alpha}$ where $\alpha\in(0,5)$. We prove that the semigroup
corresponding to the system is polynomially stable and the decay rate depends
on the degeneracy speed $\alpha$. | 2111.06431v1 |
2022-01-22 | Absorption of charged particles in Perfectly-Matched-Layers by optimal damping of the deposited current | Perfectly-Matched Layers (PML) are widely used in Particle-In-Cell
simulations, in order to absorb electromagnetic waves that propagate out of the
simulation domain. However, when charged particles cross the interface between
the simulation domain and the PMLs, a number of numerical artifacts can arise.
In order to mitigate these artifacts, we introduce a new PML algorithm whereby
the current deposited by the macroparticles in the PML is damped by an
analytically-derived, optimal coefficient. The benefits of this new algorithm
is illustrated in practical simulations. | 2201.09084v2 |
2023-02-23 | Hopf-Like Bifurcation in a Wave Equation at a Removable Singularity | It is shown that a one-dimensional damped wave equation with an odd time
derivative nonlinearity exhibits small amplitude bifurcating time periodic
solutions, when the bifurcation parameter is the linear damping coefficient is
positive and accumulates to zero. The upshot is that the singularity of the
linearized operator at criticality which stems from the well known small
divisor problem for the wave operator, is entirely removed without the need to
exclude parameters via Diophantine conditions, nor the use of accelerated
convergence schemes. Only the contraction mapping principle is used. | 2302.12092v2 |
2023-03-24 | Exponential decay estimates for semilinear wave-type equations with time-dependent time delay | In this paper, we analyze a semilinear damped second order evolution equation
with time-dependent time delay and time-dependent delay feedback coefficient.
The nonlinear term satisfies a local Lipschitz continuity assumption. Under
appropriate conditions, we prove well-posedness and exponential stability of
our model for small initial data. Our arguments combine a Lyapunov functional
approach with some continuity arguments. Moreover, as an application of our
abstract results, the damped wave equation with a source term and delay
feedback is analyzed. | 2303.14208v1 |
2023-06-13 | Stability of asymptotically Hamiltonian systems with damped oscillatory and stochastic perturbations | A class of asymptotically autonomous systems on the plane with oscillatory
coefficients is considered. It is assumed that the limiting system is
Hamiltonian with a stable equilibrium. The effect of damped multiplicative
stochastic perturbations of white noise type on the stability of the system is
discussed. It is shown that different long-term asymptotic regimes for
solutions are admissible in the system and the stochastic stability of the
equilibrium depends on the realized regime. In particular, we show that stable
phase locking is possible in the system due to decaying stochastic
perturbations. The proposed analysis is based on a combination of the averaging
technique and the construction of stochastic Lyapunov functions. | 2306.07694v1 |
2023-07-27 | Best Ulam constants for damped linear oscillators with variable coefficients | This study uses an associated Riccati equation to study the Ulam stability of
non-autonomous linear differential vector equations that model the damped
linear oscillator. In particular, the best (minimal) Ulam constants for these
non-autonomous linear differential vector equations are derived. These robust
results apply to vector equations with solutions that blow up in finite time,
as well as to vector equations with solutions that exist globally on
$(-\infty,\infty)$. Illustrative, non-trivial examples are presented,
highlighting the main results. | 2307.15103v1 |
2023-09-04 | On the small-mass limit for stationary solutions of stochastic wave equations with state dependent friction | We investigate the convergence, in the small mass limit, of the stationary
solutions of a class of stochastic damped wave equations, where the friction
coefficient depends on the state and the noisy perturbation if of
multiplicative type. We show that the Smoluchowski-Kramers approximation that
has been previously shown to be true in any fixed time interval, is still valid
in the long time regime. Namely we prove that the first marginals of any
sequence of stationary solutions for the damped wave equation converge to the
unique invariant measure of the limiting stochastic quasilinear parabolic
equation. The convergence is proved with respect to the Wasserstein distance
associated with the $H^{-1}$ norm. | 2309.01549v1 |
2023-09-21 | Inverse problems for a quasilinear strongly damped wave equation arising in nonlinear acoustics | We consider inverse problems for a Westervelt equation with a strong damping
and a time-dependent potential $q$. We first prove that all boundary
measurements, including the initial data, final data, and the lateral boundary
measurements, uniquely determine $q$ and the nonlinear coefficient $\beta$. The
proof is based on complex geometric optics construction and the approach
proposed by Isakov. Further, by considering fundamental solutions supported in
a half-space constructed by H\"ormander, we prove that with vanishing initial
conditions the Dirichlet-to-Neumann map determines $q$ and $\beta$. | 2309.11775v1 |
2023-12-29 | On damping a control system of arbitrary order with global aftereffect on a tree | We study a problem of damping a control system described by
functional-differential equations of natural order $n$ and neutral type with
non-smooth complex coefficients on an arbitrary tree with global delay. The
latter means that the delay propagates through internal vertices of the tree.
Minimization of the energy functional of the system leads to a variational
problem. We establish its equivalence to a certain self-adjoint boundary value
problem on the tree for equations of order $2n$ with nonlocal quasi-derivatives
and multidirectional shifts of the argument, as well as Kirchhoff-type
conditions emerging at the internal vertices. The unique solvability of both
problems is proved. | 2312.17592v1 |
2024-01-11 | Weak collision effect on nonlinear Landau damping for the Vlasov-Poisson-Fokker-Planck system | We investigate the impact of weak collisions on Landau damping in the
Vlasov-Poisson-Fokker-Planck system on a torus, specifically focusing on its
proximity to a Maxwellian distribution. In the case where the Gevrey index
satisfies $\frac{1}{s}<3$, we establish the global stability and enhanced
dissipation of small initial data, which remain unaffected by the small
diffusion coefficient $\nu$. For Gevrey index $\frac{1}{s}\ge3$, we prove the
global stability and enhanced dissipation of initial data, whose size is on the
order of $O(\nu^a)$ for any $a>\frac{1-3s}{3-3s}$. Our analysis provides
insights into the effects of phase mixing, enhanced dissipation, and plasma
echoes. | 2401.05601v3 |
2014-11-24 | Damping of liquid sloshing by foams | When a container is set in motion, the free surface of the liquid starts to
oscillate or slosh. Such effects can be observed when a glass of water is
handled carelessly and the fluid sloshes or even spills over the rims of the
container. However, beer does not slosh as readily as water, which suggests
that foam could be used to damp sloshing. In this work, we study experimentally
the effect on sloshing of a liquid foam placed on top of a liquid bath. We
generate a monodisperse two-dimensional liquid foam in a rectangular container
and track the motion of the foam. The influence of the foam on the sloshing
dynamics is experimentally characterized: only a few layers of bubbles are
sufficient to significantly damp the oscillations. We rationalize our
experimental findings with a model that describes the foam contribution to the
damping coefficient through viscous dissipation on the walls of the container.
Then we extend our study to confined three-dimensional liquid foam and observe
that the behavior of 2D and confined 3D systems are very similar. Thus we
conclude that only the bubbles close to the walls have a significant impact on
the dissipation of energy. The possibility to damp liquid sloshing using foam
is promising in numerous industrial applications such as the transport of
liquefied gas in tankers or for propellants in rocket engines. | 1411.6542v2 |
2019-05-22 | Ultra-low magnetic damping in Co 2 Mn-based Heusler compounds: promising materials for spintronic | The prediction of ultra-low magnetic damping in Co 2 MnZ Heusler half-metal
thin-film magnets is explored in this study and the damping response is shown
to be linked to the underlying electronic properties. By substituting the Z
elements in high crystalline quality films (Co 2 MnZ with Z=Si, Ge, Sn, Al, Ga,
Sb), electronic properties such as the minority spin band gap, Fermi energy
position in the gap and spin polarization can be tuned and the consequence on
magnetization dynamics analyzed. The experimental results allow us to directly
explore the interplay of spin polarization, spin gap, Fermi energy position and
the magnetic damping obtained in these films, together with ab initio
calculation predictions. The ultra-low magnetic damping coefficients measured
in the range 4.1 10-4-9 10-4 for Co 2 MnSi, Ge, Sn, Sb are the lowest values
obtained on a conductive layer and offers a clear experimental demonstration of
theoretical predictions on Half-Metal Magnetic Heusler compounds and a pathway
for future materials design. | 1905.08987v1 |
2019-07-29 | Breather arrest in a chain of damped oscillators with Hertzian contact | We explore breather propagation in the damped oscillatory chain with
essentially nonlinear (non-linearizable) nearest-neighbour coupling.
Combination of the damping and the substantially nonlinear coupling leads to
rather unusual two-stage pattern of the breather propagation. The first stage
occurs at finite fragment of the chain and is characterized by power-law decay
of the breather amplitude. The second stage is characterized by extremely small
breather amplitudes that decay hyper-exponentially with the site number. Thus,
practically, one can speak about finite penetration depth of the breather. This
phenomenon is referred to as breather arrest (BA). As particular example, we
explore the chain with Hertzian contacts. Dependencies of the breather
penetration depth on the initial excitation and on the damping coefficient on
the breather penetration depth obey power laws. The results are rationalized by
considering beating responses in a system of two damped linear oscillators with
strongly nonlinear (non-linearizable) coupling. Initial excitation of one of
these oscillators leads to strictly finite number of beating cycles. Then, the
beating cycle in this simplified system is associated with the passage of the
discrete breather between the neighbouring sites in the chain. Somewhat
surprisingly, this simplified model reliably predicts main quantitative
features of the breather arrest in the chain, including the exponents in
numerically observed power laws. | 1907.12462v1 |
2019-12-09 | Analytical solution of linearized equations of the Morris-Lecar neuron model at large constant stimulation | The classical biophysical Morris-Lecar model of neuronal excitability
predicts that upon stimulation of the neuron with a sufficiently large constant
depolarizing current there exists a finite interval of the current values where
periodic spike generation occurs. Above the upper boundary of this interval,
there is four-stage damping of the spike amplitude: 1) minor primary damping,
which reflects a typical transient to stationary dynamic state, 2) plateau of
nearly undamped periodic oscillations, 3) strong damping, and 4) reaching a
constant asymptotic value of the neuron potential. We have shown that in the
vicinity of the asymptote the Morris-Lecar equations can be reduced to the
standard equation for exponentially damped harmonic oscillations. Importantly,
all coefficients of this equation can be explicitly expressed through
parameters of the original Morris-Lecar model, enabling direct comparison of
the numerical and analytical solutions for the neuron potential dynamics at
later stages of the spike amplitude damping. | 1912.04083v4 |
2022-05-10 | Nonlinear damping quantification from phase-resonant tests under base excitation | The present work addresses the experimental identification of
amplitude-dependent modal parameters (modal frequency, damping ratio, Fourier
coefficients of periodic modal oscillation). Phase-resonant testing has emerged
as an important method for this task, as it substantially reduces the amount of
data required for the identification compared to conventional
frequency-response testing at different excitation/response levels. In the case
of shaker-stinger excitation, the applied excitation force is commonly measured
in order to quantify the amplitude-dependent modal damping ratio from the
phase-resonant test data. In the case of base excitation, however, the applied
excitation force is challenging or impossible to measure. In this work we
develop an original method for damping quantification from phase-resonant
tests. It relies solely on response measurement; it avoids the need to resort
to force measurement. The key idea is to estimate the power provided by the
distributed inertia force imposed by the base motion. We develop both a
model-free and a model-based variant of the method. We validate the developed
method first in virtual experiments of a friction-damped and a geometrically
nonlinear system, and then in a physical experiment involving a thin beam
clamped at both ends via bolted joints. We conclude that the method is highly
robust and provides high accuracy already for a reasonable number of sensors. | 2205.04735v1 |
2001-11-16 | Resonances and superlattice pattern stabilization in two-frequency forced Faraday waves | We investigate the role weakly damped modes play in the selection of Faraday
wave patterns forced with rationally-related frequency components m*omega and
n*omega. We use symmetry considerations to argue for the special importance of
the weakly damped modes oscillating with twice the frequency of the critical
mode, and those oscillating primarily with the "difference frequency"
|n-m|*omega and the "sum frequency" (n+m)*omega. We then perform a weakly
nonlinear analysis using equations of Zhang and Vinals (1997, J. Fluid Mech.
336) which apply to small-amplitude waves on weakly inviscid, semi-infinite
fluid layers. For weak damping and forcing and one-dimensional waves, we
perform a perturbation expansion through fourth order which yields analytical
expressions for onset parameters and the cubic bifurcation coefficient that
determines wave amplitude as a function of forcing near onset. For stronger
damping and forcing we numerically compute these same parameters, as well as
the cubic cross-coupling coefficient for competing waves travelling at an angle
theta relative to each other. The resonance effects predicted by symmetry are
borne out in the perturbation results for one spatial dimension, and are
supported by the numerical results in two dimensions. The difference frequency
resonance plays a key role in stabilizing superlattice patterns of the SL-I
type observed by Kudrolli, Pier and Gollub (1998, Physica D 123). | 0111039v2 |
2019-07-08 | Single-spectrum prediction of kurtosis of water waves in a non-conservative model | We study statistical properties after a sudden episode of wind for water
waves propagating in one direction. A wave with random initial conditions is
propagated using a forced-damped higher order Nonlinear Schr\"odinger equation
(NLS). During the wind episode, the wave action increases, the spectrum
broadens, the spectral mean shifts up and the Benjamin-Feir index (BFI) and the
kurtosis increase. Conversely, after the wind episode, the opposite occurs for
each quantity. The kurtosis of the wave height distribution is considered the
main parameter that can indicate whether rogue waves are likely to occur in a
sea state, and the BFI is often mentioned as a means to predict the kurtosis.
However, we find that while there is indeed a quadratic relation between these
two, this relationship is dependent on the details of the forcing and damping.
Instead, a simple and robust quadratic relation does exist between the kurtosis
and the bandwidth. This could allow for a single-spectrum assessment of the
likelihood of rogue waves in a given sea state. In addition, as the kurtosis
depends strongly on the damping and forcing coefficients, by combining the
bandwidth measurement with the damping coefficient, the evolution of the
kurtosis after the wind episode can be predicted. | 1907.03490v1 |
2020-07-19 | Global existence and convergence to the modified Barenblatt solution for the compressible Euler equations with physical vacuum and time-dependent damping | In this paper, the smooth solution of the physical vacuum problem for the one
dimensional compressible Euler equations with time-dependent damping is
considered. Near the vacuum boundary, the sound speed is $C^{1/2}$-H\"{o}lder
continuous. The coefficient of the damping depends on time, given by this form
$\frac{\mu}{(1+t)^\lambda}$, $\lambda$, $\mu>0$, which decays by order
$-\lambda$ in time. Under the assumption that $0<\lambda<1$, $0<\mu$ or
$\lambda=1$, $2<\mu$, we will prove the global existence of smooth solutions
and convergence to the modified Barenblatt solution of the related porous media
equation with time-dependent dissipation and the same total mass when the
initial data of the Euler equations is a small perturbation of that of the
Barenblatt solution. The pointwise convergence rates of the density, velocity
and the expanding rate of the physical vacuum boundary are also given. The
proof is based on space-time weighted energy estimates, elliptic estimates and
Hardy inequality in the Lagrangian coordinates. Our result is an extension of
that in Luo-Zeng [Comm. Pure Appl. Math. 69 (2016), no. 7, 1354-1396], where
the authors considered the physical vacuum free boundary problem of the
compressible Euler equations with constant-coefficient damping. | 2007.14802v2 |
2018-10-30 | Effect of Landau damping on ion acoustic solitary waves in a multi-species collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons | A Korteweg-de Vries (KdV) equation including the effect of Landau damping is
derived to study the propagation of weakly nonlinear and weakly dispersive ion
acoustic waves in a collisionless unmagnetized plasma consisting of warm
adiabatic ions and two different species of electrons at different
temperatures. The hotter energetic electron species follows the nonthermal
velocity distribution of Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)]
whereas the cooler electron species obeys the Boltzmann distribution. It is
found that the coefficient of the nonlinear term of this KdV like evolution
equation vanishes along different family of curves in different parameter
planes. In this context, a modified KdV (MKdV) equation including the effect of
Landau damping effectively describes the nonlinear behaviour of ion acoustic
waves. It has also been observed that the coefficients of the nonlinear terms
of the KdV and MKdV like evolution equations including the effect of Landau
damping, are simultaneously equal to zero along a family of curves in the
parameter plane. In this situation, we have derived a further modified KdV
(FMKdV) equation including the effect of Landau damping to describe the
nonlinear behaviour of ion acoustic waves. In fact, different modified KdV like
evolution equations including the effect of Landau damping have been derived to
describe the nonlinear behaviour of ion acoustic waves in different region of
parameter space. The method of Ott & Sudan [Phys. Fluids 12, 2388 (1969)] has
been applied to obtain the solitary wave solution of the evolution equation
having the nonlinear term $(\phi^{(1)})^{r}\frac{\partial \phi^{(1)}}{\partial
\xi}$, where $\phi^{(1)}$ is the first order perturbed electrostatic potential
and $r =1,2,3$. We have found that the amplitude of the solitary wave solution
decreases with time for all $r =1,2,3$. | 1810.12739v1 |
2003-01-15 | Resonant triad dynamics in weakly damped Faraday waves with two-frequency forcing | Many of the interesting patterns seen in recent multi-frequency Faraday
experiments can be understood on the basis of three-wave interactions (resonant
triads). In this paper we consider two-frequency forcing and focus on a
resonant triad that occurs near the bicritical point where two pattern-forming
modes with distinct wavenumbers emerge simultaneously. This triad has been
observed directly (in the form of rhomboids) and has also been implicated in
the formation of quasipatterns and superlattices. We show how the symmetries of
the undamped unforced problem (time translation, time reversal, and Hamiltonian
structure) can be used, when the damping is weak, to obtain general scaling
laws and additional qualitative properties of the normal form coefficients
governing the pattern selection process near onset; such features help to
explain why this particular triad is seen only for certain "low" forcing
ratios, and predict the existence of drifting solutions and heteroclinic
cycles. We confirm the anticipated parameter dependence of the coefficients and
investigate its dynamical consequences using coefficients derived numerically
from a quasipotential formulation of the Faraday problem due to Zhang and
Vinals. | 0301015v1 |
2011-04-25 | Exactly Solvable Nonhomogeneous Burgers Equations with Variable Coefficients | We consider a nonhomogeneous Burgers equation with time variable
coefficients, and obtain an explicit solution of the general initial value
problem in terms of solution to a corresponding linear ODE. Special exact
solutions such as generalized shock and multi-shock solitary waves, triangular
wave, N-wave and rational type solutions are found and discussed. As exactly
solvable models, we study forced Burgers equations with constant damping and an
exponentially decaying diffusion coefficient. Different type of exact solutions
are obtained for the critical, over and under damping cases, and their behavior
is illustrated explicitly. In particular, the existence of inelastic type of
collisions is observed by constructing multi-shock solitary wave solutions, and
for the rational type solutions the motion of the pole singularities is
described. | 1104.4717v1 |
2011-06-03 | Shear viscous effects on the primordial power spectrum from warm inflation | We compute the primordial curvature spectrum generated during warm inflation,
including shear viscous effects. The primordial spectrum is dominated by the
thermal fluctuations of the radiation bath, sourced by the dissipative term of
the inflaton field. The dissipative coefficient \Upsilon, computed from first
principles in the close-to-equilibrium approximation, depends in general on the
temperature T, and this dependence renders the system of the linear
fluctuations coupled. Whenever the dissipative coefficient is larger than the
Hubble expansion rate H, there is a growing mode in the fluctuations before
horizon crossing. However, dissipation intrinsically means departures from
equilibrium, and therefore the presence of a shear viscous pressure in the
radiation fluid. This in turn acts as an extra friction term for the radiation
fluctuations that tends to damp the growth of the perturbations. Independently
of the T functional dependence of the dissipation and the shear viscosity, we
find that when the shear viscous coefficient \zeta_s is larger than 3 \rho_r/H
at horizon crossing, \rho_r being the radiation energy density, the shear
damping effect wins and there is no growing mode in the spectrum. | 1106.0701v1 |
2012-07-18 | Attractiveness of periodic orbits in parametrically forced systemswith time-increasing friction | We consider dissipative one-dimensional systems subject to a periodic force
and study numerically how a time-varying friction affects the dynamics. As a
model system, particularly suited for numerical analysis, we investigate the
driven cubic oscillator in the presence of friction. We find that, if the
damping coefficient increases in time up to a final constant value, then the
basins of attraction of the leading resonances are larger than they would have
been if the coefficient had been fixed at that value since the beginning. From
a quantitative point of view, the scenario depends both on the final value and
the growth rate of the damping coefficient. The relevance of the results for
the spin-orbit model are discussed in some detail. | 1207.4319v1 |
2016-09-30 | Origin of the effective mobility in non-linear active micro-rheology | The distinction between the damping coefficient and the effective non-linear
mobility of driven particles in active micro-rheology of supercooled liquids is
explained in terms of individual and collective dynamics. The effective
mobility arises as a collective effect which gives insight into the energy
landscape of the system. On the other hand, the damping coefficient is a
constant that modulates the effect of external forces over the thermal energy
which particles have at their disposition to perform Brownian motion. For long
times, these thermal fluctuations become characterized in terms of an effective
temperature that is a consequence of the dynamic coupling between kinetic and
configurational degrees of freedom induced by the presence of the strong
external force. The interplay between collective mobility and effective
temperature allows to formulate a generalized Stokes-Einstein relation that may
be used to determine the collective diffusion coefficient. The explicit
relations we deduce reproduce simulation data remarkably well. | 1609.09853v1 |
2017-04-24 | Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas | In this paper, a reduced model of quasilinear diffusion by a small Larmor
radius approximation is derived to couple the Maxwell's equations and the
Fokker-Planck equation self-consistently for ion cyclotron range of frequency
waves in a tokamak. The reduced model ensures the important properties of the
full model by Kennel-Engelmann diffusion, such as diffusion directions, wave
polarizations, and H-theorem. The kinetic energy change (W-dot) is used to
derive the reduced model diffusion coefficients for the fundamental damping and
the second harmonic damping to the lowest order of the finite Larmor radius
expansion. The quasilinear diffusion coefficients are implemented in a coupled
code (TORIC-CQL3D) with the equivalent reduced model of dielectric tensor. We
also present the simulations of the ITER minority heating scenario, in which
the reduced model is verified within the allowable errors from the full model
results. | 1704.07283v1 |
2017-04-19 | Refractive index of dense materials | We show that applying the Lorentz-Lorenz transformation to the refractive
index of metals, semiconductors and insulators allows for a less empirical
modeling of this refractive index. | 1704.05718v1 |
1998-10-01 | Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model | We study the effects of finite temperature on the dynamics of non-planar
vortices in the classical, two-dimensional anisotropic Heisenberg model with
XY- or easy-plane symmetry. To this end, we analyze a generalized
Landau-Lifshitz equation including additive white noise and Gilbert damping.
Using a collective variable theory with no adjustable parameters we derive an
equation of motion for the vortices with stochastic forces which are shown to
represent white noise with an effective diffusion constant linearly dependent
on temperature. We solve these stochastic equations of motion by means of a
Green's function formalism and obtain the mean vortex trajectory and its
variance. We find a non-standard time dependence for the variance of the
components perpendicular to the driving force. We compare the analytical
results with Langevin dynamics simulations and find a good agreement up to
temperatures of the order of 25% of the Kosterlitz-Thouless transition
temperature. Finally, we discuss the reasons why our approach is not
appropriate for higher temperatures as well as the discreteness effects
observed in the numerical simulations. | 9810011v1 |
2004-07-21 | A selfconsistent theory of current-induced switching of magnetization | A selfconsistent theory of the current-induced switching of magnetization
using nonequilibrium Keldysh formalism is developed for a junction of two
ferromagnets separated by a nonmagnetic spacer. It is shown that the
spin-transfer torques responsible for current-induced switching of
magnetization can be calculated from first principles in a steady state when
the magnetization of the switching magnet is stationary. The spin-transfer
torque is expressed in terms of one-electron surface Green functions for the
junction cut into two independent parts by a cleavage plane immediately to the
left and right of the switching magnet. The surface Green functions are
calculated using a tight-binding Hamiltonian with parameters determined from a
fit to an {\it ab initio} band structure.This treatment yields the spin
transfer torques taking into account rigorously contributions from all the
parts of the junction. To calculate the hysteresis loops of resistance versus
current, and hence to determine the critical current for switching, the
microscopically calculated spin-transfer torques are used as an input into the
phenomenological Landau-Lifshitz equation with Gilbert damping. The present
calculations for Co/Cu/Co(111) show that the critical current for switching is
$\approx 10^7A/cm^2$, which is in good agreement with experiment. | 0407562v2 |
2006-02-24 | Magnetization dynamics in dysprosium orthoferrites via inverse Faraday effect | The ultrafast non-thermal control of magnetization has recently become
feasible in canted antiferromagnets through photomagnetic instantaneous pulses
[A.V. Kimel {\it et al.}, Nature {\bf 435}, 655 (2005)]. In this experiment
circularly polarized femtosecond laser pulses set up a strong magnetic field
along the wave vector of the radiation through the inverse Faraday effect,
thereby exciting non-thermally the spin dynamics of dysprosium orthoferrites. A
theoretical study is performed by using a model for orthoferrites based on a
general form of free energy whose parameters are extracted from experimental
measurements. The magnetization dynamics is described by solving coupled
sublattice Landau-Lifshitz-Gilbert equations whose damping term is associated
with the scattering rate due to magnon-magnon interaction. Due to the inverse
Faraday effect and the non-thermal excitation, the effect of the laser is
simulated by magnetic field Gaussian pulses with temporal width of the order of
hundred femtoseconds. When the field is along the z-axis, a single resonance
mode of the magnetization is excited. The amplitude of the magnetization and
out-of-phase behavior of the oscillations for fields in z and -z directions are
in good agreement with the cited experiment. The analysis of the effect of the
temperature shows that magnon-magnon scattering mechanism affects the decay of
the oscillations on the picosecond scale. Finally, when the field pulse is
along the x-axis, another mode is excited, as observed in experiments. In this
case the comparison between theoretical and experimental results shows some
discrepancies whose origin is related to the role played by anisotropies in
orthoferrites. | 0602593v1 |
2006-04-19 | Stress - and Magneto-Impedance in Co71-xFexCr7Si8B14 (x = 0, 2) amorphous ribbons | Systematic measurements of stress impedance (SI) and magneto-impedance (MI)
have been carried out using Co-rich amorphous ribbons of nominal composition
Co71-xFexCr7Si8B14 (x = 0, 2) at various excitation frequencies and bias fields
and at room temperature. The impedance, Z, for both the samples was found to be
very sensitive functions of applied tensile stress (up to 100MPa) exhibiting a
maximum SI ratio as much as 80% at low frequency ~ 0.1MHz. The nature of
variation of impedance, Z, changes with the excitation frequency especially at
higher frequencies in MHz region where it exhibits a peak. Magnetization
measurements were also performed to observe the effects of applied stress and
magnetization decreases with the application of stress confirming the negative
magnetostriction co-efficient of both the samples. Both the samples exhibited
negative magneto-impedance when the variation of Z is observed with the applied
bias magnetic field, H. Maximum MI ratio as large as 99% has been observed for
both the samples at low fields ~ 27Oe. The impedance as functions of applied
magnetic field, Z(H), decreases with the application of stress thus making the
MI curves broader. Based on the electromagnetic screening and magnetization
dynamics and incorporating the Gilbert and the Bloch-Bloembergen damping and
stress dependent anisotropy, the SI has been calculated and is found to
describe well the stress and field dependence of impedance of the two samples. | 0604438v2 |
2010-05-25 | Structural, static and dynamic magnetic properties of CoMnGe thin films on a sapphire a-plane substrate | Magnetic properties of CoMnGe thin films of different thicknesses (13, 34,
55, 83, 100 and 200 nm), grown by RF sputtering at 400{\deg}C on single crystal
sapphire substrates, were studied using vibrating sample magnetometry (VSM) and
conventional or micro-strip line (MS) ferromagnetic resonance (FMR). Their
behavior is described assuming a magnetic energy density showing twofold and
fourfold in-plane anisotropies with some misalignment between their principal
directions. For all the samples, the easy axis of the fourfold anisotropy is
parallel to the c-axis of the substrate while the direction of the twofold
anisotropy easy axis varies from sample to sample and seems to be strongly
influenced by the growth conditions. Its direction is most probably monitored
by the slight unavoidable angle of miscut the Al2O3 substrate. The twofold
in-plane anisotropy field is almost temperature independent, in contrast with
the fourfold field which is a decreasing function of the temperature. Finally,
we study the frequency dependence of the observed line-width of the resonant
mode and we conclude to a typical Gilbert damping constant of 0.0065 for the
55-nm-thick film. | 1005.4595v3 |
2011-06-22 | Effect of spin diffusion on current generated by spin motive force | Spin motive force is a spin-dependent force on conduction electrons induced
by magnetization dynamics. In order to examine its effects on magnetization
dynamics, it is indispensable to take into account spin accumulation, spin
diffusion, and spin-flip scattering since the spin motive force is in general
nonuniform. We examine the effects of all these on the way the spin motive
force generates the charge and spin currents in conventional situations, where
the conduction electron spin relaxation dynamics is much faster than the
magnetization dynamics. When the spin-dependent electric field is spatially
localized, which is common in experimental situations, we find that the
conservative part of the spin motive force is unable to generate the charge
current due to the cancelation effect by the diffusion current. We also find
that the spin current is a nonlocal function of the spin motive force and can
be effectively expressed in terms of nonlocal Gilbert damping tensor. It turns
out that any spin independent potential such as Coulomb potential does not
affect our principal results. At the last part of this paper, we apply our
theory to current-induced domain wall motion. | 1106.4389v2 |
2011-07-11 | Spin and charge transport induced by gauge fields in a ferromagnet | We present a microscopic theory of spin-dependent motive force ("spin motive
force") induced by magnetization dynamics in a conducting ferromagnet, by
taking account of spin relaxation of conduction electrons. The theory is
developed by calculating spin and charge transport driven by two kinds of gauge
fields; one is the ordinary electromagnetic field $A^{\rm em}_{\mu}$, and the
other is the effective gauge field $A^{z}_{\mu}$ induced by dynamical magnetic
texture. The latter acts in the spin channel and gives rise to a spin motive
force. It is found that the current induced as a linear response to
$A^{z}_{\mu}$ is not gauge-invariant in the presence of spin-flip processes.
This fact is intimately related to the non-conservation of spin via Onsager
reciprocity, so is robust, but indicates a theoretical inconsistency. This
problem is resolved by considering the time dependence of spin-relaxation
source terms in the "rotated frame", as in the previous study on Gilbert
damping [J. Phys. Soc. Jpn. {\bf 76}, 063710 (2007)]. This effect restores the
gauge invariance while keeping spin non-conservation. It also gives a
dissipative spin motive force expected as a reciprocal to the dissipative spin
torque ("$\beta$-term"). | 1107.2165v3 |
2012-07-02 | Establishing micromagnetic parameters of ferromagnetic semiconductor (Ga,Mn)As | (Ga,Mn)As is at the forefront of research exploring the synergy of magnetism
with the physics and technology of semiconductors, and has led to discoveries
of new spin-dependent phenomena and functionalities applicable to a wide range
of material systems. Its recognition and utility as an ideal model material for
spintronics research has been undermined by the large scatter in reported
semiconducting doping trends and micromagnetic parameters. In this paper we
establish these basic material characteristics by individually optimizing the
highly non-equilibrium synthesis for each Mn-doping level and by simultaneously
determining all micromagnetic parameters from one set of magneto-optical
pump-and-probe measurements. Our (Ga,Mn)As thin-film epilayers, spannig the
wide range of accessible dopings, have sharp thermodynamic Curie point
singularities typical of uniform magnetic systems. The materials show
systematic trends of increasing magnetization, carrier density, and Curie
temperature (reaching 188 K) with increasing doping, and monotonous doping
dependence of the Gilbert damping constant of ~0.1-0.01 and the spin stiffness
of ~2-3 meVnm^2. These results render (Ga,Mn)As well controlled degenerate
semiconductor with basic magnetic characteristics comparable to common band
ferromagnets. | 1207.0310v1 |
2013-03-14 | Spin-torque effects in thermally assisted magnetization reversal: Method of statistical moments | Thermal fluctuations of nanomagnets driven by spin-polarized currents are
treated via the Landau-Lifshitz-Gilbert equation generalized to include both
the random thermal noise field and the Slonczewski spin-transfer torque term.
By averaging this stochastic (Langevin) equation over its realizations, the
explicit infinite hierarchy of differential-recurrence relations for
statistical moments (averaged spherical harmonics) is derived for arbitrary
demagnetizing factors and magnetocrystalline anisotropy for the generic
nanopillar model of a spin-torque device comprising two ferromagnetic strata
representing the free and fixed layers and a nonmagnetic conducting spacer all
sandwiched between two ohmic contacts. The influence of thermal fluctuations
and spin-transfer torques on relevant switching characteristics, such as the
stationary magnetization, the magnetization reversal time, etc., is calculated
by solving the hierarchy for wide ranges of temperature, damping, external
magnetic field, and spin-polarized current indicating new spin-torque effects
in the thermally assisted magnetization reversal comprising several orders of
magnitude. In particular, a pronounced dependence of the switching
characteristics on the directions of the external magnetic field and the spin
polarization exists. | 1303.3476v4 |
2013-06-19 | Asymmetric Ferromagnetic Resonance, Universal Walker Breakdown, and Counterflow Domain Wall Motion in the Presence of Multiple Spin-Orbit Torques | We study the motion of several types of domain wall profiles in spin-orbit
coupled magnetic nanowires and also the influence of spin-orbit interaction on
the ferromagnetic resonance of uniform magnetic films. We extend previous
studies by fully considering not only the field-like contribution from the
spin-orbit torque, but also the recently derived Slonczewski-like spin-orbit
torque. We show that the latter interaction affects both the domain wall
velocity and the Walker breakdown threshold non-trivially, which suggests that
it should be accounted in experimental data analysis. We find that the presence
of multiple spin-orbit torques may render the Walker breakdown to be universal
in the sense that the threshold is completely independent on the
material-dependent Gilbert damping, non-adiabaticity, and the chirality of the
domain wall. We also find that domain wall motion against the current injection
is sustained in the presence of multiple spin-orbit torques and that the wall
profile will determine the qualitative influence of these different types of
torques (e.g. field-like and Slonczewski-like). In addition, we consider a
uniform ferromagnetic layer under a current bias, and find that the resonance
frequency becomes asymmetric against the current direction in the presence of
Slonczewski-like spin-orbit coupling. This is in contrast with those cases
where such an interaction is absent, where the frequency is found to be
symmetric with respect to the current direction. This finding shows that
spin-orbit interactions may offer additional control over pumped and absorbed
energy in a ferromagnetic resonance setup by manipulating the injected current
direction. | 1306.4680v1 |
2013-11-29 | Magnon radiation by moving Abrikosov vortices in ferromagnetic superconductors and superconductor-ferromagnet multilayers | In systems combining type-II superconductivity and magnetism the
non-stationary magnetic field of moving Abrikosov vortices may excite spin
waves, or magnons. This effect leads to the appearance of an additional damping
force acting on the vortices. By solving the London and Landau-Lifshitz-Gilbert
equations we calculate the magnetic moment induced force acting on vortices in
ferromagnetic superconductors and superconductor/ferromagnet superlattices. If
the vortices are driven by a dc force, magnon generation due to the Cherenkov
resonance starts as the vortex velocity exceeds some threshold value. For an
ideal vortex lattice this leads to an anisotropic contribution to the
resistivity and to the appearance of resonance peaks on the current voltage
characteristics. For a disordered vortex array the current will exhibit a
step-like increase at some critical voltage. If the vortices are driven by an
ac force with a frequency \omega, the interaction with magnetic moments will
lead to a frequency-dependent magnetic contribution \eta_M to the vortex
viscosity. If \omega is below the ferromagnetic resonance frequency \omega_F,
vortices acquire additional inertia. For \omega > \omega_F dissipation is
enhanced due to magnon generation. The viscosity \eta_M can be extracted from
the surface impedance of the ferromagnetic superconductor. Estimates of the
magnetic force acting on vortices for the U-based ferromagnetic superconductors
and cuprate/manganite superlattices are given. | 1311.7620v1 |
2014-03-03 | Observations and Implications of Large-Amplitude Longitudinal Oscillations in a Solar Filament | On 20 August 2010 an energetic disturbance triggered large-amplitude
longitudinal oscillations in a nearby filament. The triggering mechanism
appears to be episodic jets connecting the energetic event with the filament
threads. In the present work we analyze this periodic motion in a large
fraction of the filament to characterize the underlying physics of the
oscillation as well as the filament properties. The results support our
previous theoretical conclusions that the restoring force of large-amplitude
longitudinal oscillations is solar gravity, and the damping mechanism is the
ongoing accumulation of mass onto the oscillating threads. Based on our
previous work, we used the fitted parameters to determine the magnitude and
radius of curvature of the dipped magnetic field along the filament, as well as
the mass accretion rate onto the filament threads. These derived properties are
nearly uniform along the filament, indicating a remarkable degree of
cohesiveness throughout the filament channel. Moreover, the estimated mass
accretion rate implies that the footpoint heating responsible for the thread
formation, according to the thermal nonequilibrium model, agrees with previous
coronal heating estimates. We estimate the magnitude of the energy released in
the nearby event by studying the dynamic response of the filament threads, and
discuss the implications of our study for filament structure and heating. | 1403.0381v1 |
2015-01-16 | Direct measurement of the magnetic anisotropy field in Mn--Ga and Mn--Co--Ga Heusler films | The static and dynamic magnetic properties of tetragonally distorted Mn--Ga
based alloys were investigated. Static properties are determined in magnetic
fields up to 6.5~T using SQUID magnetometry. For the pure Mn$_{1.6}$Ga film,
the saturation magnetisation is 0.36~MA/m and the coercivity is 0.29~T. Partial
substitution of Mn by Co results in Mn$_{2.6}$Co$_{0.3}$Ga$_{1.1}$. The
saturation magnetisation of those films drops to 0.2~MA/m and the coercivity is
increased to 1~T.
Time-resolved magneto-optical Kerr effect (TR-MOKE) is used to probe the
high-frequency dynamics of Mn--Ga. The ferromagnetic resonance frequency
extrapolated to zero-field is found to be 125~GHz with a Gilbert damping,
$\alpha$, of 0.019. The anisotropy field is determined from both SQUID and
TR-MOKE to be 4.5~T, corresponding to an effective anisotropy density of
0.81~MJ/m$^3$.
Given the large anisotropy field of the Mn$_{2.6}$Co$_{0.3}$Ga$_{1.1}$ film,
pulsed magnetic fields up to 60~T are used to determine the field strength
required to saturate the film in the plane. For this, the extraordinary Hall
effect was employed as a probe of the local magnetisation. By integrating the
reconstructed in--plane magnetisation curve, the effective anisotropy energy
density for Mn$_{2.6}$Co$_{0.3}$Ga$_{1.1}$ is determined to be 1.23~MJ/m$^3$. | 1501.03973v1 |
2015-06-02 | Respective influence of in-plane and out-of-plane spin-transfer torques in magnetization switching of perpendicular magnetic tunnel junctions | The relative contributions of in-plane (damping-like) and out-of-plane
(field-like) spin-transfer-torques in the magnetization switching of
out-of-plane magnetized magnetic tunnel junctions (pMTJ) has been theoretically
analyzed using the transformed Landau-Lifshitz (LL) equation with the STT
terms. It is demonstrated that in a pMTJ structure obeying macrospin dynamics,
the out-of-plane torque influences the precession frequency but it does not
contribute significantly to the STT switching process (in particular to the
switching time and switching current density), which is mostly determined by
the in-plane STT contribution. This conclusion is confirmed by finite
temperature and finite writing pulse macrospin simulations of the current-field
switching diagrams. It contrasts with the case of STT-switching in in-plane
magnetized MTJ in which the field-like term also influences the switching
critical current. This theoretical analysis was successfully applied to the
interpretation of voltage-field STT switching diagrams experimentally measured
on perpendicular MTJ pillars 36 nm in diameter, which exhibit macrospin-like
behavior. The physical nonequivalence of Landau and Gilbert dissipation terms
in presence of STT-induced dynamics is also discussed. | 1506.00780v2 |
2015-08-28 | Control of magnetic relaxation by electric-field-induced ferroelectric phase transition and inhomogeneous domain switching | Electric-field modulation of magnetism in strain-mediated multiferroic
heterostructures is considered a promising scheme for enabling memory and
magnetic microwave devices with ultralow power consumption. However, it is not
well understood how electric-field-induced strain influences magnetic
relaxation, an important physical process for device applications. Here we
investigate resonant magnetization dynamics in ferromagnet/ferrolectric
multiferroic heterostructures, FeGaB/PMN-PT and NiFe/PMN-PT, in two distinct
strain states provided by electric-field-induced ferroelectric phase
transition. The strain not only modifies magnetic anisotropy but also magnetic
relaxation. In FeGaB/PMN-PT, we observe a nearly two-fold change in intrinsic
Gilbert damping by electric field, which is attributed to strain-induced tuning
of spin-orbit coupling. By contrast, a small but measurable change in extrinsic
linewidth broadening is attributed to inhomogeneous ferroelastic domain
switching during the phase transition of the PMN-PT substrate. | 1508.07290v2 |
2016-04-05 | Homodyne-detected ferromagnetic resonance of in-plane magnetized nano-contacts: composite spin wave resonances and their excitation mechanism | This work provides a detailed investigation of the measured in-plane
field-swept homodyne-detected ferromagnetic resonance (FMR) spectra of an
extended Co/Cu/NiFe pseudo spin valve stack using a nanocontact (NC) geometry.
The magnetodynamics are generated by a pulse-modulated microwave current and
the resulting rectified dc mixing voltage, which appears across the NC at
resonance, is detected using a lock-in amplifier. Most notably, we find that
the measured spectra of the NiFe layer are composite in nature and highly
asymmetric, consistent with the broadband excitation of multiple modes.
Additionally, the data must be fit with two Lorentzian functions in order to
extract a reasonable value for the Gilbert damping of the NiFe. Aided by
micromagnetic simulations, we conclude that (i) for in-plane fields the rf
Oersted field in the vicinity of the NC plays the dominant role in generating
the observed spectra, (ii) in addition to the FMR mode, exchange dominated spin
waves are also generated, and (iii) the NC diameter sets the mean wavevector of
the exchange dominated spin wave, in good agreement with the dispersion
relation. | 1604.01389v1 |
2017-01-10 | Motion of skyrmions in nanowires driven by magnonic momentum-transfer forces | We study the motion of magnetic skyrmions in a nanowire induced by a
spin-wave current $J$ flowing out of a driving layer close to the edge of the
wire. By applying micromagnetic simulation and an analysis of the effective
Thiele equation, we find that the skyrmion trajectory is governed by an
interplay of both forces due to the magnon current and the wire boundary. The
skyrmion is attracted to the driving layer and is accelerated by the repulsive
force due to the wire boundary. We consider both cases of a driving
longitudinal and transverse to the nanowire, but a steady-state motion of the
skyrmion is only obtained for a transverse magnon current. For the latter case,
we find in the limit of low current densities $J$ the velocity-current relation
$v \sim J/\alpha$ where $v$ is the skyrmion velocity and $\alpha$ is the
Gilbert damping. For large $J$ in case of strong driving, the skyrmion is
pushed into the driving layer resulting in a drop of the skyrmion velocity and,
eventually, the destruction of the skyrmion. | 1701.02430v2 |
2017-01-19 | Ultrafast Electron-Lattice Coupling Dynamics in VO2 and V2O3 Thin Films | Ultrafast optical pump - optical probe and optical pump - terahertz probe
spectroscopy were performed on vanadium dioxide (VO2) and vanadium sesquioxide
(V2O3) thin films over a wide temperature range. A comparison of the
experimental data from these two different techniques and two different
vanadium oxides, in particular a comparison of the electronic oscillations
generated by the photoinduced longitudinal acoustic modulation, reveals the
strong electron-phonon coupling that exists in the metallic state of both
materials. The low energy Drude response of V2O3 appears more susceptible than
VO2 to ultrafast strain control. Additionally, our results provide a
measurement of the temperature dependence of the sound velocity in both
systems, revealing a four- to fivefold increase in VO2 and a three- to fivefold
increase in V2O3 across the phase transition. Our data also confirm
observations of strong damping and phonon anharmonicity in the metallic phase
of VO2, and suggest that a similar phenomenon might be at play in the metallic
phase of V2O3. More generally, our simple table-top approach provides relevant
and detailed information about dynamical lattice properties of vanadium oxides,
opening the way to similar studies in other complex materials. | 1701.05531v1 |
2017-02-21 | All-optical Detection of Spin Hall Angle in W/CoFeB/SiO2 Heterostructures by Varying Tungsten Layer Thickness | The development of advanced spintronics devices hinges on the efficient
generation and utilization of pure spin current. In materials with large
spin-orbit coupling, the spin Hall effect may convert charge current to pure
spin current and a large conversion efficiency, which is quantified by spin
Hall angle (SHA), is desirable for the realization of miniaturized and energy
efficient spintronic devices. Here, we report a giant SHA in beta-tungsten
(\b{eta}-W) thin films in Sub/W(t)/Co20Fe60B20(3 nm)/SiO2(2 nm)
heterostructures with variable W thickness. We employed an all-optical
time-resolved magneto-optical Kerr effect microscope for an unambiguous
determination of SHA using the principle of modulation of Gilbert damping of
the adjacent ferromagnetic layer by the spin-orbit torque from the W layer. A
non-monotonic variation of SHA with W layer thickness (t) is observed with a
maximum of about 0.4 at about t = 3 nm, followed by a sudden reduction to a
very low value at t = 6 nm. This variation of SHA with W-thickness correlates
well with the thickness dependent structural phase transition and resistivity
variation of W above the spin diffusion length of W, while below this length
the interfacial electronic effect at W/CoFeB influences the estimation of SHA. | 1702.06258v1 |
2017-03-21 | Annealing stability of magnetic tunnel junctions based on dual MgO free layers and [Co/Ni] based thin synthetic antiferromagnet fixed system | We study the annealing stability of bottom-pinned perpendicularly magnetized
magnetic tunnel junctions based on dual MgO free layers and thin fixed systems
comprising a hard [Co/Ni] multilayer antiferromagnetically coupled to thin a Co
reference layer and a FeCoB polarizing layer. Using conventional magnetometry
and advanced broadband ferromagnetic resonance, we identify the properties of
each sub-unit of the magnetic tunnel junction and demonstrate that this
material option can ensure a satisfactory resilience to the 400$^\circ$C
thermal annealing needed in solid-state magnetic memory applications. The dual
MgO free layer possesses an anneal-robust 0.4 T effective anisotropy and
suffers only a minor increase of its Gilbert damping from 0.007 to 0.010 for
the toughest annealing conditions. Within the fixed system, the ferro-coupler
and texture-breaking TaFeCoB layer keeps an interlayer exchange above 0.8
mJ/m$^2$, while the Ru antiferrocoupler layer within the synthetic
antiferromagnet maintains a coupling above -0.5 mJ/m$^2$. These two strong
couplings maintain the overall functionality of the tunnel junction upon the
toughest annealing despite the gradual degradation of the thin Co layer
anisotropy that may reduce the operation margin in spin torque memory
applications. Based on these findings, we propose further optimization routes
for the next generation magnetic tunnel junctions. | 1703.07154v1 |
2017-08-03 | Evolution of the interfacial perpendicular magnetic anisotropy constant of the Co$_2$FeAl/MgO interface upon annealing | We investigate thickness series of films of the Heusler alloy Co$_2$FeAl in
order to study the effect of annealing on the interface with a MgO layer and on
the bulk magnetic properties. Our results reveal that while the perpendicular
interface anisotropy constant $K^{\perp}_{\rm S}$ is zero for the as-deposited
samples, its value increases with annealing up to a value of $1.14\, \pm
\,0.07$~mJ/m$^2$ for the series annealed at 320$^{\rm o}$C and of $2.07\, \pm
\,0.7$~mJ/m$^2$ for the 450$^{\rm o}$C annealed series owing to a strong
modification of the interface during the thermal treatment. This large value
ensures a stabilization of a perpendicular magnetization orientation for a
thickness below 1.7~nm. The data additionally shows that the in-plane biaxial
anisotropy constant has a different evolution with thickness in as-deposited
and annealed systems. The Gilbert damping parameter $\alpha$ shows minima for
all series for a thickness of 40~nm and an absolute minimum value of
$2.8\pm0.1\cdot10^{-3}$. The thickness dependence is explained in terms of an
inhomogenous magnetization state generated by the interplay between the
different anisotropies of the system and by crystalline disorder. | 1708.01126v2 |
2017-08-08 | Spin-orbit-torque driven magnetoimpedance in Pt-layer/magnetic-ribbon heterostructures | When a flow of electron passes through a paramagnetic layer with strong
spin-orbit-coupling such as platinum (Pt), a net spin current is produced via
spin Hall effect (SHE). This spin current can exert a torque on the
magnetization of an adjacent ferromagnetic layer which can be probed via
magnetization dynamic response, e.g. spin-torque ferromagnetic resonance
(ST-FMR). Nevertheless, that effect in lower frequency magnetization dynamic
regime (MHz) where skin effect occurs in high permeability ferromagnetic
conductors namely the magneto-impedance (MI) effect can be fundamentally
important which has not been studied so far. Here, by utilizing the MI effect
in magnetic-ribbon/Pt heterostructure with high magnetic permeability that
allows the ac current effectively confined at the skin depth of ~100 nm
thickness, the effect of spin-orbit-torque (SOT) induced by the SHE probed via
MI measurement is investigated. We observed a systematic MI frequency shift
that increases by increasing the applied current amplitude and thickness of the
Pt layer (varying from 0 nm to 20 nm). In addition, the role of Pt layer in
ribbon/Pt heterostructure is evaluated with ferromagnetic resonance (FMR)
effect representing standard Gilbert damping increase as the result of presence
of the SHE. Our results unveil the role of SOT in dynamic control of the
transverse magnetic permeability probed with impedance spectroscopy as useful
and valuable technique for detection of future SHE devices. | 1708.02402v2 |
2017-12-20 | Second-harmonic magnetic response characterizing magnetite-based colloid | Nonlinear second-harmonic magnetic response (M2) was used to characterize an
aqueous colloidal solution of dextran-coated magnetite (Fe3O4) nanoparticles.
Data analysis with the formalism based on Gilbert-Landau-Lifshitz equation for
stochastic dynamics of superparamagnetic (SP) particles ensured extensive
quantifying of the system via a set of magnetic and magnetodynamic parameters,
such as the mean magnetic moment, the damping constant, the longitudinal
relaxation time, the magnetic anisotropy field and energy, and others. Combined
with transmission electron microscopy and dynamic light scattering, M2
technique allowed obtaining additional parameters, viz., the dextran-coating
thickness and the interparticle magnetic dipolar energy. Aggregated colloidal
nanoparticles were shown to be magnetically correlated inside the aggregate due
to magnetic dipole-dipole (d-d) coupling within the correlation radius ~50 nm.
With the d-d coupling account, the volume distribution of the aggregates
recovered from M2 measurements is well consistent with electron microscopy
results. From electron magnetic resonance, abrupt change of SP dynamics with
increasing external magnetic field was observed and explained. The presented
study exemplifies a novel M2-based procedure of comprehensive quantitative
characterization applicable for a wide variety of SP systems. | 1712.07534v1 |
2018-02-09 | Monocrystalline free standing 3D yttrium iron garnet magnon nano resonators | Nano resonators in which mechanical vibrations and spin waves can be coupled
are an intriguing concept that can be used in quantum information processing to
transfer information between different states of excitation. Until now, the
fabrication of free standing magnetic nanostructures which host long lived spin
wave excitatons and may be suitable as mechanical resonators seemed elusive. We
demonstrate the fabrication of free standing monocrystalline yttrium iron
garnet (YIG) 3D nanoresonators with nearly ideal magnetic properties. The
freestanding 3D structures are obtained using a complex lithography process
including room temperature deposition and lift-off of amorphous YIG and
subsequent crystallization by annealing. The crystallization nucleates from the
substrate and propagates across the structure even around bends over distances
of several micrometers to form e.g. monocrystalline resonators as shown by
transmission electron microscopy. Spin wave excitations in individual
nanostructures are imaged by time resolved scanning Kerr microscopy. The narrow
linewidth of the magnetic excitations indicates a Gilbert damping constant of
only $\alpha = 2.6 \times 10^{-4}$ rivalling the best values obtained for
epitaxial YIG thin film material. The new fabrication process represents a leap
forward in magnonics and magnon mechanics as it provides 3D YIG structures of
unprecedented quality. At the same time it demonstrates a completely new route
towards the fabrication of free standing crystalline nano structures which may
be applicable also to other material systems. | 1802.03176v2 |
2018-11-30 | Dynamical precession of spin in the two-dimensional spin-orbit coupled systems | We investigate the spin dynamics in the two-dimensional spin-orbit coupled
system subject to an in-plane ($x$-$y$ plane) constant electric field, which is
assumed to be turned on at the moment $t=0$. The equation of spin precession in
linear response to the switch-on of the electric field is derived in terms of
Heisenberg's equation by the perturbation method up to the first order of the
electric field. The dissipative effect, which is responsible for bringing the
dynamical response to an asymptotic result, is phenomenologically implemented
\`{a} la the Landau-Lifshitz-Gilbert equation by introducing damping terms upon
the equation of spin dynamics. Mediated by the dissipative effect, the
resulting spin dynamics asymptotes to a stationary state, where the spin and
the momentum-dependent effective magnetic field are aligned again and have
nonzero components in the out-of-plane ($z$) direction. In the linear response
regime, the asymptotic response obtained by the dynamical treatment is in full
agreement with the stationary response as calculated in the Kubo formula, which
is a time-independent approach treating the applied electric field as
completely time-independent. Our method provides a new perspective on the
connection between the dynamical and stationary responses. | 1811.12626v2 |
2019-03-08 | Spin-transfer torques for domain walls in antiferromagnetically coupled ferrimagnets | Antiferromagnetic materials are outstanding candidates for next generation
spintronic applications, because their ultrafast spin dynamics makes it
possible to realize several orders of magnitude higher-speed devices than
conventional ferromagnetic materials1. Though spin-transfer torque (STT) is a
key for electrical control of spins as successfully demonstrated in
ferromagnetic spintronics, experimental understanding of STT in
antiferromagnets has been still lacking despite a number of pertinent
theoretical studies2-5. Here, we report experimental results on the effects of
STT on domain-wall (DW) motion in antiferromagnetically-coupled ferrimagnets.
We find that non-adiabatic STT acts like a staggered magnetic field and thus
can drive DWs effectively. Moreover, the non-adiabaticity parameter {\beta} of
STT is found to be significantly larger than the Gilbert damping parameter
{\alpha}, challenging our conventional understanding of the non-adiabatic STT
based on ferromagnets as well as leading to fast current-induced
antiferromagnetic DW motion. Our study will lead to further vigorous
exploration of STT for antiferromagnetic spin textures for fundamental physics
on spin-charge interaction as wells for efficient electrical control of
antiferromagnetic devices. | 1903.03251v1 |
2019-03-26 | Engineering of spin mixing conductance in Ru/FeCo/Ru interfaces: Effect of Re Doping | We have deposited polycrystalline Re doped $(Fe_{65}Co_{35})_{100-x}Re_{x}$
(0 $\leq$ x $\leq$ 12.6 at\%) thin films grown under identical conditions and
sandwiched between thin layers of Ru in order to study the phenomenon of spin
pumping as a function of Re concentration. In-plane and out-of-plane
ferromagnetic resonance spectroscopy results show an enhancement of the Gilbert
damping with an increase in Re doping. We found evidence of an increase in the
real part of effective spin mixing conductance
[Re($g^{\uparrow\downarrow}_{eff}$)] with the increase in Re doping of 6.6
at\%, while a decrease is evident at higher Re doping. The increase in
Re($g^{\uparrow\downarrow}_{eff}$) can be linked to the Re doping induced
change of the interface electronic structure in the non-magnetic Ru layer and
the effect interfacial spin-orbit coupling has on the effective spin-mixing
conductance. The lowest and highest values of
Re($g^{\uparrow\downarrow}_{eff}$) are found to be 9.883(02) $nm^{-2}$ and
19.697(02) $nm^{-2}$ for 0 at\% and 6.6 at\% Re doping, respectively. The
saturation magnetization decreases with increasing Re doping, from 2.362(13) T
for the undoped film to 1.740(03) T for 12.6 at\% Re doping. This study opens a
new direction of tuning the spin-mixing conductance in magnetic
heterostructures by doping of the ferromagnetic layerr, which is essential for
the realization of energy efficient operation of spintronic devices. | 1903.10966v2 |
2019-12-16 | Spin-current manipulation of photoinduced magnetization dynamics in heavy metal / ferromagnet double layer based nanostructures | Spin currents offer a way to control static and dynamic magnetic properties,
and therefore they are crucial for next-generation MRAM devices or spin-torque
oscillators. Manipulating the dynamics is especially interesting within the
context of photo-magnonics. In typical $3d$ transition metal ferromagnets like
CoFeB, the lifetime of light-induced magnetization dynamics is restricted to
about 1 ns, which e.g. strongly limits the opportunities to exploit the wave
nature in a magnonic crystal filtering device. Here, we investigate the
potential of spin-currents to increase the spin wave lifetime in a functional
bilayer system, consisting of a heavy metal (8 nm of $\beta$-Tantalum
(Platinum)) and 5 nm CoFeB. Due to the spin Hall effect, the heavy metal layer
generates a transverse spin current when a lateral charge current passes
through the strip. Using time-resolved all-optical pump-probe spectroscopy, we
investigate how this spin current affects the magnetization dynamics in the
adjacent CoFeB layer. We observed a linear spin current manipulation of the
effective Gilbert damping parameter for the Kittel mode from which we were able
to determine the system's spin Hall angles. Furthermore, we measured a strong
influence of the spin current on a high-frequency mode. We interpret this mode
an an exchange dominated higher order spin-wave resonance. Thus we infer a
strong dependence of the exchange constant on the spin current. | 1912.07728v1 |
2020-01-09 | Role of longitudinal fluctuations in L$1_0$ FePt | L$1_0$ FePt is a technologically important material for a range of novel data
storage applications. In the ordered FePt structure the normally non-magnetic
Pt ion acquires a magnetic moment, which depends on the local field originating
from the neighboring Fe atoms. In this work a model of FePt is constructed,
where the induced Pt moment is simulated by using combined longitudinal and
rotational spin dynamics. The model is parameterized to include a linear
variation of the moment with the exchange field, so that at the Pt site the
magnetic moment depends on the Fe ordering. The Curie temperature of FePt is
calculated and agrees well with similar models that incorporate the Pt dynamics
through an effective Fe-only Hamiltonian. By computing the dynamic correlation
function the anisotropy field and the Gilbert damping are extracted over a
range of temperatures. The anisotropy exhibits a power-law dependence with
temperature with exponent $n\approx2.1$. This agrees well with what observed
experimentally and it is obtained without including a two-ion anisotropy term
as in other approaches. Our work shows that incorporating longitudinal
fluctuations into spin dynamics calculations is crucial for understanding the
properties of materials with induced moments. | 2001.03074v1 |
2020-05-07 | Effect of interfacial oxidation layer in spin pumping experiments on Ni$_{80}$Fe$_{20}$/SrIrO$_3$ heterostructures | SrIrO$_3$ with its large spin-orbit coupling and low charge conductivity has
emerged as a potential candidate for efficient spin-orbit torque magnetization
control in spintronic devices. We here report on the influence of an
interfacial oxide layer on spin pumping experiments in Ni$_{80}$Fe$_{20}$
(NiFe)/SrIrO$_3$ bilayer heterostructures. To investigate this scenario we have
carried out broadband ferromagnetic resonance (BBFMR) measurements, which
indicate the presence of an interfacial antiferromagnetic oxide layer. We
performed in-plane BBFMR experiments at cryogenic temperatures, which allowed
us to simultaneously study dynamic spin pumping properties (Gilbert damping)
and static magnetic properties (such as the effective magnetization and
magnetic anisotropy). The results for NiFe/SrIrO$_3$ bilayer thin films were
analyzed and compared to those from a NiFe/NbN/SrIrO$_3$ trilayer reference
sample, where a spin-transparent, ultra-thin NbN layer was inserted to prevent
oxidation of NiFe. At low temperatures, we observe substantial differences in
the magnetization dynamics parameters of these samples, which can be explained
by an antiferromagnetic interfacial layer in the NiFe/SrIrO$_3$ bilayers. | 2005.03727v1 |
2020-05-28 | Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-$T_{\rm c}$ superconductors | An understanding of the missing antinodal electronic excitations in the
pseudogap state is essential for uncovering the physics of the underdoped
cuprate high temperature superconductors. The majority of high temperature
experiments performed thus far, however, have been unable to discern whether
the antinodal states are rendered unobservable due to their damping, or whether
they vanish due to their gapping. Here we distinguish between these two
scenarios by using quantum oscillations to examine whether the small Fermi
surface pocket, found to occupy only 2% of the Brillouin zone in the underdoped
cuprates, exists in isolation against a majority of completely gapped density
of states spanning the antinodes, or whether it is thermodynamically coupled to
a background of ungapped antinodal states. We find that quantum oscillations
associated with the small Fermi surface pocket exhibit a signature sawtooth
waveform characteristic of an isolated two-dimensional Fermi surface pocket.
This finding reveals that the antinodal states are destroyed by a hard gap that
extends over the majority of the Brillouin zone, placing strong constraints on
a drastic underlying origin of quasiparticle disappearance over almost the
entire Brillouin zone in the pseudogap regime. | 2005.14123v1 |
2020-06-01 | Enhancement in Thermally Generated Spin Voltage at Pd/NiFe$_2$O$_4$ Interfaces by the Growth on Lattice-Matched Substrates | Efficient spin injection from epitaxial ferrimagnetic NiFe$_2$O$_4$ thin
films into a Pd layer is demonstrated via spin Seebeck effect measurements in
the longitudinal geometry. The NiFe$_2$O$_4$ films (60 nm to 1 $\mu$m) are
grown by pulsed laser deposition on isostructural spinel MgAl$_2$O$_4$,
MgGa$_2$O$_4$, and CoGa$_2$O$_4$ substrates with lattice mismatch varying
between 3.2% and 0.2%. For the thinner films ($\leq$ 330 nm), an increase in
the spin Seebeck voltage is observed with decreasing lattice mismatch, which
correlates well with a decrease in the Gilbert damping parameter as determined
from ferromagnetic resonance measurements. High resolution transmission
electron microscopy studies indicate substantial decrease of antiphase boundary
and interface defects that cause strain-relaxation, i.e., misfit dislocations,
in the films with decreasing lattice mismatch. This highlights the importance
of reducing structural defects in spinel ferrites for efficient spin injection.
It is further shown that angle-dependent spin Seebeck effect measurements
provide a qualitative method to probe for in-plane magnetic anisotropies
present in the films. | 2006.00777v1 |
2020-06-10 | Study of magnetic interface and its effect in Fe/NiFe bilayers of alternating order | We present a comprehensive study on the magnetization reversal in Fe/NiFe
bilayer system by alternating the order of the magnetic layers. All the samples
show growth-induced uniaxial magnetic anisotropy due to oblique angle
deposition technique. Strong interfacial exchange coupling between the Fe and
NiFe layers leads to the single-phase hysteresis loops in the bilayer system.
The strength of coupling being dependent on the interface changes upon
alternating the order of magnetic layers. The magnetic parameters such as
coercivity HC, and anisotropy field HK become almost doubled when NiFe layer is
grown over the Fe layers. This enhancement in the magnetic parameters is
primarily dependent on the increase of the thickness and magnetic moment of
Fe-NiFe interfacial layer as revealed from the polarized neutron reectivity
(PNR) data of the bilayer samples. The difference in the thickness and
magnetization of the Fe-NiFe interfacial layer indicates the modification of
the microstructure by alternating the order of the magnetic layers of the
bilayers. The interfacial magnetic moment increased by almost 18 % when NiFe
layer is grown over the Fe layer. In spite of the different values of
anisotropy fields and modified interfacial exchange coupling, the Gilbert
damping constant values of the ferromagnetic bilayers remain similar to single
NiFe layer. | 2006.05756v1 |
2020-09-07 | Spin pumping in d-wave superconductor/ferromagnet hybrids | Spin-pumping across ferromagnet/superconductor (F/S) interfaces has attracted
much attention lately. Yet the focus has been mainly on s-wave
superconductors-based systems whereas (high-temperature) d-wave superconductors
such as YBa2Cu3O7-d (YBCO) have received scarce attention despite their
fundamental and technological interest. Here we use wideband ferromagnetic
resonance to study spin-pumping effects in bilayers that combine a soft
metallic Ni80Fe20 (Py) ferromagnet and YBCO. We evaluate the spin conductance
in YBCO by analyzing the magnetization dynamics in Py. We find that the Gilbert
damping exhibits a drastic drop as the heterostructures are cooled across the
normal-superconducting transition and then, depending on the S/F interface
morphology, either stays constant or shows a strong upturn. This unique
behavior is explained considering quasiparticle density of states at the YBCO
surface, and is a direct consequence of zero-gap nodes for particular
directions in the momentum space. Besides showing the fingerprint of d-wave
superconductivity in spin-pumping, our results demonstrate the potential of
high-temperature superconductors for fine tuning of the magnetization dynamics
in ferromagnets using k-space degrees of freedom of d-wave/F interfaces. | 2009.03196v3 |
2020-10-17 | Multiscale modelling of magnetostatic effects on magnetic nanoparticles with application to hyperthermia | We extend a renormalization group-based course-graining method for
micromagnetic simulations to include properly scaled magnetostatic
interactions. We apply the method in simulations of dynamic hysteresis loops at
clinically relevant sweep rates and at 310 K of iron oxide nanoparticles (NPs)
of the kind that have been used in preclinical studies of magnetic
hyperthermia. The coarse-graining method, along with a time scaling involving
sweep rate and Gilbert damping parameter, allow us to span length scales from
the unit cell to NPs approximately 50 nm in diameter with reasonable simulation
times. For both NPs and the nanorods composing them, we report effective
uniaxial anisotropy strengths and saturation magnetizations, which differ from
those of the bulk materials magnetite and maghemite of which they are made, on
account of the combined non-trivial effects of temperature, inter-rod exchange,
magnetostatic interactions and the degree of orientational order within the
nanorod composites. The effective parameters allow treating the NPs as single
macrospins, and we find for the test case of calculating loops for two aligned
NPs that using the dipole approximation is sufficient for distances beyond 1.5
times the NP diameter. We also present a study on relating integration time
step to micromagnetic cell size, finding that the optimal time step size scales
approximately linearly with cell volume. | 2010.08848v1 |
2021-02-09 | Unconventional quantum vortex matter state hosts quantum oscillations in the underdoped high-temperature cuprate superconductors | A central question in the underdoped cuprates pertains to the nature of the
pseudogap ground state. A conventional metallic ground state of the pseudogap
region has been argued to host quantum oscillations upon destruction of the
superconducting order parameter by modest magnetic fields. Here we use low
applied measurement currents and millikelvin temperatures on ultra-pure single
crystals of underdoped YBa$_2$Cu$_3$O$_{6+x}$ to unearth an unconventional
quantum vortex matter ground state characterized by vanishing electrical
resistivity, magnetic hysteresis, and non-ohmic electrical transport
characteristics beyond the highest laboratory accessible static fields. A new
model of the pseudogap ground state is now required to explain quantum
oscillations that are hosted by the bulk quantum vortex matter state without
experiencing sizeable additional damping in the presence of a large maximum
superconducting gap; possibilities include a pair density wave. | 2102.04927v2 |
2021-03-11 | Long-range spin transport on the surface of topological Dirac semimetal | We theoretically propose the long-range spin transport mediated by the
gapless surface states of topological Dirac semimetal (TDSM). Low-dissipation
spin current is a building block of next-generation spintronics devices. While
conduction electrons in metals and spin waves in ferromagnetic insulators
(FMIs) are the major carriers of spin current, their propagation length is
inevitably limited due to the Joule heating or the Gilbert damping. In order to
suppress dissipation and realize long-range spin transport, we here make use of
the spin-helical surface states of TDSMs, such as $\mathrm{Cd_3 As_2}$ and
$\mathrm{Na_3 Bi}$, which are robust against disorder. Based on a junction of
two FMIs connected by a TDSM, we demonstrate that the magnetization dynamics in
one FMI induces a spin current on the TDSM surface flowing to the other FMI. By
both the analytical transport theory on the surface and the numerical
simulation of real-time evolution in the bulk, we find that the induced spin
current takes a universal semi-quantized value that is insensitive to the
microscopic coupling structure between the FMI and the TDSM. We show that this
surface spin current is robust against disorder over a long range, which
indicates that the TDSM surface serves as a promising system for realizing
spintronics devices. | 2103.06519v1 |
2021-04-09 | Spin diffusion length associated to out-of-plane resistivity of Pt thin films in spin pumping experiments | We present a broadband ferromagnetic resonance study of the Gilbert damping
enhancement ($\Delta \alpha$) due to spin pumping in NiFe/Pt bilayers. The
bilayers, which have negligible interfacial spin memory loss, are studied as a
function of the Pt layer thickness ($t_{\text{Pt}}$) and temperature (100-293
K). Within the framework of diffusive spin pumping theory, we demonstrate that
Dyakonov-Perel (DP) or Elliot-Yaffet (EY) spin relaxation mechanisms acting
alone are incompatible with our observations. In contrast, if we consider that
the relation between spin relaxation characteristic time ($\tau_{\text{s}}$)
and momentum relaxation characteristic time ($\tau_{\text{p}}$) is determined
by a superposition of DP and EY mechanisms, the qualitative and quantitative
agreement with experimental results is excellent. Remarkably, we found that
$\tau_{\text{p}}$ must be determined by the out-of-plane electrical resistivity
($\rho$) of the Pt film and hence its spin diffusion length
($\lambda_{\text{Pt}}$) is independent of $t_{\text{Pt}}$. Our work settles the
controversy regarding the $t_{\text{Pt}}$ dependence of $\lambda_{\text{Pt}}$
by demonstrating its fundamental connection with $\rho$ considered along the
same direction of spin current flow. \end{abstract} | 2104.04426v1 |
2021-05-05 | Ni$_{80}$Fe$_{20}$ Nanotubes with Optimized Spintronic Functionalities Prepared by Atomic Layer Deposition | Permalloy Ni$_{80}$Fe$_{20}$ is one of the key magnetic materials in the
field of magnonics. Its potential would be further unveiled if it could be
deposited in three dimensional (3D) architectures of sizes down to the
nanometer. Atomic Layer Deposition, ALD, is the technique of choice for
covering arbitrary shapes with homogeneous thin films. Early successes with
ferromagnetic materials include nickel and cobalt. Still, challenges in
depositing ferromagnetic alloys reside in the synthesis via decomposing the
consituent elements at the same temperature and homogeneously. We report
plasma-enhanced ALD to prepare permalloy Ni$_{80}$Fe$_{20}$ thin films and
nanotubes using nickelocene and iron(III) tert-butoxide as metal precursors,
water as the oxidant agent and an in-cycle plasma enhanced reduction step with
hydrogen. We have optimized the ALD cycle in terms of Ni:Fe atomic ratio and
functional properties. We obtained a Gilbert damping of 0.013, a resistivity of
28 $\mu\Omega$cm and an anisotropic magnetoresistance effect of 5.6 $\%$ in the
planar thin film geometry. We demonstrate that the process also works for
covering GaAs nanowires, resulting in permalloy nanotubes with high aspect
ratios and diameters of about 150 nm. Individual nanotubes were investigated in
terms of crystal phase, composition and spin-dynamic response by microfocused
Brillouin Light Scattering. Our results enable NiFe-based 3D spintronics and
magnonic devices in curved and complex topology operated in the GHz frequency
regime. | 2105.01969v1 |
2021-06-23 | Spin dynamics of itinerant electrons: local magnetic moment formation and Berry phase | The state-of-the-art theoretical description of magnetic materials relies on
solving effective Heisenberg spin problems or their generalizations to
relativistic or multi-spin-interaction cases that explicitly assume the
presence of local magnetic moments in the system. We start with a general
interacting fermionic model that is often obtained in ab initio electronic
structure calculations and show that the corresponding spin problem can be
introduced even in the paramagnetic regime, which is characterized by a zero
average value of the magnetization. Further, we derive a physical criterion for
the formation of the local magnetic moment and confirm that the latter exists
already at high temperatures well above the transition to the ordered magnetic
state. The use of path-integral techniques allows us to disentangle spin and
electronic degrees of freedom and to carefully separate rotational dynamics of
the local magnetic moment from Higgs fluctuations of its absolute value. It
also allows us to accurately derive the topological Berry phase and relate it
to a physical bosonic variable that describes dynamics of the spin degrees of
freedom. As the result, we demonstrate that the equation of motion in the case
of a large magnetic moment takes a conventional Landau-Lifshitz form that
explicitly accounts for the Gilbert damping due to itinerant nature of the
original electronic model. | 2106.12462v3 |
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