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2021-01-23 | Oscillation time and damping coefficients in a nonlinear pendulum | We establish a relationship between the normalized damping coefficients and
the time that takes a nonlinear pendulum to complete one oscillation starting
from an initial position with vanishing velocity. We establish some conditions
on the nonlinear restitution force so that this oscillation time does not
depend monotonically on the viscosity damping coefficient. | 2101.09400v2 |
2024-03-26 | On a class of nonautonomous quasilinear systems with general time-gradually-degenerate damping | In this paper, we study two systems with a time-variable coefficient and
general time-gradually-degenerate damping. More explicitly, we construct the
Riemann solutions to the time-variable coefficient Zeldovich approximation and
time-variable coefficient pressureless gas systems both with general
time-gradually-degenerate damping. Applying the method of similar variables and
nonlinear viscosity, we obtain classical Riemann solutions and delta shock wave
solutions. | 2403.17732v1 |
2013-11-14 | The dimension of the leafwise reduced cohomology | Geometric conditions are given so that the leafwise reduced cohomology is of
infinite dimension, specially for foliations with dense leaves on closed
manifolds. The main new definition involved is the intersection number of
subfoliations with "appropriate coefficients". The leafwise reduced cohomology
is also described for homogeneous foliations with dense leaves on closed
nilmanifolds. | 1311.3518v1 |
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 |
2005-01-27 | Current-induced macrospin vs spin-wave excitations in spin valves | The mode dependence of current-induced magnetic excitations in spin valves is
studied theoretically. The torque exerted on the magnetization by transverse
spin currents as well as the Gilbert damping constant are found to depend
strongly on the wave length of the excitation (spin wave). Analytic expressions
are presented for the critical currents that excite a selected spin wave. The
onset of macrospin (zero wavelength) vs finite wavelength instabilities depends
on the device parameters and the current direction, in agreement with recent
experimental findings. | 0501672v3 |
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 |
2011-04-15 | Lagrangian approach and dissipative magnetic systems | A Lagrangian is introduced which includes the coupling between magnetic
moments $\mathbf{m}$ and the degrees of freedom $\boldsymbol{\sigma}$ of a
reservoir. In case the system-reservoir coupling breaks the time reversal
symmetry the magnetic moments perform a damped precession around an effective
field which is self-organized by the mutual interaction of the moments. The
resulting evolution equation has the form of the Landau-Lifshitz-Gilbert
equation. In case the bath variables are constant vector fields the moments
$\mathbf{m}$ fulfill the reversible Landau-Lifshitz equation. Applying
Noether's theorem we find conserved quantities under rotation in space and
within the configuration space of the moments. | 1104.3002v1 |
2011-07-04 | Minimization of the Switching Time of a Synthetic Free Layer in Thermally Assisted Spin Torque Switching | We theoretically studied the thermally assisted spin torque switching of a
synthetic free layer and showed that the switching time is minimized if the
condition H_J=|H_s|/(2 alpha) is satisfied, where H_J, H_s and alpha are the
coupling field of two ferromagnetic layers, the amplitude of the spin torque,
and the Gilbert damping constant. We also showed that the coupling field of the
synthetic free layer can be determined from the resonance frequencies of the
spin-torque diode effect. | 1107.0753v2 |
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 |
2013-03-12 | Thermally excited spin waves in a nano-structure: thermal gradient vs. constant temperature | Using micromagnetic simulations, we have investigated spin dynamics in a
nanostructure in the presence of thermal fluctuations. In particular, we have
studied the effects of a uniform temperature and of a uniform thermal gradient.
In both cases, the stochastic field leads to an increase of the precession
angle of the magnetization, and to a mild decreas of the linewidth of the
resonance peaks. Our results indicate that the Gilbert damping parameter plays
the role of control parameter for the amplification of spin waves. | 1303.2895v1 |
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 |
2015-02-09 | 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 |
2015-07-24 | Boosting Domain Wall Propagation by Notches | We report a counter-intuitive finding that notches in an otherwise
homogeneous magnetic nanowire can boost current-induced domain wall (DW)
propagation. DW motion in notch-modulated wires can be classified into three
phases: 1) A DW is pinned around a notch when the current density is below the
depinning current density. 2) DW propagation velocity is boosted by notches
above the depinning current density and when non-adiabatic spin-transfer torque
strength $\beta$ is smaller than the Gilbert damping constant $\alpha$. The
boost can be manyfold. 3) DW propagation velocity is hindered when $\beta >
\alpha$. The results are explained by using the Thiele equation. | 1507.06748v1 |
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 |
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 |
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 |
2020-01-17 | Fermi Level Controlled Ultrafast Demagnetization Mechanism in Half-Metallic Heusler Alloy | The electronic band structure-controlled ultrafast demagnetization mechanism
in Co2FexMn1-xSi Heusler alloy is underpinned by systematic variation of
composition. We find the spin-flip scattering rate controlled by spin density
of states at Fermi level is responsible for non-monotonic variation of
ultrafast demagnetization time ({\tau}M) with x with a maximum at x = 0.4.
Furthermore, Gilbert damping constant exhibits an inverse relationship with
{\tau}M due to the dominance of inter-band scattering mechanism. This
establishes a unified mechanism of ultrafast spin dynamics based on Fermi level
position. | 2001.06217v1 |
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 |
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 |
2012-10-25 | Decay rates for the damped wave equation on the torus | We address the decay rates of the energy for the damped wave equation when
the damping coefficient $b$ does not satisfy the Geometric Control Condition
(GCC). First, we give a link with the controllability of the associated
Schr\"odinger equation. We prove in an abstract setting that the observability
of the Schr\"odinger group implies that the semigroup associated to the damped
wave equation decays at rate $1/\sqrt{t}$ (which is a stronger rate than the
general logarithmic one predicted by the Lebeau Theorem).
Second, we focus on the 2-dimensional torus. We prove that the best decay one
can expect is $1/t$, as soon as the damping region does not satisfy GCC.
Conversely, for smooth damping coefficients $b$, we show that the semigroup
decays at rate $1/t^{1-\eps}$, for all $\eps >0$. The proof relies on a second
microlocalization around trapped directions, and resolvent estimates.
In the case where the damping coefficient is a characteristic function of a
strip (hence discontinuous), St\'{e}phane Nonnenmacher computes in an appendix
part of the spectrum of the associated damped wave operator, proving that the
semigroup cannot decay faster than $1/t^{2/3}$. In particular, our study shows
that the decay rate highly depends on the way $b$ vanishes. | 1210.6879v1 |
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 |
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 |
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 |
2020-10-15 | Spin injection characteristics of Py/graphene/Pt by gigahertz and terahertz magnetization dynamics driven by femtosecond laser pulse | Spin transport characteristics of graphene has been extensively studied so
far. The spin transport along c-axis is however reported by rather limited
number of papers. We have studied spin transport characteristics through
graphene along c-axis with permalloy(Py)/graphene(Gr)/Pt by gigahertz (GHz) and
terahertz (THz) magnetization dynamics driven by femtosecond laser pulses. The
relatively simple sample structure does not require electrodes on the sample.
The graphene layer was prepared by chemical vapor deposition and transferred on
Pt film. The quality of graphene layer was characterized by Raman microscopy.
Time resolved magneto-optical Kerr effect is used to characterize gigahertz
magnetization dynamics. Magnetization precession is clearly observed both for
Pt/Py and Pt/Gr/Py. The Gilbert damping constant of Pt/Py was 0.015, indicates
spin pumping effect from Py to Pt. The Gilbert damping constant of Pt/Gr/Py is
found to be 0.011, indicates spin injection is blocked by graphene layer. We
have also performed the measurement of THz emission for Pt/Py and Pt/Gr/Py.
While the THz emission is clearly observed for Pt/Py, a strong reduction of THz
emission is observed for Pt/Gr/Py. With these two different experiments, and
highly anisotropic resistivity of graphite, we conclude that the vertical spin
transport is strongly suppressed by the graphene layer. | 2010.07694v1 |
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 |
2021-09-13 | Control of magnetization dynamics by substrate orientation in YIG thin films | Yttrium Iron Garnet (YIG) and bismuth (Bi) substituted YIG (Bi0.1Y2.9Fe5O12,
BYG) films are grown in-situ on single crystalline Gadolinium Gallium Garnet
(GGG) substrates [with (100) and (111) orientations] using pulsed laser
deposition (PLD) technique. As the orientation of the Bi-YIG film changes from
(100) to (111), the lattice constant is enhanced from 12.384 {\AA} to 12.401
{\AA} due to orientation dependent distribution of Bi3+ ions at dodecahedral
sites in the lattice cell. Atomic force microscopy (AFM) images show smooth
film surfaces with roughness 0.308 nm in Bi-YIG (111). The change in substrate
orientation leads to the modification of Gilbert damping which, in turn, gives
rise to the enhancement of ferromagnetic resonance (FMR) line width. The best
values of Gilbert damping are found to be (0.54)*10-4, for YIG (100) and
(6.27)*10-4, for Bi-YIG (111) oriented films. Angle variation measurements of
the Hr are also performed, that shows a four-fold symmetry for the resonance
field in the (100) grown film. In addition, the value of effective
magnetization (4{\pi}Meff) and extrinsic linewidth ({\Delta}H0) are observed to
be dependent on substrate orientation. Hence PLD growth can assist
single-crystalline YIG and BYG films with a perfect interface that can be used
for spintronics and related device applications. | 2109.05901v1 |
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 |
2022-09-01 | Growth parameters of Bi0.1Y2.9Fe5O12 thin films for high frequency applications | The growth and characterization of Bismuth (Bi) substituted YIG (Bi-YIG,
Bi0.1Y2.9Fe5O12) thin films are reported. Pulsed laser deposited (PLD) films
with thicknesses ranging from 20 to 150 nm were grown on Gadolinium Gallium
Garnet substrates. Two substrate orientations of (100) and (111) were
considered. The enhanced distribution of Bi3+ ions at dodecahedral site along
(111) is observed to lead to an increment in lattice constant from 12.379
angstrom in (100) to 12.415 angstrom in (111) oriented films. Atomic force
microscopy images showed decreasing roughness with increasing film thickness.
Compared to (100) grown films, (111) oriented films showed an increase in
ferromagnetic resonance linewidth and consequent increase in Gilbert damping.
The lowest Gilbert damping values are found to be (1.06) * 10E-4 for (100) and
(2.30) * 10E-4 for (111) oriented films with thickness of 150 nm. The observed
values of extrinsic linewidth, effective magnetization, and anisotropic field
are related to thickness of the films and substrate orientation. In addition,
the in-plane angular variation established four-fold symmetry for the (100)
deposited films unlike the case of (111) deposited films. This study prescribes
growth conditions for PLD grown single-crystalline Bi-YIG films towards desired
high frequency and magneto-optical device applications. | 2209.00558v1 |
2019-10-17 | Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms | We prove the global existence of small data solution in all space dimension
for weakly coupled systems of semi-linear effectively damped wave, with
different time-dependent coefficients in the dissipation terms. Moreover,
nonlinearity terms $ f(t,u) $ and $ g(t,v) $ satisfying some properties of the
parabolic equation. We study the problem in several classes of regularity. | 1910.07731v1 |
2021-10-10 | Global existence of solutions for semilinear damped wave equations with variable coefficients | We consider the Cauchy problem for the damped wave equations with variable
coefficients a(x) having power type nonlinearity |u|^p. We discuss the global
existence of solutions for small initial data and investigate the relation
between the range of a(x) and the order p. | 2110.04718v2 |
2023-04-23 | Decay rates for a variable-coefficient wave equation with nonlinear time-dependent damping | In this paper, a class of variable-coefficient wave equations equipped with
time-dependent damping and the nonlinear source is considered. We show that the
total energy of the system decays to zero with an explicit and precise decay
rate estimate under different assumptions on the feedback with the help of the
method of weighted energy integral. | 2304.11522v1 |
2019-07-10 | Determination of the damping co-efficient of electrons in optically transparent glasses at the true resonance frequency in the ultraviolet from an analysis of the Lorentz-Maxwell model of dispersion | The Lorentz-Maxwell model of dispersion of light has been analyzed in this
paper to determine the true resonance frequency in the ultraviolet for the
electrons in optically transparent glasses and the damping coefficient at this
frequency. For this we needed the refractive indices of glass in the optical
frequency range. We argue that the true resonance condition in the absorption
region prevails when the frequency at which the absorption coefficient is
maximum is the same as the frequency at which the average energy per cycle of
the electrons is also a maximum. We have simultaneously solved the two
equations obtained from the two maxima conditions numerically to arrive at a
unique solution for the true resonance frequency and the damping coefficient at
this frequency. Assuming the damping coefficient to be constant over a small
frequency range in the absorption region, we have determined the frequencies at
which the extinction coefficient and the reflectance are maxima. These
frequencies match very well with the published data for silica glasses
available from the literature. | 1907.04499v1 |
2012-07-17 | Asymptotic Dynamics of a Class of Coupled Oscillators Driven by White Noises | This paper is devoted to the study of the asymptotic dynamics of a class of
coupled second order oscillators driven by white noises. It is shown that any
system of such coupled oscillators with positive damping and coupling
coefficients possesses a global random attractor. Moreover, when the damping
and the coupling coefficients are sufficiently large, the global random
attractor is a one-dimensional random horizontal curve regardless of the
strength of the noises, and the system has a rotation number, which implies
that the oscillators in the system tend to oscillate with the same frequency
eventually and therefore the so called frequency locking is successful. The
results obtained in this paper generalize many existing results on the
asymptotic dynamics for a single second order noisy oscillator to systems of
coupled second order noisy oscillators. They show that coupled damped second
order oscillators with large damping have similar asymptotic dynamics as the
limiting coupled first order oscillators as the damping goes to infinite and
also that coupled damped second order oscillators have similar asymptotic
dynamics as their proper space continuous counterparts, which are of great
practical importance. | 1207.3864v1 |
2020-09-22 | Sharp exponential decay rates for anisotropically damped waves | In this article, we study energy decay of the damped wave equation on compact
Riemannian manifolds where the damping coefficient is anisotropic and modeled
by a pseudodifferential operator of order zero. We prove that the energy of
solutions decays at an exponential rate if and only if the damping coefficient
satisfies an anisotropic analogue of the classical geometric control condition,
along with a unique continuation hypothesis. Furthermore, we compute an
explicit formula for the optimal decay rate in terms of the spectral abscissa
and the long-time averages of the principal symbol of the damping over
geodesics, in analogy to the work of Lebeau for the isotropic case. We also
construct genuinely anisotropic dampings which satisfy our hypotheses on the
flat torus. | 2009.10832v2 |
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 |
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 |
2016-10-01 | The destabilizing effect of external damping: Singular flutter boundary for the Pfluger column with vanishing external dissipation | Elastic structures loaded by nonconservative positional forces are prone to
instabilities induced by dissipation: it is well-known in fact that internal
viscous damping destabilizes the marginally stable Ziegler's pendulum and
Pfluger column (of which the Beck's column is a special case), two structures
loaded by a tangential follower force. The result is the so-called
'destabilization paradox', where the critical force for flutter instability
decreases by an order of magnitude when the coefficient of internal damping
becomes infinitesimally small. Until now external damping, such as that related
to air drag, is believed to provide only a stabilizing effect, as one would
intuitively expect. Contrary to this belief, it will be shown that the effect
of external damping is qualitatively the same as the effect of internal
damping, yielding a pronounced destabilization paradox. Previous results
relative to destabilization by external damping of the Ziegler's and Pfluger's
elastic structures are corrected in a definitive way leading to a new
understanding of the destabilizating role played by viscous terms. | 1611.03886v1 |
2018-05-16 | Stabilization rates for the damped wave equation with Hölder-regular damping | We study the decay rate of the energy of solutions to the damped wave
equation in a setup where the geometric control condition is violated. We
consider damping coefficients which are $0$ on a strip and vanish like
polynomials, $x^{\beta}$. We prove that the semigroup cannot be stable at rate
faster than $1/t^{(\beta+2)/(\beta+3)}$ by producing quasimodes of the
associated stationary damped wave equation. We also prove that the semigroup is
stable at rate at least as fast as $1/t^{(\beta+2)/(\beta+4)}$. These two
results establish an explicit relation between the rate of vanishing of the
damping and rate of decay of solutions. Our result partially generalizes a
decay result of Nonnemacher in which the damping is an indicator function on a
strip. | 1805.06535v3 |
2014-02-07 | One-dimensional random attractor and rotation number of the stochastic damped sine-Gordon equation | This paper is devoted to the study of the asymptotic dynamics of the
stochastic damped sine-Gordon equation with homogeneous Neumann boundary
condition. It is shown that for any positive damping and diffusion
coefficients, the equation possesses a random attractor, and when the damping
and diffusion coefficients are sufficiently large, the random attractor is a
one-dimensional random horizontal curve regardless of the strength of noise.
Hence its dynamics is not chaotic. It is also shown that the equation has a
rotation number provided that the damping and diffusion coefficients are
sufficiently large, which implies that the solutions tend to oscillate with the
same frequency eventually and the so called frequency locking is successful. | 1402.1787v1 |
2021-02-01 | Blow-up and lifespan estimates for a damped wave equation in the Einstein-de Sitter spacetime with nonlinearity of derivative type | In this article, we investigate the blow-up for local solutions to a
semilinear wave equation in the generalized Einstein - de Sitter spacetime with
nonlinearity of derivative type. More precisely, we consider a semilinear
damped wave equation with a time-dependent and not summable speed of
propagation and with a time-dependent coefficient for the linear damping term
with critical decay rate. We prove in this work that the results obtained in a
previous work, where the damping coefficient takes two particular values $0$ or
$2$, can be extended for any positive damping coefficient. In the blow-up case,
the upper bound of the exponent of the nonlinear term is given, and the
lifespan estimate of the global existence time is derived as well. | 2102.01137v2 |
2023-10-24 | Frictional weakening of a granular sheared layer due to viscous rolling revealed by Discrete Element Modeling | Considering a 3D sheared granular layer modeled with discrete elements, it is
well known the rolling resistance significantly influences the mechanical
behavior. Even if the rolling resistance role has been deeply investigated as
it is commonly used to represent the the roughness of the grains and the
interparticle locking, the role of rolling viscous damping coefficient has been
largely overlooked so far. This parameter is rarely used or only to dissipate
the energy and to converge numerically. This paper revisits the physical role
of those coefficients with a parametric study of the rolling friction and the
rolling damping for a sheared layer at different shear speeds and different
confinement pressures. It has been observed that the damping coefficient
induces a frictional weakening. Hence, competition between the rolling
resistance and the rolling damping occurs. Angular resistance aims to avoid
grains rolling, decreasing the difference between the angular velocities of
grains. Whereas, angular damping acts in the opposite, avoiding a change in the
difference between the angular velocities of grains. In consequence, grains
keep rolling and the sample strength decreases. This effect must be considered
to not overestimate the frictional response of a granular layer. | 2310.15945v1 |
2019-04-24 | On the Energy Decay Rate of the Fractional Wave Equation on $\mathbb{R}$ with Relatively Dense Damping | We establish upper bounds for the decay rate of the energy of the damped
fractional wave equation when the averages of the damping coefficient on all
intervals of a fixed length are bounded below. If the power of the fractional
Laplacian, $s$, is between 0 and 2, the decay is polynomial. For $s \ge 2$, the
decay is exponential. Second, we show that our assumption on the damping is
necessary for the energy to decay exponentially. | 1904.10946v3 |
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 |
2023-02-13 | Damping of gravitational waves in f(R) gravity | We study the damping of $f(R)$ gravitational waves by matter in flat
spacetime and in expanding universe. In the former case, we find that the
Landau damping of scalar mode in $f(R)$ theory exists, while that of the tensor
mode in general relativity does not; we also present the viscosity coefficients
and dispersion relations of the two modes. In the later case, we investigate
the evolution of tensor and scalar modes in Friedmann-Robertson-Walker (FRW)
cosmology with a matter distribution; by considering the case of $f(R)=R+\al
R^2$, we analysis the influence of parameter $\al$ on wave damping,and put
restrictions on its magnitude. | 2302.06402v2 |
2023-03-20 | Nonlinear Damping and Field-aligned Flows of Propagating Shear Alfvén Waves with Braginskii Viscosity | Braginskii MHD provides a more accurate description of many plasma
environments than classical MHD since it actively treats the stress tensor
using a closure derived from physical principles. Stress tensor effects
nonetheless remain relatively unexplored for solar MHD phenomena, especially in
nonlinear regimes. This paper analytically examines nonlinear damping and
longitudinal flows of propagating shear Alfv\'en waves. Most previous studies
of MHD waves in Braginskii MHD considered the strict linear limit of vanishing
wave perturbations. We show that those former linear results only apply to
Alfv\'en wave amplitudes in the corona that are so small as to be of little
interest, typically a wave energy less than $10^{-11}$ times the energy of the
background magnetic field. For observed wave amplitudes, the Braginskii viscous
dissipation of coronal Alfv\'en waves is nonlinear and a factor around $10^9$
stronger than predicted by the linear theory. Furthermore, the dominant damping
occurs through the parallel viscosity coefficient $\eta_0$, rather than the
perpendicular viscosity coefficient $\eta_2$ in the linearized solution. This
paper develops the nonlinear theory, showing that the wave energy density
decays with an envelope $(1+z/L_d)^{-1}$. The damping length $L_d$ exhibits an
optimal damping solution, beyond which greater viscosity leads to lower
dissipation as the viscous forces self-organise the longitudinal flow to
suppress damping. Although the nonlinear damping greatly exceeds the linear
damping, it remains negligible for many coronal applications. | 2303.11128v1 |
2024-01-09 | Damping Separation of Finite Open Systems in Gravity-Related Experiments in the Free Molecular Flow Regime | The residual gas damping of the test mass (TM) in the free molecular flow
regime is studied in the finite open systems for high-precision gravity-related
experiments. Through strict derivation, we separate the damping coefficients
for two finite open systems, i.e., the bi-plate system and the sensor core
system, into base damping and diffusion damping. This elucidates the
relationship between the free damping in the infinite gas volume and the
proximity damping in the constrained volume, unifies them into one microscopic
picture, and allows us to point out three pathways of energy dissipation in the
bi-plate gap. We also provide the conditions that need to be met to achieve
this separation. In applications, for space gravitational wave detection, our
results for the residual gas damping coefficient for the 4TM torsion balance
experiment is the closest one to the experimental and simulation data compared
to previous models. For the LISA mission, our estimation for residual gas
acceleration noise at the sensitive axis is consistent with the simulation
result, within about $5\%$ difference. In addition, in the test of the
gravitational inverse-square law, our results suggest that the constraint on
the distance between TM and the conducting membrane can be reduced by about
$28\%$. | 2401.04808v1 |
2010-09-20 | Diffusive properties of persistent walks on cubic lattices with application to periodic Lorentz gases | We calculate the diffusion coefficients of persistent random walks on cubic
and hypercubic lattices, where the direction of a walker at a given step
depends on the memory of one or two previous steps. These results are then
applied to study a billiard model, namely a three-dimensional periodic Lorentz
gas. The geometry of the model is studied in order to find the regimes in which
it exhibits normal diffusion. In this regime, we calculate numerically the
transition probabilities between cells to compare the persistent random-walk
approximation with simulation results for the diffusion coefficient. | 1009.3922v1 |
2012-11-13 | Critical exponent for the semilinear wave equation with scale invariant damping | In this paper we consider the critical exponent problem for the semilinear
damped wave equation with time-dependent coefficients. We treat the scale
invariant cases. In this case the asymptotic behavior of the solution is very
delicate and the size of coefficient plays an essential role. We shall prove
that if the power of the nonlinearity is greater than the Fujita exponent, then
there exists a unique global solution with small data, provided that the size
of the coefficient is sufficiently large. We shall also prove some blow-up
results even in the case that the coefficient is sufficiently small. | 1211.2900v1 |
2010-12-07 | Turbulence damping as a measure of the flow dimensionality | The dimensionality of turbulence in fluid layers determines their properties.
We study electromagnetically driven flows in finite depth fluid layers and show
that eddy viscosity, which appears as a result of three-dimensional motions,
leads to increased bottom damping. The anomaly coefficient, which characterizes
the deviation of damping from the one derived using a quasi-two-dimensional
model, can be used as a measure of the flow dimensionality. Experiments in
turbulent layers show that when the anomaly coefficient becomes high, the
turbulent inverse energy cascade is suppressed. In the opposite limit
turbulence can self-organize into a coherent flow. | 1012.1371v1 |
2012-01-05 | Damped bead on a rotating circular hoop - a bifurcation zoo | The evergreen problem of a bead on a rotating hoop shows a multitude of
bifurcations when the bead moves with friction. This motion is studied for
different values of the damping coefficient and rotational speeds of the hoop.
Phase portraits and trajectories corresponding to all different modes of motion
of the bead are presented. They illustrate the rich dynamics associated with
this simple system. For some range of values of the damping coefficient and
rotational speeds of the hoop, linear stability analysis of the equilibrium
points is inadequate to classify their nature. A technique involving
transformation of coordinates and order of magnitude arguments is presented to
examine such cases. This may provide a general framework to investigate other
complex systems. | 1201.1218v1 |
2015-08-24 | Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients | We study the asymptotic behavior of solutions for the semilinear damped wave
equation with variable coefficients. We prove that if the damping is effective,
and the nonlinearity and other lower order terms can be regarded as
perturbations, then the solution is approximated by the scaled Gaussian of the
corresponding linear parabolic problem. The proof is based on the scaling
variables and energy estimates. | 1508.05778v3 |
2018-07-17 | On the blow-up for critical semilinear wave equations with damping in the scattering case | We consider the Cauchy problem for semilinear wave equations with variable
coefficients and time-dependent scattering damping in $\mathbf{R}^n$, where
$n\geq 2$. It is expected that the critical exponent will be Strauss' number
$p_0(n)$, which is also the one for semilinear wave equations without damping
terms. Lai and Takamura (2018) have obtained the blow-up part, together with
the upper bound of lifespan, in the sub-critical case $p<p_0(n)$. In this
paper, we extend their results to the critical case $p=p_0(n)$. The proof is
based on Wakasa and Yordanov (2018), which concerns the blow-up and upper bound
of lifespan for critical semilinear wave equations with variable coefficients. | 1807.06164v1 |
2013-09-19 | Van der Waals Coefficients for the Alkali-metal Atoms in the Material Mediums | The damping coefficients for the alkali atoms are determined very accurately
by taking into account the optical properties of the atoms and three distinct
types of trapping materials such as Au (metal), Si (semi-conductor) and
vitreous SiO2 (dielectric). Dynamic dipole polarizabilities are calculated
precisely for the alkali atoms that reproduce the damping coefficients in the
perfect conducting medium within 0.2% accuracy. Upon the consideration of the
available optical data of the above wall materials, the damping coefficients
are found to be substantially different than those of the ideal conductor. We
also evaluated dispersion coefficients for the alkali dimers and compared them
with the previously reported values. These coefficients are fitted into a
ready-to-use functional form to aid the experimentalists the interaction
potentials only with the knowledge of distances. | 1309.4897v1 |
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 |
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 |
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 |
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 |
2014-10-02 | Investigation of the temperature-dependence of ferromagnetic resonance and spin waves in Co2FeAl0.5Si0.5 | Co2FeAl0.5Si0.5 (CFAS) is a Heusler compound that is of interest for
spintronics applications, due to its high spin polarization and relatively low
Gilbert damping constant. In this study, the behavior of ferromagnetic
resonance as a function of temperature was investigated in CFAS, yielding a
decreasing trend of damping constant as the temperature was increased from 13
to 300 K. Furthermore, we studied spin waves in CFAS using both frequency
domain and time domain techniques, obtaining group velocities and attenuation
lengths as high as 26 km/s and 23.3 um, respectively, at room temperature. | 1410.0439v1 |
2014-12-12 | Spin waves in micro-structured yttrium iron garnet nanometer-thick films | We investigated the spin-wave propagation in a micro-structured yttrium iron
garnet waveguide of $40$ nm thickness. Utilizing spatially-resolved Brillouin
light scattering microscopy, an exponential decay of the spin-wave amplitude of
$(10.06 \pm 0.83)$ $\mu$m was observed. This leads to an estimated Gilbert
damping constant of $\alpha=(8.79\pm 0.73)\times 10^{-4}$, which is larger than
damping values obtained through ferromagnetic resonance measurements in
unstructured films. The theoretically calculated spatial interference of
waveguide modes was compared to the spin-wave pattern observed experimentally
by means of Brillouin light scattering spectroscopy. | 1412.4032v1 |
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 |
2016-06-21 | 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 |
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 |
2017-06-05 | Consistent microscopic analysis of spin pumping effects | We present a consistent microscopic study of spin pumping effects for both
metallic and insulating ferromagnets. As for metallic case, we present a simple
quantum mechanical picture of the effect as due to the electron spin flip as a
result of a nonadiabatic (off-diagonal) spin gauge field. The effect of
interface spin-orbit interaction is briefly discussed. We also carry out
field-theoretic calculation to discuss on the equal footing the spin current
generation and torque effects such as enhanced Gilbert damping constant and
shift of precession frequency both in metallic and insulating cases. For thick
ferromagnetic metal, our study reproduces results of previous theories such as
the correspondence between the dc component of the spin current and enhancement
of the damping. For thin metal and insulator, the relation turns out to be
modified. For the insulating case, driven locally by interface $sd$ exchange
interaction due to magnetic proximity effect, physical mechanism is distinct
from the metallic case. Further study of proximity effect and interface
spin-orbit interaction would be crucial to interpret experimental results in
particular for insulators. | 1706.01185v1 |
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 |
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 |
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 |
2018-10-11 | Propagating spin waves in nanometer-thick yttrium iron garnet films: Dependence on wave vector, magnetic field strength and angle | We present a comprehensive investigation of propagating spin waves in
nanometer-thick yttrium iron garnet (YIG) films. We use broadband spin-wave
spectroscopy with integrated coplanar waveguides (CPWs) and microstrip antennas
on top of continuous and patterned YIG films to characterize spin waves with
wave vectors up to 10 rad/$\mu$m. All films are grown by pulsed laser
deposition. From spin-wave transmission spectra, parameters such as the Gilbert
damping constant, spin-wave dispersion relation, group velocity, relaxation
time, and decay length are derived and their dependence on magnetic bias field
strength and angle is systematically gauged. For a 40-nm-thick YIG film, we
obtain a damping constant of $3.5 \times 10^{-4}$ and a maximum decay length of
1.2 mm. Our experiments reveal a strong variation of spin-wave parameters with
magnetic bias field and wave vector. Spin-wave properties change considerably
up to a magnetic bias field of about 30 mT and above a field angle of
$\theta_{H} = 20^{\circ}$, where $\theta_{H} = 0^{\circ}$ corresponds to the
Damon-Eshbach configuration. | 1810.04973v1 |
2019-05-30 | Predicting New Iron Garnet Thin Films with Perpendicular Magnetic Anisotropy | Perpendicular magnetic anisotropy (PMA) is a necessary condition for many
spintronic applications like spin-orbit torques switching, logic and memory
devices. An important class of magnetic insulators with low Gilbert damping at
room temperature are iron garnets, which only have a few PMA types such as
terbium and samarium iron garnet. More and stable PMA garnet options are
necessary for researchers to be able to investigate new spintronic phenomena.
In this study, we predict 20 new substrate/magnetic iron garnet film pairs with
stable PMA at room temperature. The effective anisotropy energies of 10
different garnet films that are lattice-matched to 5 different commercially
available garnet substrates have been calculated using shape, magnetoelastic
and magnetocrystalline anisotropy terms. Strain type, tensile or compressive
depending on substrate choice, as well as the sign and the magnitude of the
magnetostriction constants of garnets determine if a garnet film may possess
PMA. We show the conditions in which Samarium, Gadolinium, Terbium, Holmium,
Dysprosium and Thulium garnets may possess PMA on the investigated garnet
substrate types. Guidelines for obtaining garnet films with low damping are
presented. New PMA garnet films with tunable saturation moment and field may
improve spin-orbit torque memory and compensated magnonic thin film devices. | 1905.13042v1 |
2019-07-17 | Inhomogeneous domain walls in spintronic nanowires | In case of a spin-polarized current, the magnetization dynamics in nanowires
are governed by the classical Landau-Lifschitz equation with Gilbert damping
term, augmented by a typically non-variational Slonczewski term. Taking axial
symmetry into account, we study the existence of domain wall type coherent
structure solutions, with focus on one space dimension and spin-polarization,
but our results also apply to vanishing spin-torque term. Using methods from
bifurcation theory for arbitrary constant applied fields, we prove the
existence of domain walls with non-trivial azimuthal profile, referred to as
inhomogeneous. We present an apparently new type of domain wall, referred to as
non-flat, whose approach of the axial magnetization has a certain oscillatory
character. Additionally, we present the leading order mechanism for the
parameter selection of flat and non-flat inhomogeneous domain walls for an
applied field below a threshold, which depends on anisotropy, damping, and
spin-transfer. Moreover, numerical continuation results of all these domain
wall solutions are presented. | 1907.07470v2 |
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 |
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