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2021-02-20 | Fast magnetization reversal of a magnetic nanoparticle induced by cosine chirp microwave field pulse | We investigate the magnetization reversal of single-domain magnetic
nanoparticle driven by the circularly polarized cosine chirp microwave pulse
(CCMP). The numerical findings, based on the Landau-Lifshitz-Gilbert equation,
reveal that the CCMP is by itself capable of driving fast and energy-efficient
magnetization reversal. The microwave field amplitude and initial frequency
required by a CCMP are much smaller than that of the linear down-chirp
microwave pulse. This is achieved as the frequency change of the CCMP closely
matches the frequency change of the magnetization precession which leads to an
efficient stimulated microwave energy absorption (emission) by (from) the
magnetic particle before (after) it crosses over the energy barrier. We further
find that the enhancement of easy-plane shape anisotropy significantly reduces
the required microwave amplitude and the initial frequency of CCMP. We also
find that there is an optimal Gilbert damping for fast magnetization reversal.
These findings may provide a pathway to realize the fast and low-cost memory
device. | 2102.10394v2 |
2021-07-24 | Electron-Phonon Scattering governs both Ultrafast and Precessional Magnetization Dynamics in Co-Fe Alloys | Recent investigations have advanced the understanding of how
structure-property relationships in ferromagnetic metal alloys affect the
magnetization dynamics on nanosecond time-scales. A similar understanding for
magnetization dynamics on femto- to pico-second time-scales does not yet exist.
To address this, we perform time-resolved magneto optic Kerr effect (TRMOKE)
measurements of magnetization dynamics in Co-Fe alloys on femto- to nano-second
regimes. We show that Co-Fe compositions that exhibit low Gilbert damping
parameters also feature prolonged ultrafast demagnetization upon
photoexcitation. We analyze our experimental TR-MOKE data with the
three-temperature-model (3TM) and the Landau-Lifshitz-Gilbert equation. These
analyses reveal a strong compositional dependence of the dynamics across all
time-scales on the strength of electron-phonon interactions. Our findings are
beneficial to the spintronics and magnonics community, and will aid in the
quest for energy-efficient magnetic storage applications. | 2107.11699v1 |
2022-09-07 | Convergence analysis of an implicit finite difference method for the inertial Landau-Lifshitz-Gilbert equation | The Landau-Lifshitz-Gilbert (LLG) equation is a widely used model for fast
magnetization dynamics in ferromagnetic materials. Recently, the inertial LLG
equation, which contains an inertial term, has been proposed to capture the
ultra-fast magnetization dynamics at the sub-picosecond timescale.
Mathematically, this generalized model contains the first temporal derivative
and a newly introduced second temporal derivative of magnetization.
Consequently, it produces extra difficulties in numerical analysis due to the
mixed hyperbolic-parabolic type of this equation with degeneracy. In this work,
we propose an implicit finite difference scheme based on the central difference
in both time and space. A fixed point iteration method is applied to solve the
implicit nonlinear system. With the help of a second order accurate constructed
solution, we provide a convergence analysis in $H^1$ for this numerical scheme,
in the $\ell^\infty (0, T; H_h^1)$ norm. It is shown that the proposed method
is second order accurate in both time and space, with unconditional stability
and a natural preservation of the magnetization length. In the hyperbolic
regime, significant damping wave behaviors of magnetization at a shorter
timescale are observed through numerical simulations. | 2209.02914v2 |
2022-09-16 | Pseudo-PT symmetric Dirac equation : effect of a new mean spin angular momentum operator on Gilbert damping | The pseudo-PT symmetric Dirac equation is proposed and analyzed by using a
non-unitary Foldy-Wouthuysen transformations. A new spin operator PT symmetric
expectation value (called the mean spin operator) for an electron interacting
with a time-dependent electromagnetic field is obtained. We show that spin
magnetization - which is the quantity usually measured experimentally - is not
described by the standard spin operator but by this new mean spin operator to
properly describe magnetization dynamics in ferromagnetic materials and the
corresponding equation of motion is compatible with the phenomenological model
of the Landau-Lifshitz-Gilbert equation (LLG). | 2209.07908v1 |
2022-11-15 | Nonlinear sub-switching regime of magnetization dynamics in photo-magnetic garnets | We analyze, both experimentally and numerically, the nonlinear regime of the
photo-induced coherent magnetization dynamics in cobalt-doped yttrium iron
garnet films. Photo-magnetic excitation with femtosecond laser pulses reveals a
strongly nonlinear response of the spin subsystem with a significant increase
of the effective Gilbert damping. By varying both laser fluence and the
external magnetic field, we show that this nonlinearity originates in the
anharmonicity of the magnetic energy landscape. We numerically map the
parameter workspace for the nonlinear photo-induced spin dynamics below the
photo-magnetic switching threshold. Corroborated by numerical simulations of
the Landau-Lifshitz-Gilbert equation, our results highlight the key role of the
cubic symmetry of the magnetic subsystem in reaching the nonlinear spin
precession regime. These findings expand the fundamental understanding of
laser-induced nonlinear spin dynamics as well as facilitate the development of
applied photo-magnetism. | 2211.08048v2 |
2023-08-16 | Discovery and regulation of chiral magnetic solitons: Exact solution from Landau-Lifshitz-Gilbert equation | The Landau-Lifshitz-Gilbert (LLG) equation has emerged as a fundamental and
indispensable framework within the realm of magnetism. However, solving the LLG
equation, encompassing full nonlinearity amidst intricate complexities,
presents formidable challenges. In this context, we develop a precise mapping
through geometric representation, establishing a direct linkage between the LLG
equation and an integrable generalized nonlinear Schr\"odinger equation. This
novel mapping provides accessibility towards acquiring a great number of exact
spatiotemporal solutions. Notably, exact chiral magnetic solitons, critical for
stability and controllability in propagation with and without damping effects
are discovered. Our formulation provides exact solutions for the long-standing
fully nonlinear problem, facilitating practical control through spin current
injection in magnetic memory applications. | 2308.08331v1 |
2007-08-30 | Asymptotic improvement of the Gilbert-Varshamov bound for linear codes | The Gilbert-Varshamov bound states that the maximum size A_2(n,d) of a binary
code of length n and minimum distance d satisfies A_2(n,d) >= 2^n/V(n,d-1)
where V(n,d) stands for the volume of a Hamming ball of radius d. Recently
Jiang and Vardy showed that for binary non-linear codes this bound can be
improved to A_2(n,d) >= cn2^n/V(n,d-1) for c a constant and d/n <= 0.499. In
this paper we show that certain asymptotic families of linear binary [n,n/2]
random double circulant codes satisfy the same improved Gilbert-Varshamov
bound. | 0708.4164v1 |
2013-11-20 | Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Permutation Codes | Given positive integers $n$ and $d$, let $M(n,d)$ denote the maximum size of
a permutation code of length $n$ and minimum Hamming distance $d$. The
Gilbert-Varshamov bound asserts that $M(n,d) \geq n!/V(n,d-1)$ where $V(n,d)$
is the volume of a Hamming sphere of radius $d$ in $\S_n$.
Recently, Gao, Yang, and Ge showed that this bound can be improved by a
factor $\Omega(\log n)$, when $d$ is fixed and $n \to \infty$. Herein, we
consider the situation where the ratio $d/n$ is fixed and improve the
Gilbert-Varshamov bound by a factor that is \emph{linear in $n$}. That is, we
show that if $d/n < 0.5$, then $$ M(n,d)\geq cn\,\frac{n!}{V(n,d-1)} $$ where
$c$ is a positive constant that depends only on $d/n$. To establish this
result, we follow the method of Jiang and Vardy. Namely, we recast the problem
of bounding $M(n,d)$ into a graph-theoretic framework and prove that the
resulting graph is locally sparse. | 1311.4925v1 |
2002-12-05 | Dynamic stiffness of spin valves | The dynamics of the magnetic order parameters of
ferromagnet/normal-metal/ferromagnet spin valves and isolated ferromagnets may
be very different. We investigate the role of the nonequilibrium spin-current
exchange between the ferromagnets in the magnetization precession and
switching. We find a (low-temperature) critical current bias for a coherent
current-induced magnetization excitation in spin valves, which unifies and
generalizes previous ideas of Slonczewski and Berger. In the absence of an
applied bias, the effect of the spin transfer can be expressed as
magnetic--configuration-dependent Gilbert damping. | 0212130v2 |
2005-01-13 | Magnetization noise in magnetoelectronic nanostructures | By scattering theory we show that spin current noise in normal electric
conductors in contact with nanoscale ferromagnets increases the magnetization
noise by means of a fluctuating spin-transfer torque. Johnson-Nyquist noise in
the spin current is related to the increased Gilbert damping due to spin
pumping, in accordance with the fluctuation-dissipation theorem. Spin current
shot noise in the presence of an applied bias is the dominant contribution to
the magnetization noise at low temperatures. | 0501318v1 |
2006-05-08 | Microscopic Calculation of Spin Torques in Disordered Ferromagnets | Effects of conduction electrons on magnetization dynamics, represented by
spin torques, are calculated microscopically in the first order in spatial
gradient and time derivative of magnetization. Special attention is paid to the
so-called $\beta$-term and the Gilbert damping, $\alpha$, in the presence of
electrons' spin-relaxation processes, which are modeled by quenched magnetic
(and spin-orbit) impurities. The obtained results such as $\alpha \ne \beta$
hold for localized as well as itinerant ferromagnetism. | 0605186v1 |
2006-11-27 | Microscopic Calculation of Spin Torques and Forces | Spin torques, that is, effects of conduction electrons on magnetization
dynamics, are calculated microscopically in the first order in spatial gradient
and time derivative of magnetization. Special attention is paid to the
so-called \beta-term and the Gilbert damping, \alpha, in the presence of
electrons' spin-relaxation processes, which are modeled by quenched magnetic
impurities. Two types of forces that the electric/spin current exerts on
magnetization are identified based on a general formula relating the force to
the torque. | 0611669v1 |
2007-10-15 | Ferromagnetic resonance study of polycrystalline Fe_{1-x}V_x alloy thin films | Ferromagnetic resonance has been used to study the magnetic properties and
magnetization dynamics of polycrystalline Fe$_{1-x}$V$_{x}$ alloy films with
$0\leq x < 0.7$. Films were produced by co-sputtering from separate Fe and V
targets, leading to a composition gradient across a Si substrate. FMR studies
were conducted at room temperature with a broadband coplanar waveguide at
frequencies up to 50 GHz using the flip-chip method. The effective
demagnetization field $4 \pi M_{\mathrm{eff}}$ and the Gilbert damping
parameter $\alpha$ have been determined as a function of V concentration. The
results are compared to those of epitaxial FeV films. | 0710.2826v2 |
2008-10-25 | The domain wall spin torque-meter | We report the direct measurement of the non-adiabatic component of the
spin-torque in domain walls. Our method is independent of both the pinning of
the domain wall in the wire as well as of the Gilbert damping parameter. We
demonstrate that the ratio between the non-adiabatic and the adiabatic
components can be as high as 1, and explain this high value by the importance
of the spin-flip rate to the non-adiabatic torque. Besides their fundamental
significance these results open the way for applications by demonstrating a
significant increase of the spin torque efficiency. | 0810.4633v1 |
2008-12-03 | Observation of ferromagnetic resonance in strontium ruthenate (SrRuO3) | We report the observation of ferromagnetic resonance (FMR) in SrRuO3 using
the time-resolved magneto-optical Kerr effect. The FMR oscillations in the
time-domain appear in response to a sudden, optically induced change in the
direction of easy-axis anistropy. The high FMR frequency, 250 GHz, and large
Gilbert damping parameter, alpha ~ 1, are consistent with strong spin-orbit
coupling. We find that the parameters associated with the magnetization
dynamics, including alpha, have a non-monotonic temperature dependence,
suggestive of a link to the anomalous Hall effect. | 0812.0832v1 |
2011-02-26 | Dynamics of Skyrmion Crystals in Metallic Thin Films | We study the collective dynamics of the Skyrmion crystal (SkX) in thin films
of ferromagnetic metals resulting from the nontrivial Skyrmion topology. We
show that the current-driven motion of the crystal reduces the topological Hall
effect and the Skyrmion trajectories bend away from the direction of the
electric current (the Skyrmion Hall effect). We find a new dissipation
mechanism in non-collinear spin textures that can lead to a much faster spin
relaxation than Gilbert damping, calculate the dispersion of phonons in the
SkX, and discuss effects of impurity pinning of Skyrmions. | 1102.5384v2 |
2013-07-29 | Theoretical Study of Spin-Torque Oscillator with Perpendicularly Magnetized Free Layer | The magnetization dynamics of spin torque oscillator (STO) consisting of a
perpendicularly magnetized free layer and an in-plane magnetized pinned layer
was studied by solving the Landau-Lifshitz-Gilbert equation. We derived the
analytical formula of the relation between the current and the oscillation
frequency of the STO by analyzing the energy balance between the work done by
the spin torque and the energy dissipation due to the damping. We also found
that the field-like torque breaks the energy balance, and change the
oscillation frequency. | 1307.7427v1 |
2014-06-10 | Influence of Ta insertions on the magnetic properties of MgO/CoFeB/MgO films probed by ferromagnetic resonance | We show by vector network analyzer ferromagnetic resonance measurements that
low Gilbert damping {\alpha} down to 0.006 can be achieved in perpendicularly
magnetized MgO/CoFeB/MgO thin films with ultra-thin insertions of Ta in the
CoFeB layer. While increasing the number of Ta insertions allows thicker CoFeB
layers to remain perpendicular, the effective areal magnetic anisotropy does
not improve with more insertions, and also comes with an increase in {\alpha}. | 1406.2491v2 |
2014-09-24 | Dissipationless Multiferroic Magnonics | We propose that the magnetoelectric effect in multiferroic insulators with
coplanar antiferromagnetic spiral order, such as BiFeO$_{3}$, enables
electrically controlled dissipationless magnonics. Applying an oscillating
electric field in these materials with frequency as low as household frequency
can activate Goldstone modes that manifests fast planar rotations of spins,
whose motion is not obstructed by crystalline anisotropy. Combining with spin
ejection mechanisms, such a fast planar rotation can deliver electricity at
room temperature over a distance of the magnetic domain, which is free from the
energy loss due to Gilbert damping. | 1409.6900v2 |
2015-06-02 | Current-Driven Motion of Magnetic Domain Wall with Many Bloch Lines | The current-driven motion of a domain wall (DW) in a ferromagnet with many
Bloch lines (BLs) via the spin transfer torque is studied theoretically. It is
found that the motion of BLs changes the current-velocity ($j$-$v$)
characteristic dramatically. Especially, the critical current density to
overcome the pinning force is reduced by the factor of the Gilbert damping
coefficient $\alpha$ even compared with that of a skyrmion. This is in sharp
contrast to the case of magnetic field driven motion, where the existence of
BLs reduces the mobility of the DW. | 1506.00723v1 |
2016-01-23 | Nonlinear magnetization dynamics of antiferromagnetic spin resonance induced by intense terahertz magnetic field | We report on the nonlinear magnetization dynamics of a HoFeO3 crystal induced
by a strong terahertz magnetic field resonantly enhanced with a split ring
resonator and measured with magneto-optical Kerr effect microscopy. The
terahertz magnetic field induces a large change (~40%) in the spontaneous
magnetization. The frequency of the antiferromagnetic resonance decreases in
proportion to the square of the magnetization change. A modified
Landau-Lifshitz-Gilbert equation with a phenomenological nonlinear damping term
quantitatively reproduced the nonlinear dynamics. | 1601.06213v1 |
2017-08-11 | Gradient expansion formalism for generic spin torques | We propose a new quantum-mechanical formalism to calculate spin torques based
on the gradient expansion, which naturally involves spacetime gradients of the
magnetization and electromagnetic fields. We have no assumption in the
small-amplitude formalism or no difficulty in the SU($2$) gauge transformation
formalism. As a representative, we calculate the spin renormalization, Gilbert
damping, spin-transfer torque, and $\beta$-term in a three-dimensional
ferromagnetic metal with nonmagnetic and magnetic impurities being taken into
account within the self-consistent Born approximation. Our results serve as a
first-principles formalism for spin torques. | 1708.03424v1 |
2019-06-03 | Magnon-phonon interactions in magnetic insulators | We address the theory of magnon-phonon interactions and compute the
corresponding quasi-particle and transport lifetimes in magnetic insulators
with focus on yttrium iron garnet at intermediate temperatures from anisotropy-
and exchange-mediated magnon-phonon interactions, the latter being derived from
the volume dependence of the Curie temperature. We find in general weak effects
of phonon scattering on magnon transport and the Gilbert damping of the
macrospin Kittel mode. The magnon transport lifetime differs from the
quasi-particle lifetime at shorter wavelengths. | 1906.01042v1 |
2012-09-14 | Skyrmion Dynamics in Multiferroic Insulator | Recent discovery of Skyrmion crystal phase in insulating multiferroic
compound Cu$_2$OSeO$_3$ calls for new ways and ideas to manipulate the
Skyrmions in the absence of spin transfer torque from the conduction electrons.
It is shown here that the position-dependent electric field, pointed along the
direction of the average induced dipole moment of the Skyrmion, can induce the
Hall motion of Skyrmion with its velocity orthogonal to the field gradient.
Finite Gilbert damping produces longitudinal motion. We find a rich variety of
resonance modes excited by a.c. electric field. | 1209.3120v1 |
2019-09-17 | Microwave induced tunable subharmonic steps in superconductor-ferromagnet-superconductor Josephson junction | We investigate the coupling between ferromagnet and superconducting phase
dynamics in superconductor-ferromagnet-superconductor Josephson junction. The
current-voltage characteristics of the junction demonstrate a pattern of
subharmonic current steps which forms a devil's staircase structure. We show
that a width of the steps becomes maximal at ferromagnetic resonance. Moreover,
we demonstrate that the structure of the steps and their widths can be tuned by
changing the frequency of the external magnetic field, ratio of Josephson to
magnetic energy, Gilbert damping and the junction size. | 1909.08004v1 |
2019-09-19 | Magnetization dynamics of the compensated ferrimagnet $Mn_{2}Ru_{x}Ga$ | Here we study both static and time-resolved dynamic magnetic properties of
the compensated ferrimagnet from room temperature down to 10K, thus crossing
the magnetic compensation temperature $T_{M}$. The behaviour is analysed with a
model of a simple collinear ferrimagnet with uniaxial anisotropy and
site-specific gyromagnetic ratios. We find a maximum zero-applied-field
resonance frequency of $\sim$160GHz and a low intrinsic Gilbert damping
$\alpha$$\sim$0.02, making it a very attractive candidate for various
spintronic applications. | 1909.09085v1 |
2020-04-17 | Collective coordinate study of spin wave emission from dynamic domain wall | We study theoretically the spin wave emission from a moving domain wall in a
ferromagnet. Introducing a deformation mode describing a modulation of the wall
thickness in the collective coordinate description, we show that thickness
variation couples to the spin wave linearly and induces spin wave emission. The
dominant emitted spin wave turns out to be polarized in the out-of wall plane
($\phi$)-direction. The emission contributes to the Gilbert damping parameter
proportional to $\hbar\omega_\phi/K$, the ratio of the angular frequency
$\omega_\phi$ of $\phi$ and the easy-axis anisotropy energy $K$. | 2004.08082v1 |
2015-02-09 | Large amplitude oscillation of magnetization in spin-torque oscillator stabilized by field-like torque | Oscillation frequency of spin torque oscillator with a perpendicularly
magnetized free layer and an in-plane magnetized pinned layer is theoretically
investigated by taking into account the field-like torque. It is shown that the
field-like torque plays an important role in finding the balance between the
energy supplied by the spin torque and the dissipation due to the damping,
which results in a steady precession. The validity of the developed theory is
confirmed by performing numerical simulations based on the
Landau-Lifshitz-Gilbert equation. | 1502.02699v1 |
2019-11-28 | Transport properties of spin superfluids: comparing easy-plane ferro- and antiferromagnets | We present a study on spin-superfluid transport based on an atomistic,
classical spin model. Easy-plane ferro- as well as antiferromagnets are
considered, which allows for a direct comparison of these two material classes
based on the same model assumptions. We find a spin-superfluid transport which
is robust against variations of the boundary conditions, thermal fluctuations,
and dissipation modeled via Gilbert damping. Though the spin accumulations is
smaller for antiferromagnets the range of the spin-superfluid transport turns
out to be identical for ferro- and antiferromagnets. Finally, we calculate and
explore the role of the driving frequency and especially the critical
frequency, where phase slips occur and the spin accumulation breaks down. | 1911.12786v1 |
2021-03-10 | Anisotropic superconducting spin transport at magnetic interfaces | We present a theoretical investigation of anisotropic superconducting spin
transport at a magnetic interface between a p-wave superconductor and a
ferromagnetic insulator. Our formulation describes the ferromagnetic resonance
modulations due to spin current generation depending on spin-triplet Cooper
pair, including the frequency shift and enhanced Gilbert damping, in a unified
manner. We find that the Cooper pair symmetry is detectable from the
qualitative behavior of the ferromagnetic resonance modulation. Our theory
paves the way toward anisotropic superconducting spintronics. | 2103.05871v3 |
2022-01-16 | Ferromagnetic resonance modulation in $d$-wave superconductor/ferromagnetic insulator bilayer systems | We investigate ferromagnetic resonance (FMR) modulation in $d$-wave
superconductor (SC)/ferromagnetic insulator (FI) bilayer systems theoretically.
The modulation of the Gilbert damping in these systems reflects the existence
of nodes in the $d$-wave SC and shows power-law decay characteristics within
the low-temperature and low-frequency limit. Our results indicate the
effectiveness of use of spin pumping as a probe technique to determine the
symmetry of unconventional SCs with high sensitivity for nanoscale thin films. | 2201.06060v2 |
2022-09-28 | Unidirectional magnetic coupling | We show that interlayer Dzyaloshinskii-Moriya interaction in combination with
non-local Gilbert damping gives rise to unidirectional magnetic coupling. That
is, the coupling between two magnetic layers -- say the left and right layer --
is such that dynamics of the left layer leads to dynamics of the right layer,
but not vice versa. We discuss the implications of this result for the magnetic
susceptibility of a magnetic bilayer, electrically-actuated spin-current
transmission, and unidirectional spin-wave packet generation and propagation.
Our results may enable a route towards spin-current and spin-wave diodes and
further pave the way to design spintronic devices via reservoir engineering. | 2209.14179v1 |
2023-08-11 | Dynamical Majorana Ising spin response in a topological superconductor-magnet hybrid by microwave irradiation | We study a dynamical spin response of surface Majorana modes in a topological
superconductor-magnet hybrid under microwave irradiation. We find a method to
toggle between dissipative and non-dissipative Majorana Ising spin dynamics by
adjusting the external magnetic field angle and the microwave frequency. This
reflects the topological nature of the Majorana modes, enhancing the Gilbert
damping of the magnet, thereby, providing a detection method for the Majorana
Ising spins. Our findings illuminate a magnetic probe for Majorana modes,
paving the path to innovative spin devices. | 2308.05955v2 |
2007-05-14 | Identification of the dominant precession damping mechanism in Fe, Co, and Ni by first-principles calculations | The Landau-Lifshitz equation reliably describes magnetization dynamics using
a phenomenological treatment of damping. This paper presents first-principles
calculations of the damping parameters for Fe, Co, and Ni that quantitatively
agree with existing ferromagnetic resonance measurements. This agreement
establishes the dominant damping mechanism for these systems and takes a
significant step toward predicting and tailoring the damping constants of new
materials. | 0705.1990v1 |
2006-06-27 | Theoretical limit of the minimal magnetization switching field and the optimal field pulse for Stoner particles | The theoretical limit of the minimal magnetization switching field and the
optimal field pulse design for uniaxial Stoner particles are investigated. Two
results are obtained. One is the existence of a theoretical limit of the
smallest magnetic field out of all possible designs. It is shown that the limit
is proportional to the damping constant in the weak damping regime and
approaches the Stoner-Wohlfarth (SW) limit at large damping. For a realistic
damping constant, this limit is more than ten times smaller than that of
so-called precessional magnetization reversal under a non-collinear static
field. The other is on the optimal field pulse design: If the magnitude of a
magnetic field does not change, but its direction can vary during a reversal
process, there is an optimal design that gives the shortest switching time. The
switching time depends on the field magnitude, damping constant, and magnetic
anisotropy. However, the optimal pulse shape depends only on the damping
constant. | 0606681v1 |
2006-10-04 | On the dynamics of spin systems in the Landau-Lifshitz theory | In the framework of the Landau-Lifshitz equations without any dissipation (an
approximation which may also be helpful for finite but weak Gilbert damping),
with all interactions included, for general ground states, geometries and
domain structures, and many types of effective fields the dynamics of the spin
precession around this ground state is considered.
At first the precession is treated in the linear approximation. For the
eigenmodes of the precession one has a `rule of geometric mean' for the
eigenfrequencies. For the eigenmodes pseudo-orthogonality relations are
obtained, which reflect the gyrotropic and elliptic character of the spin
precession and differ from those known from the Schrodinger equation. Moreover,
pseudo-orthogonality relations are valid 'everywhere' (e.g., both in the outer
region and in the core region of a magnetic vortex).
Then also some aspects of the nonlinear mode coupling with emphasis on
`confluence' and `splitting' processes of elementary magnetic spin-wave
excitations are considered. At the same time these processes contribute to the
Gilbert damping.
There are thus essential differences to quantum mechanics, although at a
first glance one discovers many similarities. From the results one may also get
insights of why these systems are so complex that (although the essential
quantities depend only on the local values of the partially long-ranged
effective magnetic fields) practically only detailed experiments and computer
simulations make sense. | 0610122v4 |
2016-04-26 | First principles studies of the Gilbert damping and exchange interactions for half-metallic Heuslers alloys | Heusler alloys have been intensively studied due to the wide variety of
properties that they exhibit. One of these properties is of particular interest
for technological applications, i.e. the fact that some Heusler alloys are
half-metallic. In the following, a systematic study of the magnetic properties
of three different Heusler families $\textrm{Co}_2\textrm{Mn}\textrm{Z}$,
$\text{Co}_2\text{Fe}\text{Z}$ and $\textrm{Mn}_2\textrm{V}\textrm{Z}$ with
$\text{Z}=\left(\text{Al, Si, Ga, Ge}\right)$ is performed. A key aspect is the
determination of the Gilbert damping from first principles calculations, with
special focus on the role played by different approximations, the effect that
substitutional disorder and temperature effects. Heisenberg exchange
interactions and critical temperature for the alloys are also calculated as
well as magnon dispersion relations for representative systems, the
ferromagnetic $\textrm{Co}_2\textrm{Fe}\textrm{Si}$ and the ferrimagnetic
$\textrm{Mn}_2\textrm{V}\textrm{Al}$. Correlations effects beyond standard
density-functional theory are treated using both the local spin density
approximation including the Hubbard $U$ and the local spin density
approximation plus dynamical mean field theory approximation, which allows to
determine if dynamical self-energy corrections can remedy some of the
inconsistencies which were previously reported for these alloys. | 1604.07552v1 |
2019-10-29 | Perpendicular magnetic anisotropy in Pt/Co-based full Heusler alloy/MgO thin films structures | Perpendicular magnetic anisotropy (PMA) in ultrathin magnetic structures is a
key ingredient for the development of electrically controlled spintronic
devices. Due to their relatively large spin-polarization, high Curie
temperature and low Gilbert damping the Co-based full Heusler alloys are of
special importance from a scientific and applications point of view. Here, we
study the mechanisms responsible for the PMA in Pt/Co-based full Heusler
alloy/MgO thin films structures. We show that the ultrathin Heusler films
exhibit strong PMA even in the absence of magnetic annealing. By means of
ferromagnetic resonance experiments, we demonstrate that the effective
magnetization shows a two-regime behavior depending on the thickness of the
Heusler layers. Using Auger spectroscopy measurements, we evidence
interdiffusion at the underlayer/Heusler interface and the formation of an
interfacial CoFe-rich layer which causes the two-regime behavior. In the case
of the ultrathin films, the interfacial CoFe-rich layer promotes the strong PMA
through the electronic hybridization of the metal alloy and oxygen orbitals
across the ferromagnet/MgO interface. In addition, the interfacial CoFe-rich
layer it is also generating an increase of the Gilbert damping for the
ultrathin films beyond the spin-pumping effect. Our results illustrate that the
strong PMA is not an intrinsic property of the Heusler/MgO interface but it is
actively influenced by the interdiffusion, which can be tuned by a proper
choice of the underlayer material, as we show for the case of the Pt, Ta and Cr
underlayers. | 1910.13107v1 |
2016-12-21 | Spin Pumping, Dissipation, and Direct and Alternating Inverse Spin Hall Effects in Magnetic Insulator-Normal Metal Bilayers | We theoretically consider the spin-wave mode- and wavelength-dependent
enhancement of the Gilbert damping in magnetic insulator--normal metal bilayers
due to spin pumping as well as the enhancement's relation to direct and
alternating inverse spin Hall voltages in the normal metal. In the
long-wavelength limit, including long-range dipole interactions, the ratio of
the enhancement for transverse volume modes to that of the macrospin mode is
equal to two. With an out-of-plane magnetization, this ratio decreases with
both an increasing surface anisotropic energy and mode number. If the surface
anisotropy induces a surface state, the enhancement can be an order of
magnitude larger than for to the macrospin. With an in-plane magnetization, the
induced dissipation enhancement can be understood by mapping the anisotropy
parameter to the out-of-plane case with anisotropy. For shorter wavelengths, we
compute the enhancement numerically and find good agreement with the analytical
results in the applicable limits. We also compute the induced direct- and
alternating-current inverse spin Hall voltages and relate these to the magnetic
energy stored in the ferromagnet. Because the magnitude of the direct spin Hall
voltage is a measure of spin dissipation, it is directly proportional to the
enhancement of Gilbert damping. The alternating spin Hall voltage exhibits a
similar in-plane wave-number dependence, and we demonstrate that it is greatest
for surface-localized modes. | 1612.07020v2 |
2021-03-17 | Spin injection efficiency at metallic interfaces probed by THz emission spectroscopy | Terahertz (THz) spin-to-charge conversion has become an increasingly
important process for THz pulse generation and as a tool to probe ultrafast
spin interactions at magnetic interfaces. However, its relation to traditional,
steady state, ferromagnetic resonance techniques is poorly understood. Here we
investigate nanometric trilayers of Co/X/Pt (X=Ti, Au or Au0:85W0:15) as a
function of the 'X' layer thickness, where THz emission generated by the
inverse spin Hall effect is compared to the Gilbert damping of the
ferromagnetic resonance. Through the insertion of the 'X' layer we show that
the ultrafast spin current injected in the non-magnetic layer defines a direct
spin conductance, whereas the Gilbert damping leads to an effective spin
mixing-conductance of the trilayer. Importantly, we show that these two
parameters are connected to each other and that spin-memory losses can be
modeled via an effective Hamiltonian with Rashba fields. This work highlights
that magneto-circuits concepts can be successfully extended to ultrafast
spintronic devices, as well as enhancing the understanding of spin-to-charge
conversion processes through the complementarity between ultrafast THz
spectroscopy and steady state techniques. | 2103.09557v1 |
2022-06-06 | Probing spin dynamics of ultra-thin van der Waals magnets via photon-magnon coupling | Layered van der Waals (vdW) magnets can maintain a magnetic order even down
to the single-layer regime and hold promise for integrated spintronic devices.
While the magnetic ground state of vdW magnets was extensively studied, key
parameters of spin dynamics, like the Gilbert damping, crucial for designing
ultra-fast spintronic devices, remains largely unexplored. Despite recent
studies by optical excitation and detection, achieving spin wave control with
microwaves is highly desirable, as modern integrated information technologies
predominantly are operated with these. The intrinsically small numbers of
spins, however, poses a major challenge to this.
Here, we present a hybrid approach to detect spin dynamics mediated by
photon-magnon coupling between high-Q superconducting resonators and ultra-thin
flakes of Cr$_2$Ge$_2$Te$_6$ (CGT) as thin as 11\,nm. We test and benchmark our
technique with 23 individual CGT flakes and extract an upper limit for the
Gilbert damping parameter. These results are crucial in designing on-chip
integrated circuits using vdW magnets and offer prospects for probing spin
dynamics of monolayer vdW magnets. | 2206.02460v2 |
2023-03-13 | Experimental investigation of the effect of topological insulator on the magnetization dynamics of ferromagnetic metal: $BiSbTe_{1.5}Se_{1.5}$ and $Ni_{80}Fe_{20}$ heterostructure | We have studied ferromagnetic metal/topological insulator bilayer system to
understand magnetization dynamics of ferromagnetic metal (FM) in contact with a
topological insulator (TI). At magnetic resonance condition, the precessing
magnetization in the metallic ferromagnet ($Ni_{80}Fe_{20}$) injects spin
current into the topological insulator ($BiSbTe_{1.5}Se_{1.5}$), a phenomenon
known as spin-pumping. Due to the spin pumping effect, fast relaxation in the
ferromagnet results in the broadening of ferromagnetic resonance linewidth
($\Delta H$). We evaluated the parameters like effective Gilbert damping
coefficient ($\alpha_{eff}$), spin-mixing conductance ($g_{eff}^{\uparrow
\downarrow}$) and spin current density ($j_S^0$) to confirm a successful spin
injection due to spin-pumping into the $BiSbTe_{1.5}Se_{1.5}$ layer. TIs embody
a spin-momentum locked surface state that span the bulk band-gap. It can act
differently to the FM magnetization than the other normal metals. To probe the
effect of topological surface state, a systematic low temperature study is
crucial as surface state of TI dominates at lower temperatures. The exponential
growth of $\Delta H$ for all different thickness combination of FM/TI bilayers
and effective Gilbert damping coefficient ($\alpha_{eff}$) with lowering
temperature confirms the prediction that spin chemical bias generated from
spin-pumping induces surface current in TI due to spin-momentum locking. The
hump-like feature of magnetic anisotropy field ($H_K$)of the bilayer around 60K
suggests that the decrease of interfacial in-plane magnetic anisotropy can
result from exchange coupling between the TI surface state and the local
moments of FM layer. | 2303.07025v2 |
2022-02-10 | Non-stationary Anderson acceleration with optimized damping | Anderson acceleration (AA) has a long history of use and a strong recent
interest due to its potential ability to dramatically improve the linear
convergence of the fixed-point iteration. Most authors are simply using and
analyzing the stationary version of Anderson acceleration (sAA) with a constant
damping factor or without damping. Little attention has been paid to
nonstationary algorithms. However, damping can be useful and is sometimes
crucial for simulations in which the underlying fixed-point operator is not
globally contractive. The role of this damping factor has not been fully
understood. In the present work, we consider the non-stationary Anderson
acceleration algorithm with optimized damping (AAoptD) in each iteration to
further speed up linear and nonlinear iterations by applying one extra
inexpensive optimization. We analyze this procedure and develop an efficient
and inexpensive implementation scheme. We also show that, compared with the
stationary Anderson acceleration with fixed window size sAA(m), optimizing the
damping factors is related to dynamically packaging sAA(m) and sAA(1) in each
iteration (alternating window size $m$ is another direction of producing
non-stationary AA). Moreover, we show by extensive numerical experiments that
the proposed non-stationary Anderson acceleration with optimized damping
procedure often converges much faster than stationary AA with constant damping
or without damping. | 2202.05295v1 |
2012-08-01 | Artificial Neural Network Based Prediction of Optimal Pseudo-Damping and Meta-Damping in Oscillatory Fractional Order Dynamical Systems | This paper investigates typical behaviors like damped oscillations in
fractional order (FO) dynamical systems. Such response occurs due to the
presence of, what is conceived as, pseudo-damping and meta-damping in some
special class of FO systems. Here, approximation of such damped oscillation in
FO systems with the conventional notion of integer order damping and time
constant has been carried out using Genetic Algorithm (GA). Next, a multilayer
feed-forward Artificial Neural Network (ANN) has been trained using the GA
based results to predict the optimal pseudo and meta-damping from knowledge of
the maximum order or number of terms in the FO dynamical system. | 1208.0318v1 |
2021-02-01 | Global existence for semilinear wave equations with scaling invariant damping in 3-D | Global existence for small data Cauchy problem of semilinear wave equations
with scaling invariant damping in 3-D is established in this work, assuming
that the data are radial and the constant in front of the damping belongs to
$[1.5, 2)$. The proof is based on a weighted $L^2-L^2$ estimate for
inhomogeneous wave equation, which is established by interpolating between
energy estimate and Morawetz type estimate. | 2102.00909v1 |
2017-02-27 | Current Induced Damping of Nanosized Quantum Moments in the Presence of Spin-Orbit Interaction | Motivated by the need to understand current-induced magnetization dynamics at
the nanoscale, we have developed a formalism, within the framework of Keldysh
Green function approach, to study the current-induced dynamics of a
ferromagnetic (FM) nanoisland overlayer on a spin-orbit-coupling (SOC) Rashba
plane. In contrast to the commonly employed classical micromagnetic LLG
simulations the magnetic moments of the FM are treated {\it quantum
mechanically}. We obtain the density matrix of the whole system consisting of
conduction electrons entangled with the local magnetic moments and calculate
the effective damping rate of the FM. We investigate two opposite limiting
regimes of FM dynamics: (1) The precessional regime where the magnetic
anisotropy energy (MAE) and precessional frequency are smaller than the
exchange interactions, and (2) The local spin-flip regime where the MAE and
precessional frequency are comparable to the exchange interactions. In the
former case, we show that due to the finite size of the FM domain, the
\textquotedblleft Gilbert damping\textquotedblright does not diverge in the
ballistic electron transport regime, in sharp contrast to Kambersky's breathing
Fermi surface theory for damping in metallic FMs. In the latter case, we show
that above a critical bias the excited conduction electrons can switch the
local spin moments resulting in demagnetization and reversal of the
magnetization. Furthermore, our calculations show that the bias-induced
antidamping efficiency in the local spin-flip regime is much higher than that
in the rotational excitation regime. | 1702.08408v2 |
2018-12-18 | Thermal gradient driven domain wall dynamics | The issue of whether a thermal gradient acts like a magnetic field or an
electric current in the domain wall (DW) dynamics is investigated. Broadly
speaking, magnetization control knobs can be classified as energy-driving or
angular-momentum driving forces. DW propagation driven by a static magnetic
field is the best-known example of the former in which the DW speed is
proportional to the energy dissipation rate, and the current-driven DW motion
is an example of the latter. Here we show that DW propagation speed driven by a
thermal gradient can be fully explained as the angular momentum transfer
between thermally generated spin current and DW. We found DW-plane rotation
speed increases as DW width decreases. Both DW propagation speed along the wire
and DW-plane rotation speed around the wire decrease with the Gilbert damping.
These facts are consistent with the angular momentum transfer mechanism, but
are distinct from the energy dissipation mechanism. We further show that
magnonic spin-transfer torque (STT) generated by a thermal gradient has both
damping-like and field-like components. By analyzing DW propagation speed and
DW-plane rotation speed, the coefficient ( \b{eta}) of the field-like STT
arising from the non-adiabatic process, is obtained. It is found that \b{eta}
does not depend on the thermal gradient; increases with uniaxial anisotropy
K_(||) (thinner DW); and decreases with the damping, in agreement with the
physical picture that a larger damping or a thicker DW leads to a better
alignment between the spin-current polarization and the local magnetization, or
a better adiabaticity. | 1812.07244v2 |
2021-06-16 | Spin-Torque-driven Terahertz Auto Oscillations in Non-Collinear Coplanar Antiferromagnets | We theoretically and numerically study the terahertz auto oscillations in
thin-film metallic non-collinear coplanar antiferromagnets (AFMs), such as
$\mathrm{Mn_{3}Sn}$ and $\mathrm{Mn_{3}Ir}$, under the effect of anti-damping
spin-torque with spin polarization perpendicular to the plane of the film. To
obtain the order parameter dynamics in these AFMs, we solve three
Landau-Lifshitz-Gilbert equations coupled by exchange interactions assuming
both single- and multi-domain (micromagnetics) dynamical processes. In the
limit of strong exchange interaction, the oscillatory dynamics of the order
parameter in these AFMs, which have opposite chiralities, could be mapped to
that of a linear damped-driven pendulum in the case of $\mathrm{Mn_{3}Sn}$, and
a non-linear damped-driven pendulum in case of $\mathrm{Mn_{3}Ir}$. The
theoretical framework allows us to identify the input current requirements as a
function of the material and geometry parameters for exciting an oscillatory
response. We also obtain a closed-form approximate solution of the oscillation
frequency for large input currents in case of both $\mathrm{Mn_{3}Ir}$ and
$\mathrm{Mn_{3}Sn}$. Our analytical predictions of threshold current and
oscillation frequency agree well with the numerical results and thus can be
used as compact models to design and optimize the auto oscillator. Employing a
circuit model, based on the principle of tunnel anisotropy magnetoresistance,
we present detailed models of the output power and efficiency versus
oscillation frequency of the auto oscillator. Finally, we explore the spiking
dynamics of two unidirectional as well as bidirectional coupled AFM oscillators
using non-linear damped-driven pendulum equations. | 2106.08528v2 |
2023-01-30 | Investigation of Ultrafast Demagnetization and Gilbert Damping and their Correlation in Different Ferromagnetic Thin Films Grown Under Identical Conditions | Following the demonstration of laser-induced ultrafast demagnetization in
ferromagnetic nickel, several theoretical and phenomenological propositions
have sought to uncover its underlying physics. In this work we revisit the
three temperature model (3TM) and the microscopic three temperature model
(M3TM) to perform a comparative analysis of ultrafast demagnetization in
20-nm-thick cobalt, nickel and permalloy thin films measured using an
all-optical pump-probe technique. In addition to the ultrafast dynamics at the
femtosecond timescales, the nanosecond magnetization precession and damping are
recorded at various pump excitation fluences revealing a fluence-dependent
enhancement in both the demagnetization times and the damping factors. We
confirm that the Curie temperature to magnetic moment ratio of a given system
acts as a figure of merit for the demagnetization time, while the
demagnetization times and damping factors show an apparent sensitivity to the
density of states at the Fermi level for a given system. Further, from
numerical simulations of the ultrafast demagnetization based on both the 3TM
and the M3TM, we extract the reservoir coupling parameters that best reproduce
the experimental data and estimate the value of the spin flip scattering
probability for each system. We discuss how the fluence-dependence of
inter-reservoir coupling parameters so extracted may reflect a role played by
nonthermal electrons in the magnetization dynamics at low laser fluences. | 2301.12797v1 |
2005-10-30 | Domain instability during precessional magnetization reversal | Spin wave equations in the non-equilibrium precessing state of a
ferromagnetic system are found. They show a spin-wave instability towards
growing domains of stable magnetization. Precession of the uniform
magnetization mode is described by the Landau Lifshitz equation with the
exponentially growing in time effective Gilbert dissipation constant that could
have both signs. On the developed stages of the domain instability a
non-stationary picture of domain chaos is observed. | 0510817v1 |
2001-03-30 | Thermal magnetization fluctuations in thin films and a new physical form for magnetization damping | The effect of thermal fluctuations on a thin film magnetoresistive element
has been calculated. The technique involves adding to the basic spin dynamics a
general form of interaction with a thermal bath. For a general anisotropic
magnetic system the resulting equation can be written as a Langevin equation
for a harmonic oscillator. Our approach predicts two times smaller noise power
at low frequencies than the conventional stochastic Landau-Lifshitz-Gilbert
equation. It is shown that equivalent results can be obtained by introducing a
tensor phenomenological damping term to the gyromagnetic dynamics driven by a
thermal fluctuating field. | 0103624v3 |
2004-02-03 | First-principles study of magnetization relaxation enhancement and spin-transfer in thin magnetic films | The interface-induced magnetization damping of thin ferromagnetic films in
contact with normal-metal layers is calculated from first principles for clean
and disordered Fe/Au and Co/Cu interfaces. Interference effects arising from
coherent scattering turn out to be very small, consistent with a very small
magnetic coherence length. Because the mixing conductances which govern the
spin transfer are to a good approximation real valued, the spin pumping can be
described by an increased Gilbert damping factor but an unmodified gyromagnetic
ratio. The results also confirm that the spin-current induced magnetization
torque is an interface effect. | 0402088v2 |
2005-02-28 | Magnetization dynamics of two interacting spins in an external magnetic field | The longitudinal relaxation time of the magnetization of a system of two
exchange coupled spins subjected to a strong magnetic field is calculated
exactly by averaging the stochastic Gilbert-Landau-Lifshitz equation for the
magnetization, i.e., the Langevin equation of the process, over its
realizations so reducing the problem to a system of linear
differential-recurrence relations for the statistical moments (averaged
spherical harmonics). The system is solved in the frequency domain by matrix
continued fractions yielding the complete solution of the two-spin problem in
external fields for all values of the damping and barrier height parameters.
The magnetization relaxation time extracted from the exact solution is compared
with the inverse relaxation rate from Langer's theory of the decay of
metastable states, which yields in the high barrier and intermediate-to-high
damping limits the asymptotic behaviour of the greatest relaxation time. | 0502661v2 |
2007-06-28 | Coherent Magnetization Precession in GaMnAs induced by Ultrafast Optical Excitation | We use femtosecond optical pulses to induce, control and monitor
magnetization precession in ferromagnetic Ga0.965Mn0.035As. At temperatures
below ~40 K we observe coherent oscillations of the local Mn spins, triggered
by an ultrafast photoinduced reorientation of the in-plane easy axis. The
amplitude saturation of the oscillations above a certain pump intensity
indicates that the easy axis remains unchanged above ~TC/2. We find that the
observed magnetization precession damping (Gilbert damping) is strongly
dependent on pump laser intensity, but largely independent on ambient
temperature. We provide a physical interpretation of the observed light-induced
collective Mn-spin relaxation and precession. | 0706.4270v2 |
2008-02-14 | Light-induced magnetization precession in GaMnAs | We report dynamics of the transient polar Kerr rotation (KR) and of the
transient reflectivity induced by femtosecond laser pulses in ferromagnetic
(Ga,Mn)As with no external magnetic field applied. It is shown that the
measured KR signal consist of several different contributions, among which only
the oscillatory signal is directly connected with the ferromagnetic order in
(Ga,Mn)As. The origin of the light-induced magnetization precession is
discussed and the magnetization precession damping (Gilbert damping) is found
to be strongly influenced by annealing of the sample. | 0802.2043v2 |
2008-09-17 | Spin-transfer torque induced reversal in magnetic domains | Using the complex stereographic variable representation for the macrospin,
from a study of the nonlinear dynamics underlying the generalized
Landau-Lifshitz(LL) equation with Gilbert damping, we show that the
spin-transfer torque is effectively equivalent to an applied magnetic field. We
study the macrospin switching on a Stoner particle due to spin-transfer torque
on application of a spin polarized current. We find that the switching due to
spin-transfer torque is a more effective alternative to switching by an applied
external field in the presence of damping. We demonstrate numerically that a
spin-polarized current in the form of a short pulse can be effectively employed
to achieve the desired macro-spin switching. | 0809.2910v1 |
2009-12-30 | Spin torque and critical currents for magnetic vortex nano-oscillator in nanopillars | We calculated the main dynamic parameters of the spin polarized current
induced magnetic vortex oscillations in nanopillars, such as the range of
current density, where a vortex steady oscillations exist, the oscillation
frequency and orbit radius. We accounted for both the non-linear vortex
frequency and non-linear vortex damping. To describe the vortex excitations by
the spin polarized current we used a generalized Thiele approach to motion of
the vortex core as a collective coordinate. All the calculation results are
represented via the free layer sizes, saturation magnetization, Gilbert damping
and the degree of the spin polarization of the fixed layer. Predictions of the
developed model can be checked experimentally. | 0912.5521v1 |
2010-10-01 | Ferromagnetic resonance study of Co/Pd/Co/Ni multilayers with perpendicular anisotropy irradiated with Helium ions | We present a ferromagnetic resonance (FMR) study of the effect of Helium ion
irradiation on the magnetic anisotropy, the linewidth and the Gilbert damping
of a Co/Ni multilayer coupled to Co/Pd bilayers. The perpendicular magnetic
anisotropy decreases linearly with He ion fluence, leading to a transition to
in-plane magnetization at a critical fluence of 5x10^{14} ions/cm^2. We find
that the damping is nearly independent of fluence but the FMR linewidth at
fixed frequency has a maximum near the critical fluence, indicating that the
inhomogeneous broadening of the FMR line is a non-monotonic function of the He
ion fluence. Based on an analysis of the angular dependence of the FMR
linewidth, the inhomogeneous broadening is associated with spatial variations
in the magnitude of the perpendicular magnetic anisotropy. These results
demonstrate that ion irradiation may be used to systematically modify the
magnetic anisotropy and distribution of magnetic anisotropy parameters of
Co/Pd/Co/Ni multilayers for applications and basic physics studies. | 1010.0268v2 |
2010-11-23 | Ultra-fast magnetisation rates within the Landau-Lifshitz-Bloch model | The ultra-fast magnetisation relaxation rates during the laser-induced
magnetisation process are analyzed in terms of the Landau-Lifshitz-Bloch (LLB)
equation for different values of spin $S$. The LLB equation is equivalent in
the limit $S \rightarrow \infty$ to the atomistic Landau-Lifshitz-Gilbert (LLG)
Langevin dynamics and for $S=1/2$ to the M3TM model [B. Koopmans, {\em et al.}
Nature Mat. \textbf{9} (2010) 259]. Within the LLB model the ultra-fast
demagnetisation time ($\tau_{M}$) and the transverse damping ($\alpha_{\perp}$)
are parameterized by the intrinsic coupling-to-the-bath parameter $\lambda$,
defined by microscopic spin-flip rate. We show that for the phonon-mediated
Elliott-Yafet mechanism, $\lambda$ is proportional to the ratio between the
non-equilibrium phonon and electron temperatures.
We investigate the influence of the finite spin number and the scattering
rate parameter $\lambda$ on the magnetisation relaxation rates. The relation
between the fs demagnetisation rate and the LLG damping, provided by the LLB
theory, is checked basing on the available experimental data. A good agreement
is obtained for Ni, Co and Gd favoring the idea that the same intrinsic
scattering process is acting on the femtosecond and nanosecond timescale. | 1011.5054v1 |
2011-10-15 | Atomistic spin dynamic method with both damping and moment of inertia effects included from first principles | We consider spin dynamics for implementation in an atomistic framework and we
address the feasibility of capturing processes in the femtosecond regime by
inclusion of moment of inertia. In the spirit of an {\it s-d} -like interaction
between the magnetization and electron spin, we derive a generalized equation
of motion for the magnetization dynamics in the semi-classical limit, which is
non-local in both space and time. Using this result we retain a generalized
Landau-Lifshitz-Gilbert equation, also including the moment of inertia, and
demonstrate how the exchange interaction, damping, and moment of inertia, all
can be calculated from first principles. | 1110.3387v2 |
2011-10-24 | CoB/Ni-Based Multilayer Nanowire with High-Speed Domain Wall Motion under Low Current Control | The spin-transfer torque motion of magnetic domain walls (DWs) in a
CoB/Ni-based nanowire driven by a low current density of
(1.12\pm0.8)\times10^{11} A m^{-2} has been observed indirectly by
magnetotransport measurements. A high DW velocity of 85\pm4 m/s at zero field
was measured at the threshold current density. Upon increasing the current
density to 2.6\times10^{11} A m^{-2}, the DW velocity increases to 197\pm16 m/s
before decreasing quickly in the high-current-density regime attributed to
nonadiabatic spin-transfer torque at a low damping factor and weak pinning. The
addition of B atoms to the Co layers decreased the magnitude of saturation
magnetization, Gilbert damping factor, and density of pinning sites, making the
CoB/Ni multilayer nanowire favorable for practical applications. | 1110.5112v3 |
2013-07-10 | Scaling of spin Hall angle in 3d, 4d and 5d metals from Y3Fe5O12/metal spin pumping | Pure spin currents generated by spin pumping in ferromagnet/nonmagnet (FM/NM)
bilayers produce inverse spin Hall effect (ISHE) voltages in the NM, from which
spin pumping and transport characteristics of the NM can be extracted. Due to
its exceptionally low damping, Y3Fe5O12 (YIG) is an important and widely used
FM for microwave devices and ferromagnetic resonance (FMR) spin pumping. Here
we report systematic investigation of spin pumping from 20-nm thick YIG thin
films to a series of 3d, 4d and 5d normal metals (Cu, Ag, Ta, W, Pt and Au)
with various spin-orbit coupling strengths. From enhanced Gilbert damping
obtained from the frequency dependence of FMR linewidths and ISHE signals, the
spin Hall angles and YIG/NM interfacial spin mixing conductances are
quantitatively determined for these metals. The spin Hall angles largely vary
as the fourth power of the atomic number, corroborating the dominant role of
spin-orbit coupling across a broad range in the inverse spin Hall effect. | 1307.2648v2 |
2016-04-16 | A broadband Ferromagnetic Resonance dipper probe for magnetic damping measurements from 4.2 K to 300 K | A dipper probe for broadband Ferromagnetic Resonance (FMR) operating from 4.2
K to room temperature is described. The apparatus is based on a 2-port
transmitted microwave signal measurement with a grounded coplanar waveguide.
The waveguide generates a microwave field and records the sample response. A
3-stage dipper design is adopted for fast and stable temperature control. The
temperature variation due to FMR is in the milli-Kelvin range at liquid helium
temperature. We also designed a novel FMR probe head with a spring-loaded
sample holder. Improved signal-to-noise ratio and stability compared to a
common FMR head are achieved. Using a superconducting vector magnet we
demonstrate Gilbert damping measurements on two thin film samples using a
vector network analyzer with frequency up to 26 GHz: 1) A Permalloy film of 5
nm thickness and 2) a CoFeB film of 1.5 nm thickness. Experiments were
performed with the applied magnetic field parallel and perpendicular to the
film plane. | 1604.04688v1 |
2016-05-27 | A reduced model for precessional switching of thin-film nanomagnets under the influence of spin-torque | We study the magnetization dynamics of thin-film magnetic elements with
in-plane magnetization subject to a spin-current flowing perpendicular to the
film plane. We derive a reduced partial differential equation for the in-plane
magnetization angle in a weakly damped regime. We then apply this model to
study the experimentally relevant problem of switching of an elliptical element
when the spin-polarization has a component perpendicular to the film plane,
restricting the reduced model to a macrospin approximation. The macrospin
ordinary differential equation is treated analytically as a weakly damped
Hamiltonian system, and an orbit-averaging method is used to understand
transitions in solution behaviors in terms of a discrete dynamical system. The
predictions of our reduced model are compared to those of the full
Landau--Lifshitz--Gilbert--Slonczewski equation for a macrospin. | 1605.08698v1 |
2016-07-05 | Magnetic moment of inertia within the breathing model | An essential property of magnetic devices is the relaxation rate in magnetic
switching which strongly depends on the energy dissipation and magnetic inertia
of the magnetization dynamics. Both parameters are commonly taken as a
phenomenological entities. However very recently, a large effort has been
dedicated to obtain Gilbert damping from first principles. In contrast, there
is no ab initio study that so far has reproduced measured data of magnetic
inertia in magnetic materials. In this letter, we present and elaborate on a
theoretical model for calculating the magnetic moment of inertia based on the
torque-torque correlation model. Particularly, the method has been applied to
bulk bcc Fe, fcc Co and fcc Ni in the framework of the tight-binding
approximation and the numerical values are comparable with recent experimental
measurements. The theoretical results elucidate the physical origin of the
moment of inertia based on the electronic structure. Even though the moment of
inertia and damping are produced by the spin-orbit coupling, our analysis shows
that they are caused by undergo different electronic structure mechanisms. | 1607.01307v1 |
2016-10-14 | Nambu mechanics for stochastic magnetization dynamics | The Landau-Lifshitz-Gilbert (LLG) equation describes the dynamics of a damped
magnetization vector that can be understood as a generalization of Larmor spin
precession. The LLG equation cannot be deduced from the Hamiltonian framework,
by introducing a coupling to a usual bath, but requires the introduction of
additional constraints. It is shown that these constraints can be formulated
elegantly and consistently in the framework of dissipative Nambu mechanics.
This has many consequences for both the variational principle and for
topological aspects of hidden symmetries that control conserved quantities. We
particularly study how the damping terms of dissipative Nambu mechanics affect
the consistent interaction of magnetic systems with stochastic reservoirs and
derive a master equation for the magnetization. The proposals are supported by
numerical studies using symplectic integrators that preserve the topological
structure of Nambu equations. These results are compared to computations
performed by direct sampling of the stochastic equations and by using closure
assumptions for the moment equations, deduced from the master equation. | 1610.04598v2 |
2017-01-31 | Lack of correlation between the spin mixing conductance and the ISHE-generated voltages in CoFeB/Pt,Ta bilayers | We investigate spin pumping phenomena in polycrystalline CoFeB/Pt and
CoFeB/Ta bilayers and the correlation between the effective spin mixing
conductance $g^{\uparrow\downarrow}_{\rm eff}$ and the obtained voltages
generated by the spin-to-charge current conversion via the inverse spin Hall
effect in the Pt and Ta layers. For this purpose we measure the in-plane
angular dependence of the generated voltages on the external static magnetic
field and we apply a model to separate the spin pumping signal from the one
generated by the spin rectification effect in the magnetic layer. Our results
reveal a dominating role of anomalous Hall effect for the spin rectification
effect with CoFeB and a lack of correlation between
$g^{\uparrow\downarrow}_{\rm eff}$ and inverse spin Hall voltages pointing to a
strong role of the magnetic proximity effect in Pt in understanding the
observed increased damping. This is additionally reflected on the presence of a
linear dependency of the Gilbert damping parameter on the Pt thickness. | 1701.09110v1 |
2018-06-02 | Ultra-low damping insulating magnetic thin films get perpendicular | A magnetic material combining low losses and large Perpendicular Magnetic
Anisotropy (PMA) is still a missing brick in the magnonic and spintronic
fields. We report here on the growth of ultrathin Bismuth doped
Y$_{3}$Fe$_{5}$O$_{12}$ (BiYIG) films on Gd$_{3}$Ga$_{5}$O$_{12}$ (GGG) and
substituted GGG (sGGG) (111) oriented substrates. A fine tuning of the PMA is
obtained using both epitaxial strain and growth induced anisotropies. Both
spontaneously in-plane and out-of-plane magnetized thin films can be
elaborated. Ferromagnetic Resonance (FMR) measurements demonstrate the high
dynamic quality of these BiYIG ultrathin films, PMA films with Gilbert damping
values as low as 3 10$^{-4}$ and FMR linewidth of 0.3 mT at 8 GHz are achieved
even for films that do not exceed 30 nm in thickness. Moreover, we measure
Inverse Spin Hall Effect (ISHE) on Pt/BiYIG stacks showing that the magnetic
insulator$'$s surface is transparent to spin current making it appealing for
spintronic applications. | 1806.00658v1 |
2018-06-12 | Dynamical and current-induced Dzyaloshinskii-Moriya interaction: Role for damping, gyromagnetism, and current-induced torques in noncollinear magnets | Both applied electric currents and magnetization dynamics modify the
Dzyaloshinskii-Moriya interaction (DMI), which we call current-induced DMI
(CIDMI) and dynamical DMI (DDMI), respectively. We report a theory of CIDMI and
DDMI. The inverse of CIDMI consists in charge pumping by a time-dependent
gradient of magnetization $\partial^2 M(r,t)/\partial r\partial t$, while the
inverse of DDMI describes the torque generated by $\partial^2 M(r,t)/\partial
r\partial t$. In noncollinear magnets CIDMI and DDMI depend on the local
magnetization direction. The resulting spatial gradients correspond to torques
that need to be included into the theories of Gilbert damping, gyromagnetism,
and current-induced torques (CITs) in order to satisfy the Onsager reciprocity
relations. CIDMI is related to the modification of orbital magnetism induced by
magnetization dynamics, which we call dynamical orbital magnetism (DOM), and
spatial gradients of DOM contribute to charge pumping. We present applications
of this formalism to the CITs and to the torque-torque correlation in textured
Rashba ferromagnets. | 1806.04782v3 |
2018-03-04 | Optimization of Time-Resolved Magneto-optical Kerr Effect Signals for Magnetization Dynamics Measurements | Recently magnetic storage and magnetic memory have shifted towards the use of
magnetic thin films with perpendicular magnetic anisotropy (PMA). Understanding
the magnetic damping in these materials is crucial, but normal Ferromagnetic
Resonance (FMR) measurements face some limitations. The desire to quantify the
damping in materials with PMA has resulted in the adoption of Time-Resolved
Magneto-optical Kerr Effect (TR-MOKE) measurements. In this paper, we discuss
the angle and field dependent signals in TR-MOKE, and utilize a numerical
algorithm based on the Landau-Lifshitz-Gilbert (LLG) equation to provide
information on the optimal conditions to run TR-MOKE measurements. | 1803.01280v2 |
2012-09-17 | Nonlinear emission of spin-wave caustics from an edge mode of a micro-structured Co2Mn0.6Fe0.4Si waveguide | Magnetic Heusler materials with very low Gilbert damping are expected to show
novel magnonic transport phenomena. We report nonlinear generation of higher
harmonics leading to the emission of caustic spin-wave beams in a low-damping,
micro-structured Co2Mn0.6Fe0.4Si Heusler waveguide. The source for the higher
harmonic generation is a localized edge mode formed by the strongly
inhomogeneous field distribution at the edges of the spin-wave waveguide. The
radiation characteristics of the propagating caustic waves observed at twice
and three times the excitation frequency are described by an analytical
calculation based on the anisotropic dispersion of spin waves in a magnetic
thin film. | 1209.3669v2 |
2019-09-10 | Spin Pumping from Permalloy into Uncompensated Antiferromagnetic Co doped Zinc Oxide | Heterostructures of Co-doped ZnO and Permalloy were investigated for their
static and dynamic magnetic interaction. The highly Co-doped ZnO is
paramagentic at room temperature and becomes an uncompensated antiferromagnet
at low temperatures, showing a narrowly opened hysteresis and a vertical
exchange bias shift even in the absence of any ferromagnetic layer. At low
temperatures in combination with Permalloy an exchange bias is found causing a
horizontal as well as vertical shift of the hysteresis of the heterostructure
together with an increase in coercive field. Furthermore, an increase in the
Gilbert damping parameter at room temperature was found by multifrequency FMR
evidencing spin pumping. Temperature dependent FMR shows a maximum in magnetic
damping close to the magnetic phase transition. These measurements also
evidence the exchange bias interaction of Permalloy and long-range ordered
Co-O-Co structures in ZnO, that are barely detectable by SQUID due to the
shorter probing times in FMR. | 1909.04362v3 |
2021-05-16 | Anatomy of inertial magnons in ferromagnets | We analyze dispersion relations of magnons in ferromagnetic nanostructures
with uniaxial anisotropy taking into account inertial terms, i.e. magnetic
nutation. Inertial effects are parametrized by damping-independent parameter
$\beta$, which allows for an unambiguous discrimination of inertial effects
from Gilbert damping parameter $\alpha$. The analysis of magnon dispersion
relation shows its two branches are modified by the inertial effect, albeit in
different ways. The upper nutation branch starts at $\omega=1/ \beta$, the
lower branch coincides with FMR in the long-wavelength limit and deviates from
the zero-inertia parabolic dependence $\simeq\omega_{FMR}+Dk^2$ of the exchange
magnon. Taking a realistic experimental geometry of magnetic thin films,
nanowires and nanodiscs, magnon eigenfrequencies, eigenvectors and $Q$-factors
are found to depend on the shape anisotropy. The possibility of phase-matched
magneto-elastic excitation of nutation magnons is discussed and the condition
was found to depend on $\beta$, exchange stiffness $D$ and the acoustic
velocity. | 2105.07376v1 |
2013-11-25 | Spin-wave excitation and propagation in microstructured waveguides of yttrium iron garnet (YIG)/Pt bilayers | We present an experimental study of spin-wave excitation and propagation in
microstructured waveguides patterned from a 100 nm thick yttrium iron garnet
(YIG)/platinum (Pt) bilayer. The life time of the spin waves is found to be
more than an order of magnitude higher than in comparably sized metallic
structures despite the fact that the Pt capping enhances the Gilbert damping.
Utilizing microfocus Brillouin light scattering spectroscopy, we reveal the
spin-wave mode structure for different excitation frequencies. An exponential
spin-wave amplitude decay length of 31 {\mu}m is observed which is a
significant step towards low damping, insulator based micro-magnonics. | 1311.6305v1 |
2016-06-21 | Torsion Effects and LLG Equation | Based on the non-relativistic regime of the Dirac equation coupled to a
torsion pseudo-vector, we study the dynamics of magnetization and how it is
affected by the presence of torsion. We consider that torsion interacting terms
in Dirac equation appear in two ways one of these is thhrough the covariant
derivative considering the spin connection and gauge magnetic field and the
other is through a non-minimal spin torsion coupling. We show within this
framework, that it is possible to obtain the most general Landau, Lifshitz and
Gilbert (LLG) equation including the torsion effects, where we refer to torsion
as a geometric field playing an important role in the spin coupling process. We
show that the torsion terms can give us two important landscapes in the
magnetization dynamics: one of them related with damping and the other related
with the screw dislocation that give us a global effect like a helix damping
sharped. These terms are responsible for changes in the magnetization
precession dynamics. | 1606.06610v1 |
2018-05-04 | Superparamagnetic Relaxation Driven by Colored Noise | A theoretical investigation of magnetic relaxation processes in single domain
particles driven by colored noise is presented. Two approaches are considered;
the Landau-Lifshitz-Miyazaki-Seki equation, which is a Langevin dynamics model
based on the introduction of an Ornstein-Uhlenbeck correlated noise into the
Landau-Lifshitz-Gilbert equation and a Generalized Master Equation approach
whereby the ordinary Master Equation is modified through the introduction of an
explicit memory kernel. It is found that colored noise is likely to become
important for high anisotropy materials where the characteristic system time,
in this case the inverse Larmor precession frequency, becomes comparable to the
correlation time. When the escape time is much longer than the correlation
time, the relaxation profile of the spin has a similar exponential form to the
ordinary LLG equation, while for low barrier heights and intermediate damping,
for which the correlation time is a sizable fraction of the escape time, an
unusual bi-exponential decay is predicted as a characteristic of colored noise.
At very high damping and correlation times, the time profile of the spins
exhibits a more complicated, noisy trajectory. | 1805.01776v2 |
2020-02-27 | Ultrafast magnetization dynamics in half-metallic Co$_2$FeAl Heusler alloy | We report on optically induced, ultrafast magnetization dynamics in the
Heusler alloy $\mathrm{Co_{2}FeAl}$, probed by time-resolved magneto-optical
Kerr effect. Experimental results are compared to results from electronic
structure theory and atomistic spin-dynamics simulations. Experimentally, we
find that the demagnetization time ($\tau_{M}$) in films of
$\mathrm{Co_{2}FeAl}$ is almost independent of varying structural order, and
that it is similar to that in elemental 3d ferromagnets. In contrast, the
slower process of magnetization recovery, specified by $\tau_{R}$, is found to
occur on picosecond time scales, and is demonstrated to correlate strongly with
the Gilbert damping parameter ($\alpha$). Our results show that
$\mathrm{Co_{2}FeAl}$ is unique, in that it is the first material that clearly
demonstrates the importance of the damping parameter in the remagnetization
process. Based on these results we argue that for $\mathrm{Co_{2}FeAl}$ the
remagnetization process is dominated by magnon dynamics, something which might
have general applicability. | 2002.12255v1 |
2020-06-05 | Controlling the nonlinear relaxation of quantized propagating magnons in nanodevices | Relaxation of linear magnetization dynamics is well described by the viscous
Gilbert damping processes. However, for strong excitations, nonlinear damping
processes such as the decay via magnon-magnon interactions emerge and trigger
additional relaxation channels. Here, we use space- and time-resolved
microfocused Brillouin light scattering spectroscopy and micromagnetic
simulations to investigate the nonlinear relaxation of strongly driven
propagating spin waves in yttrium iron garnet nanoconduits. We show that the
nonlinear magnon relaxation in this highly quantized system possesses
intermodal features, i.e., magnons scatter to higher-order quantized modes
through a cascade of scattering events. We further show how to control such
intermodal dissipation processes by quantization of the magnon band in
single-mode devices, where this phenomenon approaches its fundamental limit.
Our study extends the knowledge about nonlinear propagating spin waves in
nanostructures which is essential for the construction of advanced spin-wave
elements as well as the realization of Bose-Einstein condensates in scaled
systems. | 2006.03400v2 |
2022-10-01 | Nonlinear features of the superconductor--ferromagnet--superconductor $\varphi_0$ Josephson junction in ferromagnetic resonance region | We demonstrate the manifestations of the nonlinear features in magnetic
dynamics and IV-characteristics of the $\varphi_0$ Josephson junction in the
ferromagnetic resonance region. We show that at small values of system
parameters, namely, damping, spin-orbit interaction, and Josephson to magnetic
energy ratio, the magnetic dynamics is reduced to the dynamics of the scalar
Duffing oscillator, driven by the Josephson oscillations. The role of
increasing superconducting current in the resonance region is clarified.
Shifting of the ferromagnetic resonant frequency and the reversal of its
damping dependence due to nonlinearity are demonstrated by the full
Landau-Lifshitz-Gilbert-Josephson system of equations, and in its different
approximations. Finally, we demonstrate the negative differential resistance in
the IV--characteristics, and its correlation with the foldover effect. | 2210.00366v1 |
2023-12-16 | Spin-torque nano-oscillator based on two in-plane magnetized synthetic ferrimagnets | We report the dynamic characterization of the spin-torque-driven in-plane
precession modes of a spin-torque nano-oscillator based on two different
synthetic ferrimagnets: a pinned one characterized by a strong RKKY interaction
which is exchange coupled to an antiferromagnetic layer; and a second one,
non-pinned characterized by weak RKKY coupling. The microwave properties
associated with the steady-state precession of both SyFs are characterized by
high spectral purity and power spectral density. However, frequency dispersion
diagrams of the damped and spin transfer torque modes reveal drastically
different dynamical behavior and microwave emission properties in both SyFs. In
particular, the weak coupling between the magnetic layers of the non-pinned SyF
raises discontinuous dispersion diagrams suggesting a strong influence of mode
crossing. An interpretation of the different dynamical features observed in the
damped and spin torque modes of both SyF systems was obtained by solving
simultaneously, in a macrospin approach, a linearized version of the
Landau-Lifshitz-Gilbert equation including the spin transfer torque term. | 2312.10451v2 |
1997-07-23 | Riccati parameter modes from Newtonian free damping motion by supersymmetry | We determine the class of damped modes \tilde{y} which are related to the
common free damping modes y by supersymmetry. They are obtained by employing
the factorization of Newton's differential equation of motion for the free
damped oscillator by means of the general solution of the corresponding Riccati
equation together with Witten's method of constructing the supersymmetric
partner operator. This procedure leads to one-parameter families of (transient)
modes for each of the three types of free damping, corresponding to a
particular type of %time-dependent angular frequency. %time-dependent,
antirestoring acceleration (adding up to the usual Hooke restoring
acceleration) of the form a(t)=\frac{2\gamma ^2}{(\gamma t+1)^{2}}\tilde{y},
where \gamma is the family parameter that has been chosen as the inverse of the
Riccati integration constant. In supersymmetric terms, they represent all those
one Riccati parameter damping modes having the same Newtonian free damping
partner mode | 9707019v4 |
2018-03-29 | Giant resonant nonlinear damping in nanoscale ferromagnets | Magnetic damping is a key metric for emerging technologies based on magnetic
nanoparticles, such as spin torque memory and high-resolution biomagnetic
imaging. Despite its importance, understanding of magnetic dissipation in
nanoscale ferromagnets remains elusive, and the damping is often treated as a
phenomenological constant. Here we report the discovery of a giant
frequency-dependent nonlinear damping that strongly alters the response of a
nanoscale ferromagnet to spin torque and microwave magnetic field. This novel
damping mechanism originates from three-magnon scattering that is strongly
enhanced by geometric confinement of magnons in the nanomagnet. We show that
the giant nonlinear damping can invert the effect of spin torque on a
nanomagnet leading to a surprising current-induced enhancement of damping by an
antidamping torque. Our work advances understanding of magnetic dynamics in
nanoscale ferromagnets and spin torque devices. | 1803.10925v1 |
2014-01-15 | Damping of Terahertz Plasmons in Graphene Coupled with Surface Plasmons in Heavily-Doped Substrate | Coupling of plasmons in graphene at terahert (THz) frequencies with surface
plasmons in a heavily-doped substrate is studied theoretically. We reveal that
a huge scattering rate may completely damp out the plasmons, so that proper
choices of material and geometrical parameters are essential to suppress the
coupling effect and to obtain the minimum damping rate in graphene. Even with
the doping concentration 10^{19} - 10^{20} cm^{-3} and the thickness of the
dielectric layer between graphene and the substrate 100 nm, which are typical
values in real graphene samples with a heavily-doped substrate, the increase in
the damping rate is not negligible in comparison with the
acoustic-phonon-limited damping rate. Dependence of the damping rate on
wavenumber, thicknesses of graphene-to-substrate and gate-to-graphene
separation, substrate doping concentration, and dielectric constants of
surrounding materials are investigated. It is shown that the damping rate can
be much reduced by the gate screening, which suppresses the field spread of the
graphene plasmons into the substrate. | 1401.3396v1 |
2003-09-09 | Traveling solitons in the damped driven nonlinear Schrödinger equation | The well known effect of the linear damping on the moving nonlinear
Schr\"odinger soliton (even when there is a supply of energy via the spatially
homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero
momentum does not necessarily mean zero velocity. We show that two or more
parametrically driven damped solitons can form a complex traveling with zero
momentum at a nonzero constant speed.
All traveling complexes we have found so far, turned out to be unstable.
Thus, the parametric driving is capable of sustaining the uniform motion of
damped solitons, but some additional agent is required to stabilize it. | 0309031v1 |
2007-08-28 | Linear frictional forces cause orbits to neither circularize nor precess | For the undamped Kepler potential the lack of precession has historically
been understood in terms of the Runge-Lenz symmetry. For the damped Kepler
problem this result may be understood in terms of the generalization of Poisson
structure to damped systems suggested recently by Tarasov[1]. In this
generalized algebraic structure the orbit-averaged Runge-Lenz vector remains a
constant in the linearly damped Kepler problem to leading order in the damping
coe | 0708.3827v3 |
2008-12-11 | Frequency-dependent Drude damping in Casimir force calculations | The Casimir force is calculated between Au thin films that are described by a
Drude model with a frequency dependent damping function. The model parameters
are obtained from available experimental data for Au thin films. Two cases are
considered; annealed and nonannealed films that have a different damping
function. Compared with the calculations using a Drude model with a constant
damping parameter, we observe changes in the Casimir force of a few percent.
This behavior is only observed in films of no more than 300 $\AA$ thick. | 0812.2209v1 |
2009-11-05 | Bloch oscillations in lattice potentials with controlled aperiodicity | We numerically investigate the damping of Bloch oscillations in a
one-dimensional lattice potential whose translational symmetry is broken in a
systematic manner, either by making the potential bichromatic or by introducing
scatterers at distinct lattice sites. We find that the damping strongly depends
on the ratio of lattice constants in the bichromatic potential, and that even a
small concentration of scatterers can lead to strong damping. Moreover,
mean-field interactions are able to counteract aperiodicity-induced damping of
Bloch oscillations. | 0911.1108v3 |
2012-05-11 | On radiative damping in plasma-based accelerators | Radiative damping in plasma-based electron accelerators is analyzed. The
electron dynamics under combined influence of the constant accelerating force
and the classical radiation reaction force is studied. It is shown that
electron acceleration cannot be limited by radiation reaction. If initially the
accelerating force was stronger than the radiation reaction force then the
electron acceleration is unlimited. Otherwise the electron is decelerated by
radiative damping up to a certain instant of time and then accelerated without
limits. Regardless of the initial conditions the infinite-time asymptotic
behavior of an electron is governed by self-similar solution providing
unlimited acceleration. The relative energy spread induced by the radiative
damping decreases with time in the infinite-time limit. | 1205.2436v1 |
2016-05-23 | Large time behaivor of global solutions to nonlinear wave equations with frictional and viscoelastic damping terms | In this paper, we study the Cauchy problem for a nonlinear wave equation with
frictional and viscoelastic damping terms. As is pointed out by [8], in this
combination, the frictional damping term is dominant for the viscoelastic one
for the global dynamics of the linear equation. In this note we observe that if
the initial data is small, the frictional damping term is again dominant even
in the nonlinear equation case. In other words, our main result is diffusion
phenomena: the solution is approximated by the heat kernel with a suitable
constant. Our proof is based on several estimates for the corresponding linear
equations. | 1605.07232v1 |
2021-02-28 | Stability for an inverse source problem of the damped biharmonic plate equation | This paper is concerned with the stability of the inverse source problem for
the damped biharmonic plate equation in three dimensions. The stability
estimate consists of the Lipschitz type data discrepancy and the high frequency
tail of the source function, where the latter decreases as the upper bound of
the frequency increases. The stability also shows exponential dependence on the
constant damping coefficient. The analysis employs Carleman estimates and time
decay estimates for the damped plate wave equation to obtain an exact
observability bound and depends on the study of the resonance-free region and
an upper bound of the resolvent of the biharmonic operator with respect to the
complex wavenumber. | 2103.00461v1 |
2013-08-17 | Thickness and power dependence of the spin-pumping effect in Y3Fe5O12/Pt heterostructures measured by the inverse spin Hall effect | The dependence of the spin-pumping effect on the yttrium iron garnet
(Y3Fe5O12, YIG) thickness detected by the inverse spin Hall effect (ISHE) has
been investigated quantitatively. Due to the spin-pumping effect driven by the
magnetization precession in the ferrimagnetic insulator YIG film a
spin-polarized electron current is injected into the Pt layer. This spin
current is transformed into electrical charge current by means of the ISHE. An
increase of the ISHE-voltage with increasing film thickness is observed and
compared to the theoretically expected behavior. The effective damping
parameter of the YIG/Pt samples is found to be enhanced with decreasing YIG
film thickness. The investigated samples exhibit a spin mixing conductance of
g=(7.43 \pm 0.36) \times 10^{18} m^{-2} and a spin Hall angle of theta_{ISHE} =
0.009 \pm 0.0008. Furthermore, the influence of nonlinear effects on the
generated voltage and on the Gilbert damping parameter at high excitation
powers are revealed. It is shown that for small YIG film thicknesses a
broadening of the linewidth due to nonlinear effects at high excitation powers
is suppressed because of a lack of nonlinear multi-magnon scattering channels.
We have found that the variation of the spin-pumping efficiency for thick YIG
samples exhibiting pronounced nonlinear effects is much smaller than the
nonlinear enhancement of the damping. | 1308.3787v1 |
2020-05-28 | Spintronics meets nonadiabatic molecular dynamics: Geometric spin torque and damping on noncollinear classical magnetism due to electronic open quantum system | We analyze a quantum-classical hybrid system of steadily precessing slow
classical localized magnetic moments, forming a head-to-head domain wall,
embedded into an open quantum system of fast nonequilibrium electrons. The
electrons reside within a metallic wire connected to macroscopic reservoirs.
The model captures the essence of dynamical noncollinear and noncoplanar
magnetic textures in spintronics, while making it possible to obtain the exact
time-dependent nonequilibrium density matrix of electronic system and split it
into four contributions. The Fermi surface contribution generates dissipative
(or damping-like in spintronics terminology) spin torque on the moments, and
one of the two Fermi sea contributions generates geometric torque dominating in
the adiabatic regime. When the coupling to the reservoirs is reduced, the
geometric torque is the only nonzero contribution. Locally it has both
nondissipative (or field-like in spintronics terminology) and damping-like
components, but with the sum of latter being zero, which act as the
counterparts of geometric magnetism force and electronic friction in
nonadiabatic molecular dynamics. Such current-independent geometric torque is
absent from widely used micromagnetics or atomistic spin dynamics modeling of
magnetization dynamics based on the Landau-Lifshitz-Gilbert equation, where
previous analysis of Fermi surface-type torque has severely underestimated its
magnitude. | 2005.14153v2 |
2020-09-29 | Structural Phase Dependent Giant Interfacial Spin Transparency in W/CoFeB Thin Film Heterostructure | Pure spin current has transfigured the energy-efficient spintronic devices
and it has the salient characteristic of transport of the spin angular
momentum. Spin pumping is a potent method to generate pure spin current and for
its increased efficiency high effective spin-mixing conductance (Geff) and
interfacial spin transparency (T) are essential. Here, a giant T is reported in
Sub/W(t)/Co20Fe60B20(d)/SiO2(2 nm) heterostructures in \beta-tungsten (\beta-W)
phase by employing all-optical time-resolved magneto-optical Kerr effect
technique. From the variation of Gilbert damping with W and CoFeB thicknesses,
the spin diffusion length of W and spin-mixing conductances are extracted.
Subsequently, T is derived as 0.81 \pm 0.03 for the \beta-W/CoFeB interface. A
sharp variation of Geff and T with W thickness is observed in consonance with
the thickness-dependent structural phase transition and resistivity of W. The
spin memory loss and two-magnon scattering effects are found to have negligible
contributions to damping modulation as opposed to spin pumping effect which is
reconfirmed from the invariance of damping with Cu spacer layer thickness
inserted between W and CoFeB. The observation of giant interfacial spin
transparency and its strong dependence on crystal structures of W will be
important for pure spin current based spin-orbitronic devices. | 2009.14143v1 |
2023-12-31 | Molecular Hybridization Induced Antidamping and Sizable Enhanced Spin-to-Charge Conversion in Co20Fe60B20/$β$-W/C60 Heterostructures | Development of power efficient spintronics devices has been the compelling
need in the post-CMOS technology era. The effective tunability of
spin-orbit-coupling (SOC) in bulk and at the interfaces of hybrid materials
stacking is a prerequisite for scaling down the dimension and power consumption
of these devices. In this work, we demonstrate the strong chemisorption of C60
molecules when grown on the high SOC $\beta$-W layer. The parent CFB/$\beta$-W
bilayer exhibits large spin-to-charge interconversion efficiency, which can be
ascribed to the interfacial SOC observed at the Ferromagnet/Heavy metal
interface. Further, the adsorption of C60 molecules on $\beta$-W reduces the
effective Gilbert damping by $\sim$15% in the CFB/$\beta$-W/C60
heterostructures. The anti-damping is accompanied by a gigantic $\sim$115%
enhancement in the spin-pumping induced output voltage owing to the molecular
hybridization. The non-collinear Density Functional Theory calculations confirm
the long-range enhancement of SOC of $\beta$-W upon the chemisorption of C60
molecules, which in turn can also enhance the SOC at the CFB/$\beta$-W
interface in CFB/$\beta$-W/C60 heterostructures. The combined amplification of
bulk as well interfacial SOC upon molecular hybridization stabilizes the
anti-damping and enhanced spin-to-charge conversion, which can pave the way for
the fabrication of power efficient spintronics devices. | 2401.00486v1 |
2002-04-25 | Statics and Fast Dynamics of Nanomagnets with Vortex Structure | Within the framework of the Landau-Lifshitz-Gilbert equation, using permalloy
parameters, we study the statics and dynamics of flat circular magnetic
nano-structures with an in-plane magnetic vortex configuration, putting
particular emphasis on the (planar) vorticity of the magnetic state and on the
(perpendicular) polarisation of the vortex center (which may be shifted with
respect to the center of the circle). These binary degrees of freedom can in
principle be used to manipulate two independent bits of information.
Studying switching processes induced by in-plane and out-of plane field
pulses we find that it is possible to switch the vorticity of the magnetic dot
on a time scale of 40 ps in strong enough and short enough perpendicular
external field pulses (B_z^ext \approx 0.5 T, duration \approx 40 ps). But for
realistically small values of the Gilbert damping, only the vorticity can be
switched this fast, and it turns out that it is better to dismiss the center of
the circle totally, concentrating on flat 'nano-rings' with an inner radius R_1
and an outer radius R_2. On these 'nano-rings' the vortex state is more stable,
and with respect to the switching of the vorticity these structures have
similar properties as circular dots. | 0204541v3 |
2007-03-15 | Functional Keldysh Theory of Spin Torques | We present a microscopic treatment of current-induced torques and thermal
fluctuations in itinerant ferromagnets based on a functional formulation of the
Keldysh formalism. We find that the nonequilibrium magnetization dynamics is
governed by a stochastic Landau-Lifschitz-Gilbert equation with spin transfer
torques. We calculate the Gilbert damping parameter $\alpha$ and the
non-adiabatic spin transfer torque parameter $\beta$ for a model ferromagnet.
We find that $\beta \neq \alpha$, in agreement with the results obtained using
imaginary-time methods of Kohno, Tatara and Shibata [J. Phys. Soc. Japan 75,
113706 (2006)]. We comment on the relationship between $s-d$ and
isotropic-Stoner toy models of ferromagnetism and more realistic
density-functional-theory models, and on the implications of these
relationships for predictions of the $\beta/\alpha$ ratio which plays a central
role in domain wall motion. Only for a single-parabolic-band isotropic-Stoner
model with an exchange splitting that is small compared to the Fermi energy
does $\beta/\alpha$ approach one. In addition, our microscopic formalism
incorporates naturally the fluctuations needed in a nonzero-temperature
description of the magnetization. We find that to first order in the applied
electric field, the usual form of thermal fluctuations via a phenomenological
stochastic magnetic field holds. | 0703414v2 |
2010-10-04 | Thermal fluctuation field for current-induced domain wall motion | Current-induced domain wall motion in magnetic nanowires is affected by
thermal fluctuation. In order to account for this effect, the
Landau-Lifshitz-Gilbert equation includes a thermal fluctuation field and
literature often utilizes the fluctuation-dissipation theorem to characterize
statistical properties of the thermal fluctuation field. However, the theorem
is not applicable to the system under finite current since it is not in
equilibrium. To examine the effect of finite current on the thermal
fluctuation, we adopt the influence functional formalism developed by Feynman
and Vernon, which is known to be a useful tool to analyze effects of
dissipation and thermal fluctuation. For this purpose, we construct a quantum
mechanical effective Hamiltonian describing current-induced domain wall motion
by generalizing the Caldeira-Leggett description of quantum dissipation. We
find that even for the current-induced domain wall motion, the statistical
properties of the thermal noise is still described by the
fluctuation-dissipation theorem if the current density is sufficiently lower
than the intrinsic critical current density and thus the domain wall tilting
angle is sufficiently lower than pi/4. The relation between our result and a
recent result, which also addresses the thermal fluctuation, is discussed. We
also find interesting physical meanings of the Gilbert damping alpha and the
nonadiabaticy parameter beta; while alpha characterizes the coupling strength
between the magnetization dynamics (the domain wall motion in this paper) and
the thermal reservoir (or environment), beta characterizes the coupling
strength between the spin current and the thermal reservoir. | 1010.0478v2 |
2015-06-03 | Antidamping spin-orbit torque driven by spin-flip reflection mechanism on the surface of a topological insulator: A time-dependent nonequilibrium Green function approach | Motivated by recent experiments observing spin-orbit torque (SOT) acting on
the magnetization $\vec{m}$ of a ferromagnetic (F) overlayer on the surface of
a three-dimensional topological insulator (TI), we investigate the origin of
the SOT and the magnetization dynamics in such systems. We predict that lateral
F/TI bilayers of finite length, sandwiched between two normal metal leads, will
generate a large antidamping-like SOT per very low charge current injected
parallel to the interface. The large values of antidamping-like SOT are {\it
spatially localized} around the transverse edges of the F overlayer. Our
analysis is based on adiabatic expansion (to first order in $\partial
\vec{m}/\partial t$) of time-dependent nonequilibrium Green functions (NEGFs),
describing electrons pushed out of equilibrium both by the applied bias voltage
and by the slow variation of a classical degree of freedom [such as
$\vec{m}(t)$]. From it we extract formulas for spin torque and charge pumping,
which show that they are reciprocal effects to each other, as well as Gilbert
damping in the presence of SO coupling. The NEGF-based formula for SOT
naturally splits into four components, determined by their behavior (even or
odd) under the time and bias voltage reversal. Their complex angular dependence
is delineated and employed within Landau-Lifshitz-Gilbert simulations of
magnetization dynamics in order to demonstrate capability of the predicted SOT
to efficiently switch $\vec{m}$ of a perpendicularly magnetized F overlayer. | 1506.01303v3 |
2015-07-11 | Realization of the thermal equilibrium in inhomogeneous magnetic systems by the Landau-Lifshitz-Gilbert equation with stochastic noise, and its dynamical aspects | It is crucially important to investigate effects of temperature on magnetic
properties such as critical phenomena, nucleation, pinning, domain wall motion,
coercivity, etc. The Landau-Lifshitz-Gilbert (LLG) equation has been applied
extensively to study dynamics of magnetic properties. Approaches of Langevin
noises have been developed to introduce the temperature effect into the LLG
equation. To have the thermal equilibrium state (canonical distribution) as the
steady state, the system parameters must satisfy some condition known as the
fluctuation-dissipation relation. In inhomogeneous magnetic systems in which
spin magnitudes are different at sites, the condition requires that the ratio
between the amplitude of the random noise and the damping parameter depends on
the magnitude of the magnetic moment at each site. Focused on inhomogeneous
magnetic systems, we systematically showed agreement between the stationary
state of the stochastic LLG equation and the corresponding equilibrium state
obtained by Monte Carlo simulations in various magnetic systems including
dipole-dipole interactions. We demonstrated how violations of the condition
result in deviations from the true equilibrium state. We also studied the
characteristic features of the dynamics depending on the choice of the
parameter set. All the parameter sets satisfying the condition realize the same
stationary state (equilibrium state). In contrast, different choices of
parameter set cause seriously different relaxation processes. We show two
relaxation types, i.e., magnetization reversals with uniform rotation and with
nucleation. | 1507.03075v1 |
2018-10-16 | Superfluid spin transport in ferro- and antiferromagnets | This paper focuses on spin superfluid transport, observation of which was
recently reported in antiferromagnet Cr$_2$O$_3$ [Yuan et al., Sci. Adv. 4,
eaat1098 (2018)]. This paper analyzes the role of dissipation in transformation
of spin current injected with incoherent magnons to a superfluid spin current
near the interface where spin is injected. The Gilbert damping parameter in the
Landau-Lifshitz-Gilbert theory does not describe dissipation properly, and the
dissipation parameters are calculated from the Boltzmann equation for magnons
scattered by defects. The two-fluid theory is developed similar to the
two-fluid theory for superfluids. This theory shows that the influence of
temperature variation in bulk on the superfluid spin transport (bulk Seebeck
effect) is weak at low temperatures. The scenario that the results of Yuan et
al. are connected with the Seebeck effect at the interface between the spin
detector and the sample is also discussed.
The Landau criterion for an antiferromagnet put in a magnetic field is
derived from the spectrum of collective spin modes. The Landau instability
starts in the gapped mode earlier than in the Goldstone gapless mode, in
contrast to easy-plane ferromagnets where the Goldstone mode becomes unstable.
The structure of the magnetic vortex in the geometry of the experiment is
determined. The vortex core has the skyrmion structure with finite
magnetization component normal to the magnetic field. This magnetization
creates stray magnetic fields around the exit point of the vortex line from the
sample, which can be used for experimental detection of vortices. | 1810.07020v4 |
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