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2019-06-17 | Controlling acoustic waves using magnetoelastic Fano resonances | We propose and analyze theoretically a class of energy-efficient
magneto-elastic devices for analogue signal processing. The signals are carried
by transverse acoustic waves while the bias magnetic field controls their
scattering from a magneto-elastic slab. By tuning the bias field, one can alter
the resonant frequency at which the propagating acoustic waves hybridize with
the magnetic modes, and thereby control transmission and reflection
coefficients of the acoustic waves. The scattering coefficients exhibit
Breit-Wigner/Fano resonant behaviour akin to inelastic scattering in atomic and
nuclear physics. Employing oblique incidence geometry, one can effectively
enhance the strength of magnetoelastic coupling, and thus countermand the
magnetic losses due to the Gilbert damping. We apply our theory to discuss
potential benefits and issues in realistic systems and suggest further routes
to enhance performance of the proposed devices. | 1906.07297v2 |
2017-06-02 | Power Loss for a Periodically Driven Ferromagnetic Nanoparticle in a Viscous Fluid: the Finite Anisotropy Aspects | The joint magnetic and mechanical motion of a ferromagnetic nanoparticle in a
viscous fluid is considered within the dynamical approach. The equation based
on the total momentum conservation law is used for the description of the
mechanical rotation, while the modified Landau-Lifshitz-Gilbert equation is
utilized for the description of the internal magnetic dynamics. The exact
expressions for the particles trajectories and the power loss are obtained in
the linear approximation. The comparison with the results of other widespread
approaches, such as the model of fixed particle and the model of frozen
magnetic moment, is performed. It is established that in the small oscillations
mode the damping precession of the nanopartile magnetic moment is the main
channel of energy dissipation, but the motion of the nanoparticle easy axis can
significantly influence the value of the resulting power loss. | 1706.00777v2 |
2017-06-07 | Adiabatic and nonadiabatic spin torques induced by spin-triplet supercurrent | We study spin transfer torques induced by a spin-triplet supercurrent in a
magnet with the superconducting proximity effect. By a perturbative approach,
we show that spin-triplet correlations realize new types of torques, which are
analogous to the adiabatic and non-adiabatic ($\beta$) torques, without
extrinsic spin-flip scattering. Remarkable advantages compared to conventional
spin-transfer torques are highlighted in domain wall manipulation. Oscillatory
motions of a domain wall do not occur for a small Gilbert damping, and the
threshold current density to drive its motion becomes zero in the absence of
extrinsic pinning potentials due to the nonadiabatic torque controlled by the
triplet correlations. | 1706.02296v2 |
2017-06-26 | Perpendicular magnetic anisotropy in insulating ferrimagnetic gadolinium iron garnet thin films | We present experimental control of the magnetic anisotropy in a gadolinium
iron garnet (GdIG) thin film from in-plane to perpendicular anisotropy by
simply changing the sample temperature. The magnetic hysteresis loops obtained
by SQUID magnetometry measurements unambiguously reveal a change of the
magnetically easy axis from out-of-plane to in-plane depending on the sample
temperature. Additionally, we confirm these findings by the use of temperature
dependent broadband ferromagnetic resonance spectroscopy (FMR). In order to
determine the effective magnetization, we utilize the intrinsic advantage of
FMR spectroscopy which allows to determine the magnetic anisotropy independent
of the paramagnetic substrate, while magnetometry determines the combined
magnetic moment from film and substrate. This enables us to quantitatively
evaluate the anisotropy and the smooth transition from in-plane to
perpendicular magnetic anisotropy. Furthermore, we derive the temperature
dependent $g$-factor and the Gilbert damping of the GdIG thin film. | 1706.08488v1 |
2017-09-07 | Tunable spin pumping in exchange coupled magnetic trilayers | Magnetic thin films at ferromagnetic resonance (FMR) leak angular momentum,
which may be absorbed by adjacent layers. This phenomenon, known as spin
pumping, is manifested by an increase in the resonance linewidth ($\Delta H$),
and the closely related Gilbert damping. Another effect of this transfer of
spin currents is a dynamical and long-range coupling that can drive two
magnetic layers into a collective precession when their FMR frequencies
coincide. A collective behavior is also found in magnetic trilayers with
interlayer exchange coupling (IEC). In this study we investigate the interplay
between IEC and spin pumping, using Co/Cu/Py pseudo-spin values. We employ
broadband FMR spectroscopy to explore both the frequency and coupling-strength
dependence of $\Delta H$. Our observations show that there exists a cut-off
frequency, set by the IEC strength, below which the precession is truly
collective and the spin pumping is suppressed. These results demonstrate that
it is possible to control the spin pumping efficiency by varying the frequency
or the interlayer exchange coupling. | 1709.02295v1 |
2018-08-23 | Reduced thermal stability of antiferromagnetic nanostructures | Antiferromagnetic materials hold promising prospects in novel types of
spintronics applications. Assessing the stability of antiferromagnetic
nanostructures against thermal excitations is a crucial aspect of designing
devices with a high information density. Here we use theoretical calculations
and numerical simulations to determine the mean switching time of
antiferromagnetic nanoparticles in the superparamagnetic limit. It is
demonstrated that the thermal stability is drastically reduced compared to
ferromagnetic particles in the limit of low Gilbert damping, attributed to the
exchange enhancement of the attempt frequencies. It is discussed how the system
parameters have to be engineered in order to optimize the switching rates in
antiferromagnetic nanoparticles. | 1808.07665v3 |
2018-10-19 | Magnon properties of random alloys | We study magnon properties in terms of spin stiffness, Curie temperatures and
magnon spectrum of Fe-Ni, Co-Ni and Fe-Co random alloys using a combination of
electronic structure calculations and atomistic spin dynamics simulations.
Influence of the disorder are studied in detail by use of large supercells with
random atomic arrangement. It is found that disorder affects the magnon
spectrum in vastly different ways depending on the system. Specifically, it is
more pronounced in Fe-Ni alloys compared to Fe-Co alloys. In particular, the
magnon spectrum at room temperature in Permalloy (Fe$_{20}$Ni$_{80}$) is found
to be rather diffuse in a large energy interval while in Fe$_{75}$Co$_{25}$ it
forms sharp branches. Fe-Co alloys are very interesting from a technological
point of view due to the combination of large Curie temperatures and very low
calculated Gilbert damping of $\sim$0.0007 at room temperature for Co
concentrations around 20--30\%. | 1810.08487v1 |
2015-12-02 | Bose-Einstein Condensation of Magnons Pumped by the Bulk Spin Seebeck Effect | We propose inducing Bose-Einstein condensation of magnons in a magnetic
insulator by a heat flow oriented toward its boundary. At a critical heat flux,
the oversaturated thermal gas of magnons accumulated at the boundary
precipitates the condensate, which then grows gradually as the thermal bias is
dialed up further. The thermal magnons thus pumped by the magnonic bulk (spin)
Seebeck effect must generally overcome both the local Gilbert damping
associated with the coherent magnetic dynamics as well as the radiative
spin-wave losses toward the magnetic bulk, in order to achieve the threshold of
condensation. We quantitatively estimate the requisite bias in the case of the
ferrimagnetic yttrium iron garnet, discuss different physical regimes of
condensation, and contrast it with the competing (so-called Doppler-shift) bulk
instability. | 1512.00557v1 |
2008-11-13 | Intrinsic Coupling between Current and Domain Wall Motion in (Ga,Mn)As | We consider current-induced domain wall motion and, the reciprocal process,
moving domain wall-induced current. The associated Onsager coefficients are
expressed in terms of scattering matrices. Uncommonly, in (Ga,Mn)As, the
effective Gilbert damping coefficient $\alpha_w$ and the effective out-of-plane
spin transfer torque parameter $\beta_w$ are dominated by spin-orbit
interaction in combination with scattering off the domain wall, and not
scattering off extrinsic impurities. Numerical calculations give $\alpha_w \sim
0.01$ and $\beta_w \sim 1$ in dirty (Ga,Mn)As. The extraordinary large
$\beta_w$ parameter allows experimental detection of current or voltage induced
by domain wall motion in (Ga,Mn)As. | 0811.2235v2 |
2008-11-21 | Spin Transfer Torque as a Non-Conservative Pseudo-Field | In this paper we show that the spin transfer torque can be described by a
pseudo magnetic field, proportional to the magnetic moment of the itinerant
electrons that enters the Landau-Lifshitz-Gilbert equation in the same way as
other external or internal magnetic fields. However, unlike an ordinary
magnetic field, which is always conservative in nature, the spin torque induced
pseudo field may have both conservative and non-conservative components. We
further show that the magnetic moment of itinerant electrons develops an
out-of-plane component only at non-equilibrium and this component is
responsible for the Slonczewski type switching that acts against the damping
and is always non-conservative. On the other hand, the in-plane components of
the pseudo field exist both at equilibrium and out-of-equilibrium, and are
responsible for the field like term. For tunnel based devices, this term
results in lower switching current for anti-parallel (AP) to parallel (P)
switching compared to P to AP, even when the torque magnitudes are completely
symmetric with voltage. | 0811.3472v1 |
2019-09-11 | Chaos in nanomagnet via feedback current | Nonlinear magnetization dynamics excited by spin-transfer effect with
feedback current is studied both numerically and analytically. The numerical
simulation of the Landau-Lifshitz-Gilbert equation indicates the positive
Lyapunov exponent for a certain range of the feedback rate, which identifies
the existence of chaos in a nanostructured ferromagnet. Transient behavior from
chaotic to steady oscillation is also observed in another range of the feedback
parameter. An analytical theory is also developed, which indicates the
appearance of multiple attractors in a phase space due to the feedback current.
An instantaneous imbalance between the spin-transfer torque and damping torque
causes a transition between the attractors, and results in the complex
dynamics. | 1909.05315v2 |
2020-03-24 | Spin-transfer torque driven intrinsic localized spin excitations in the presence of field-like torque | We study the existence of intrinsic localized one-spin excitation in the
Heisenberg one-dimensional ferromagnetic spin chain in the presence of
perpendicular and parallel external magnetic fields and current with
spin-transfer torque and field-like torque. The
Landau-Lifshitz-Gilbert-Slonczewski(LLGS) equation is exactly solved for the
one spin excitation in the absence of onsite anisotropy for the excitations of
spin with fields perpendicular and parallel to the chain. We show the removal
of damping in the spin excitations by appropriately introducing current and
also the enhancement of angular frequency of the oscillations due to field-like
torque in the case of both perpendicular and parallel field. The exactness of
the analytical results is verified by matching with numerical counterparts.
Further, we numerically confirm the existence of in-phase and anti-phase stable
synchronized oscillations for two spin-excitations in the presence of current
with perpendicular field and field-like torque. | 2003.11023v2 |
2020-04-02 | Stable solitons in a nearly PT-symmetric ferromagnet with spin-transfer torque | We consider the Landau-Lifshitz equation for the spin torque oscillator - a
uniaxial ferromagnet in an external magnetic field with polarised spin current
driven through it. In the absence of the Gilbert damping, the equation turns
out to be PT-symmetric. We interpret the PT-symmetry as a balance between gain
and loss - and identify the gaining and losing modes. In the vicinity of the
bifurcation point of a uniform static state of magnetisation, the PT-symmetric
Landau-Lifshitz equation with a small dissipative perturbation reduces to a
nonlinear Schr\"odinger equation with a quadratic nonlinearity. The analysis of
the Schr\"odinger dynamics demonstrates that the spin torque oscillator
supports stable magnetic solitons. The PT near-symmetry is crucial for the
soliton stability: the addition of a finite dissipative term to the
Landau-Lifshitz equation destabilises all solitons that we have found. | 2004.01245v2 |
2020-08-21 | Integration and characterization of micron-sized YIG structures with very low Gilbert damping on arbitrary substrates | We present a novel process that allows the transfer of monocrystalline
yttrium-iron-garnet microstructures onto virtually any kind of substrate. The
process is based on a recently developed method that allows the fabrication of
freestanding monocrystalline YIG bridges on gadolinium-gallium-garnet. Here the
bridges' spans are detached from the substrate by a dry etching process and
immersed in a watery solution. Using drop casting the immersed YIG platelets
can be transferred onto the substrate of choice, where the structures finally
can be reattached and thus be integrated into complex devices or experimental
geometries. Using time resolved scanning Kerr microscopy and inductively
measured ferromagnetic resonance we can demonstrate that the structures retain
their excellent magnetic quality. At room temperature we find a ferromagnetic
resonance linewidth of $\mu_0\Delta H_{HWHM}\approx 195\,\mu T$ and we were
even able to inductively measure magnon spectra on a single micron-sized
yttrium-iron-garnet platelet at a temperature of 5 K. The process is flexible
in terms of substrate material and shape of the structure. In the future this
approach will allow for new types of spin dynamics experiments up to now
unthinkable. | 2008.09390v1 |
2021-05-24 | Spin pumping of two-dimensional electron gas with Rashba and Dresselhaus spin-orbit interactions | We theoretically consider spin pumping in a junction between a ferromagnetic
insulator (FI) and a two-dimensional electron gas (2DEG) in which the Rashba
and Dresselhaus spin-orbit interactions coexist. Using second-order
perturbation theory, we derive an increase in linewidth in the case of an
interfacial exchange coupling in a ferromagnetic resonance (FMR) experiment. We
clarify how the enhancement of Gilbert damping depends on the resonant
frequency and spin orientation of the FI. We show that this setup of an FMR
experiment can provide information on the spin texture of 2DEG at the Fermi
surface. | 2105.11193v3 |
2015-02-19 | Characterization of spin relaxation anisotropy in Co using spin pumping | Ferromagnets are believed to exhibit strongly anisotropic spin relaxation,
with relaxation lengths for spin longitudinal to magnetization significantly
longer than those for spin transverse to magnetization. Here we characterize
the anisotropy of spin relaxation in Co using the spin pumping contribution to
Gilbert damping in noncollinearly magnetized Py$_{1-x}$Cu$_{x}$/Cu/Co trilayer
structures. The static magnetization angle between Py$_{1-x}$Cu$_{x}$ and Co,
adjusted under field bias perpendicular to film planes, controls the
projections of longitudinal and transverse spin current pumped from
Py$_{1-x}$Cu$_{x}$ into Co. We find nearly isotropic absorption of pure spin
current in Co using this technique; fits to a diffusive transport model yield
the longitudinal spin relaxation length $< 2$ nm in Co. The longitudinal spin
relaxation lengths found are an order of magnitude smaller than those
determined by current-perpendicular-to-planes giant magnetoresistance
measurements, but comparable with transverse spin relaxation lengths in Co
determined by spin pumping. | 1502.05687v3 |
2016-06-07 | The temperature dependence of FeRh's transport properties | The finite-temperature transport properties of FeRh compounds are
investigated by first-principles Density Functional Theory-based calculations.
The focus is on the behavior of the longitudinal resistivity with rising
temperature, which exhibits an abrupt decrease at the metamagnetic transition
point, $T = T_m$ between ferro- and antiferromagnetic phases. A detailed
electronic structure investigation for $T \geq 0$ K explains this feature and
demonstrates the important role of (i) the difference of the electronic
structure at the Fermi level between the two magnetically ordered states and
(ii) the different degree of thermally induced magnetic disorder in the
vicinity of $T_m$, giving different contributions to the resistivity. To
support these conclusions, we also describe the temperature dependence of the
spin-orbit induced anomalous Hall resistivity and Gilbert damping parameter.
For the various response quantities considered the impact of thermal lattice
vibrations and spin fluctuations on their temperature dependence is
investigated in detail. Comparison with corresponding experimental data finds
in general a very good agreement. | 1606.02072v1 |
2018-02-05 | Cooper-Pair Spin Current in a Strontium Ruthenate Heterostructure | It has been recognized that the condensation of spin-triplet Cooper pairs
requires not only the broken gauge symmetry but also the spin ordering as well.
One consequence of this is the possibility of the Cooper-pair spin current
analogous to the magnon spin current in magnetic insulators, the analogy also
extending to the existence of the Gilbert damping of the collective
spin-triplet dynamics. The recently fabricated heterostructure of the thin film
of the itinerant ferromagnet SrRuO3 on the bulk Sr2RuO4, the best-known
candidate material for the spin-triplet superconductor, offers a promising
platform for generating such spin current. We will show how such
heterostructure allows us to not only realize the long-range spin valve but
also electrically drive the collective spin mode of the spin-triplet order
parameter. Our proposal represents both a new realization of the spin
superfluidity and a transport signature of the spin-triplet superconductivity. | 1802.01599v1 |
2018-02-12 | Spin-orbit torque and spin pumping in YIG/Pt with interfacial insertion layers | We experimentally investigate spin-orbit torque and spin pumping in
Y$_3$Fe$_5$O$_{12}$(YIG)/Pt bilayers with ultrathin insertion layers at the
interface. An insertion layer of Cu suppresses both spin-orbit torque and spin
pumping, whereas an insertion layer of Ni$_{80}$Fe$_{20}$ (permalloy, Py)
enhances them, in a quantitatively consistent manner with the reciprocity of
the two spin transmission processes. However, we observe a large enhancement of
Gilbert damping with the insertion of Py that cannot be accounted for solely by
spin pumping, suggesting significant spin-memory loss due to the interfacial
magnetic layer. Our findings indicate that the magnetization at the YIG-metal
interface strongly influences the transmission and depolarization of pure spin
current. | 1802.03865v3 |
2018-11-09 | Switching of biaxial synthetic antiferromagnets: a micromagentic study | We simulate the switching behavior of nanoscale synthetic antiferromagnets
(SAFs), inspired by recent experimental progress in spin-orbit-torque switching
of crystal antiferromagnets. The SAF consists of two ferromagnetic thin films
with in-plane biaxial anisotropy and interlayer exchange coupling. Staggered
field-like Rashba spin-orbit torques from the opposite surfaces of the SAF
induce a canted net magnetization, which triggers an orthogonal torque that
drives 90$^\circ$ switching of the N\'eel vector. Such dynamics driven by the
field-like spin-orbit torque allows for faster switching with increased Gilbert
damping, without a significant detrimental increase of the threshold switching
current density. Our results point to the potential of SAFs as model systems,
based on simple ferromagnetic metals, to mimic antiferromagnetic device
physics. | 1811.04094v2 |
2019-02-12 | Characterization of spin wave propagation in (111) YIG thin films with large anisotropy | We report on long-range spin wave (SW) propagation in nanometer-thick yttrium
iron garnet (YIG) film with an ultralow Gilbert damping. The knowledge of a
wavenumber value $|\vec{k}|$ is essential for designing SW devices. Although
determining the wavenumber $|\vec{k}|$ in experiments like Brillouin light
scattering spectroscopy is straightforward, quantifying the wavenumber in
all-electrical experiments has not been widely commented upon so far. We
analyze magnetostatic spin wave (SW) propagation in YIG films in order to
determine the SW wavenumber $|\vec{k}|$ excited by the coplanar waveguide. We
show that it is crucial to consider the influence of magnetic anisotropy fields
present in YIG thin films for precise determination of SW wavenumber. With the
proposed methods we find that experimentally derived values of $|\vec{k}|$ are
in perfect agreement with that obtained from electromagnetic simulation only if
anisotropy fields are included. | 1902.04608v1 |
2019-03-20 | Nonlinear magnetization dynamics driven by strong terahertz fields | We present a comprehensive experimental and numerical study of magnetization
dynamics triggered in a thin metallic film by single-cycle terahertz pulses of
$\sim20$ MV/m electric field amplitude and $\sim1$ ps duration. The
experimental dynamics is probed using the femtosecond magneto-optical Kerr
effect (MOKE), and it is reproduced numerically using macrospin simulations.
The magnetization dynamics can be decomposed in three distinct processes: a
coherent precession of the magnetization around the terahertz magnetic field,
an ultrafast demagnetization that suddenly changes the anisotropy of the film,
and a uniform precession around the equilibrium effective field that is relaxed
on the nanosecond time scale, consistent with a Gilbert damping process.
Macrospin simulations quantitatively reproduce the observed dynamics, and allow
us to predict that novel nonlinear magnetization dynamics regimes can be
attained with existing table-top terahertz sources. | 1903.08395v2 |
2019-04-11 | Measurement of spin mixing conductance in Ni$_{81}$Fe$_{19}$/$α$-W and Ni$_{81}$Fe$_{19}$/$β$-W heterostrucutures via ferromagnetic resonance | We present measurements of interfacial Gilbert damping due to the spin
pumping effect in Ni$_{81}$Fe$_{19}$/W heterostructures. Measurements were
compared for heterostructures in which the crystallographic phase of W, either
$\alpha$(bcc)-W or $\beta$(A15)-W, was enriched through deposition conditions
and characterized using X-ray diffraction (XRD) and high-resolution
cross-sectional transmission electron microscopy (HR-XTEM). Single phase
Ni$_{81}$Fe$_{19}$/$\alpha$-W heterostructures could be realized, but
heterostructures with $\beta$-W were realized as mixed $\alpha$-$\beta$ phase.
The spin mixing conductances (SMC) for W at interfaces with Ni$_{81}$Fe$_{19}$
were found to be significantly lower than those for similarly heavy metals such
as Pd and Pt, but comparable to those for Ta, and independent of enrichment in
the $\beta$ phase. | 1904.05950v2 |
2019-05-26 | Influence of field-like torque in synchronization of spin torque oscillators | The magnetization dynamics of two parallelly coupled spin torque oscillators,
destabilization of steady states and removal of multistability, are
investigated by taking into account the influence of field-like torque. It is
shown that the existence of such torque can cancel the effect of damping and
can, therefore, cause the oscillators to exhibit synchronized oscillations in
response to direct current. Further, our results show that the presence of
field-like torque enhances the power and Q-factor of the synchronized
oscillations. The validity of the above results is confirmed by numerical and
analytical studies based on the stochastic Landau-Lifshitz-Gilbert-Slonczewski
equation. | 1905.10804v2 |
2019-05-30 | Sub-nanosecond switching in a cryogenic spin-torque spin-valve memory element with a dilute permalloy free layer | We present a study of the pulsed current switching characteristics of
spin-valve nanopillars with in-plane magnetized dilute permalloy and undiluted
permalloy free layers in the ballistic regime at low temperature. The dilute
permalloy free layer device switches much faster: the characteristic switching
time for a permalloy free (Ni0.83Fe0.17) layer device is 1.18 ns, while that
for a dilute permalloy ([Ni0.83Fe0.17]0.6Cu0.4) free layer device is 0.475 ns.
A ballistic macrospin model can capture the data trends with a reduced spin
torque asymmetry parameter, reduced spin polarization and increased Gilbert
damping for the dilute permalloy free layer relative to the permalloy devices.
Our study demonstrates that reducing the magnetization of the free layer
increases the switching speed while greatly reducing the switching energy and
shows a promising route toward even lower power magnetic memory devices
compatible with superconducting electronics. | 1905.13262v1 |
2019-07-05 | Theory for shift current of bosons: Photogalvanic spin current in ferrimagnetic and antiferromagnetic insulators | We theoretically study the optical generation of dc spin current (i.e., a
spin-current solar cell) in ordered antiferromagnetic and ferrimagnetic
insulators, motivated by a recent study on the laser-driven spinon spin current
in noncentrosymmetric quantum spin chains [H. Ishizuka and M. Sato, Phys. Rev.
Lett. 122, 197702 (2019)]. Using a non-linear response theory for magnons, we
analyze the dc spin current generated by a linearly-polarized electromagnetic
wave (typically, terahertz or gigahertz waves). Considering noncentrosymmetric
two-sublattice magnets as an example, we find a finite dc spin current
conductivity at $T=0$, where no thermally-excited magnons exist; this is in
contrast to the case of the spinon spin current, in which the optical
transition of the Fermi degenerate spinons plays an essential role. We find
that the dc spin-current conductivity is insensitive to the Gilbert damping,
i.e., it may be viewed as a shift current carried by bosonic particles
(magnons). Our estimate shows that an electric-field intensity of
$E\sim10^4-10^6$ V/cm is sufficient for an observable spin current. Our theory
indicates that the linearly-polarized electromagnetic wave generally produces a
dc spin current in noncentrosymmetric magnetic insulators. | 1907.02734v1 |
2019-07-10 | Temperature dependence of magnetic resonance in ferrimagnetic GdFeCo alloys | We provide a macroscopic theory and experimental results for magnetic
resonances of antiferromagnetically-coupled ferrimagnets. Our theory, which
interpolates the dynamics of antiferromagnets and ferromagnets smoothly, can
describe ferrimagnetic resonances across the angular momentum compensation
point. We also present experimental results for spin-torque induced
ferrimagnetic resonance at several temperatures. The spectral analysis based on
our theory reveals that the Gilbert damping parameter, which has been
considered to be strongly temperature dependent, is insensitive to temperature.
We envision that our work will facilitate further investigation of
ferrimagnetic dynamics by providing a theoretical framework suitable for a
broad range of temperatures. | 1907.04540v1 |
2019-07-11 | Improving the Signal-to-noise Ratio for Heat-Assisted Magnetic Recording by Optimizing a High/Low Tc bilayer structure | We optimize the recording medium for heat-assisted magnetic recording by
using a high/low $T_{\mathrm{c}}$ bilayer structure to reduce AC and DC noise.
Compared to a former work, small Gilbert damping $\alpha=0.02$ is considered
for the FePt like hard magnetic material. Atomistic simulations are performed
for a cylindrical recording grain with diameter $d=5\,$nm and height $h=8\,$nm.
Different soft magnetic material compositions are tested and the amount of hard
and soft magnetic material is optimized. The results show that for a soft
magnetic material with $\alpha_{\mathrm{SM}}=0.1$ and
$J_{ij,\mathrm{SM}}=7.72\times 10^{-21}\,$J/link a composition with $50\%$ hard
and $50\%$ soft magnetic material leads to the best results. Additionally, we
analyse how much the areal density can be improved by using the optimized
bilayer structure compared to the pure hard magnetic recording material. It
turns out that the optimized bilayer design allows an areal density that is
$1\,$Tb/in$^2$ higher than that of the pure hard magnetic material while
obtaining the same SNR. | 1907.05027v1 |
2019-07-19 | A cryogenic memory element based on an anomalous Josephson junction | We propose a non-volatile memory element based on a lateral ferromagnetic
Josephson junction with spin-orbit coupling and out-of-plane magnetization. The
interplay between the latter and the intrinsic exchange field of the
ferromagnet leads to a magnetoelectric effect that couples the charge current
through the junction and its magnetization, such that by applying a current
pulse the direction of the magnetic moment in F can be switched. The two memory
states are encoded in the direction of the out-of-plane magnetization. With the
aim to determine the optimal working temperature for the memory element, we
explore the noise-induced effects on the averaged stationary magnetization by
taking into account thermal fluctuations affecting both the Josephson phase and
the magnetic moment dynamics. We investigate the switching process as a
function of intrinsic parameters of the ferromagnet, such as the Gilbert
damping and strength of the spin-orbit coupling, and proposed a non-destructive
readout scheme based on a dc-SQUID. Additionally, we analyze a way to protect
the memory state from external perturbations by voltage gating in systems with
a both linear-in-momentum Rashba and Dresselhaus spin-orbit coupling. | 1907.08454v2 |
2019-07-23 | Electron transport in high-entropy alloys: Al$_{x}$CrFeCoNi as a case study | The high-entropy alloys Al$_{x}$CrFeCoNi exist over a broad range of Al
concentrations ($0 < x < 2$). With increasing Al content their structure is
changed from the fcc to bcc phase. We investigate the effect of such structural
changes on transport properties including the residual resistivity and the
anomalous Hall resistivity. We have performed a detailed comparison of the
first-principles simulations with available experimental data. We show that the
calculated residual resistivities for all studied alloy compositions are in a
fair agreement with available experimental data as concerns both the
resistivity values and concentration trends. We emphasize that a good agreement
with experiment was obtained also for the anomalous Hall resistivity. We have
completed study by estimation of the anisotropic magnetoresistance,
spin-disorder resistivity, and Gilbert damping. The obtained results prove that
the main scattering mechanism is due to the intrinsic chemical disorder whereas
the effect of spin polarization on the residual resistivity is appreciably
weaker. | 1907.09731v1 |
2019-11-27 | Ellipticity and Dissipation Effects in Magnon Spin Valves | We consider alignment-dependent spin and heat transport across a magnon spin
valve in the tunneling regime, i.e., a junction consisting of two weakly
coupled ferromagnetic insulators. We determine the difference in spin and heat
conductance between the parallel and antiparallel configuration of the
magnetization direction. The dependence of these conductances on both the
Gilbert damping and ellipticity is studied. We find that both magnon
ellipticity and dissipation open channels for magnons to tunnel through in the
antiparallel configuration. Our results highlight an important difference
between electronic and magnon spin transport in spin-valve structures and may
be important for the development of devices based on magnetic insulators. | 1911.12017v2 |
2020-07-08 | Finite-frequency spin susceptibility and spin pumping in superconductors with spin-orbit relaxation | Static spin susceptibility of superconductors with spin-orbit relaxation has
been calculated in the seminal work of A.A. Abrikosov and L.P. Gor'kov [Sov.
Phys. JETP, {\bf 15}, 752 (1962)]. Surprisingly the generalization of this
result to finite frequencies has not been done despite being quite important
for the modern topic of superconducting spintronics. The present paper fills
this gap by deriving the analytical expression for spin susceptibility. The
time-dependent spin response is shown to be captured by the quasiclassical
Eilenberger equation with collision integrals corresponding to the ordinary and
spin-orbit scattering. Using the developed formalism we study the linear spin
pumping effect between the ferromagnet and the adjacent superconducting film.
The consequences for understanding recent experiments demonstrating the
modification of Gilbert damping by the superconducting correlations are
discussed. | 2007.04372v2 |
2020-07-16 | Thermal noise effects on the magnetization switching of a ferromagnetic anomalous Josephson junction | We discuss the effects of thermal noise on the magnetic response of a lateral
ferromagnetic Josephson junction with spin-orbit coupling and out-of-plane
magnetization. The direction of the magnetic moment in the ferromagnetic layer
can be inverted by using controlled current pulses. This phenomenon is due to
the magnetoelectric effect that couples the flowing charge current and the
magnetization of the ferromagnet. We investigate the magnetization reversal
effect versus intrinsic parameters of the ferromagnet, such as the Gilbert
damping and strength of the spin-orbit coupling. We estimate the magnetization
reversing time and find the optimal values of the parameters for fast
switching. With the aim of increasing the operation temperature we study the
effects induced by thermal fluctuations on the averaged stationary
magnetization, and find the conditions that make the system more robust against
noise. | 2007.08414v3 |
2020-09-01 | Quantum Brownian Motion for Magnets | Spin precession in magnetic materials is commonly modelled with the classical
phenomenological Landau-Lifshitz-Gilbert (LLG) equation. Based on a quantized
spin+environment Hamiltonian, we here derive a general spin operator equation
of motion that describes three-dimensional precession and damping and
consistently accounts for effects arising from memory, coloured noise and
quantum statistics. The LLG equation is recovered as its classical, Ohmic
approximation. We further introduce resonant Lorentzian system--reservoir
couplings that allow a systematic comparison of dynamics between Ohmic and
non--Ohmic regimes. Finally, we simulate the full non-Markovian dynamics of a
spin in the semi--classical limit. At low temperatures, our numerical results
demonstrate a characteristic reduction and flattening of the steady state spin
alignment with an external field, caused by the quantum statistics of the
environment. The results provide a powerful framework to explore general
three-dimensional dissipation in quantum thermodynamics. | 2009.00600v2 |
2020-09-30 | Quantum hydrodynamics of spin winding | An easy-plane spin winding in a quantum spin chain can be treated as a
transport quantity, which propagates along the chain but has a finite lifetime
due to phase slips. In a hydrodynamic formulation for the winding dynamics, the
quantum continuity equation acquires a source term due to the transverse
vorticity flow. The latter reflects the phase slips and generally compromises
the global conservation law. A linear-response formalism for the nonlocal
winding transport then reduces to a Kubo response for the winding flow along
the spin chain, in conjunction with the parasitic vorticity flow transverse to
it. One-dimensional topological hydrodynamics can be recovered when the
vorticity flow is asymptotically small. Starting with a microscopic spin-chain
formulation, we focus on the asymptotic behavior of the winding transport based
on the renormalized sine-Gordon equation, incorporating phase slips as well as
Gilbert damping. A generic electrical device is proposed to manifest this
physics. We thus suggest winding conductivity as a tangible concept that can
characterize low-energy dynamics in a broad class of quantum magnets. | 2010.00144v1 |
2020-11-29 | Cross-sublattice Spin Pumping and Magnon Level Attraction in van der Waals Antiferromagnets | We theoretically study spin pumping from a layered van der Waals
antiferromagnet in its canted ground state into an adjacent normal metal. We
find that the resulting dc spin pumping current bears contributions along all
spin directions. Our analysis allows for detecting intra- and cross-sublattice
spin-mixing conductances via measuring the two in-plane spin current
components. We further show that sublattice symmetry-breaking Gilbert damping
can be realized via interface engineering and induces a dissipative coupling
between the optical and acoustic magnon modes. This realizes magnon level
attraction and exceptional points in the system. Furthermore, the dissipative
coupling and cross-sublattice spin pumping contrive to produce an
unconventional spin current in the out-of-plane direction. Our findings provide
a route to extract the spin mixing conductance matrix and uncovers the unique
opportunities, such as level attraction, offered by van der Waals
antiferromagnet-normal metal hybrids. | 2011.14314v1 |
2021-01-18 | Topological electric driving of magnetization dynamics in insulators | Established forms of electromagnetic coupling are usually conservative (in
insulators) or dissipative (in metals and semiconductors). Here we point out
the possibility of nondissipative electric driving of magnetization dynamics,
if the valence electronic states have nontrivial topology in the combined space
of crystal momentum and magnetization configuration. We provide a hybrid
insulator system to demonstrate that the topology-based nonconservative
electrical generalized force is capable of supporting sustained magnetization
motion in the presence of Gilbert damping, with quantized and steady energy
pumping into magnetization motion from the electric field. We also generalize
our results to magnetic textures, and discuss electric field induced
Dzyaloshinskii-Moriya interaction which can be nonconservative. | 2101.07164v3 |
2021-02-07 | Spinterface Induced Modification in Magnetic Properties in Co40Fe40B20/Fullerene Bilayers | Organic semiconductor/ferromagnetic bilayer thin films can exhibit novel
properties due to the formation of the spinterface at the interface.
Buckminsterfullerene (C60) has been shown to exhibit ferromagnetism at the
interface when it is placed next to a ferromagnet (FM) such as Fe or Co.
Formation of spinterface occurs due to the orbital hybridization and spin
polarized charge transfer at the interface. In this work, we have demonstrated
that one can enhance the magnetic anisotropy of the low Gilbert damping alloy
CoFeB by introducing a C60 layer. We have shown that anisotropy increases by
increasing the thickness of C60 which might be a result of the formation of
spinterface. However, the magnetic domain structure remains same in the bilayer
samples as compared to the reference CoFeB film. | 2102.03914v4 |
2021-08-05 | Spin-transfer torque driven localized spin excitations in the presence of field-like torque | We study the existence of localized one-spin excitation in the Heisenberg
one-dimensional ferromagnetic spin chain in the presence of perpendicular and
parallel external magnetic fields and current with spin-transfer torque and
field-like torque. The Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation is
exactly solved for the one spin excitation in the absence of onsite anisotropy
for the excitations of spin with fields perpendicular and parallel to the
chain. We show the removal of damping in the spin excitations by appropriately
introducing current and also the enhancement of angular frequency of the
oscillations due to field-like torque in the case of both perpendicular and
parallel field. The exactness of the analytical results is verified by matching
with numerical counterparts. Further, we numerically confirm the existence of
in-phase and anti-phase stable synchronized oscillations for two
spin-excitations in the presence of current with perpendicular field and
field-like torque. We also show that the one-spin excitation is stable against
thermal noise and gets only slightly modified against thermal fluctuations. | 2108.02380v1 |
2021-09-07 | Inertial spin dynamics in epitaxial cobalt films | We investigate the spin dynamics driven by terahertz magnetic fields in
epitaxial thin films of cobalt in its three crystalline phases. The terahertz
magnetic field generates a torque on the magnetization which causes it to
precess for about 1 ps, with a sub-picosecond temporal lag from the driving
force. Then, the magnetization undergoes natural damped THz oscillations at a
frequency characteristic of the crystalline phase. We describe the experimental
observations solving the inertial Landau-Lifshitz-Gilbert equation. Using the
results from the relativistic theory of magnetic inertia, we find that the
angular momentum relaxation time $\eta$ is the only material parameter needed
to describe all the experimental evidence. Our experiments suggest a
proportionality between $\eta$ and the strength of the magneto-crystalline
anisotropy. | 2109.03076v2 |
2021-09-26 | Transition state dynamics of a driven magnetic free layer | Magnetization switching in ferromagnetic structures is an important process
for technical applications such as data storage in spintronics, and therefore
the determination of the corresponding switching rates becomes essential. We
investigate a free-layer system in an oscillating external magnetic field
resulting in an additional torque on the spin. The magnetization dynamics
including inertial damping can be described by the phenomenological Gilbert
equation. The magnetization switching between the two stable orientations on
the sphere then requires the crossing of a potential region characterized by a
moving rank-1 saddle. We adopt and apply recent extensions of transition state
theory for driven systems to compute both the time-dependent and average
switching rates of the activated spin system in the saddle region. | 2109.12605v1 |
2021-12-24 | Skyrmion nucleation on the surface of a topological insulator | Skyrmion nucleation induced by spin-transfer torques at an interface of a
topological insulator and a ferromagnetic insulator is investigated. Due to
strong spin-orbit coupling on a surface of topological insulators, which
enhances the effect of spin torques, efficient manipulation of skyrmions is
expected, and therefore, topological insulators could provide the ideal
platform to achieve high-performance skyrmionic devices. Using micromagnetic
simulations and energetics, we evaluate properties of the skyrmion nucleation
on a surface of topological insulators, such as nucleation time, critical
electric field, and skyrmion numbers. We show that the nucleation time is
inversely proportional to the applied electric field. We also identify the
Gilbert damping and temperature dependencies of the critical field.
Furthermore, we analytically evaluate the effect of the Dzyaloshinskii-Moriya
interaction and demonstrate that the temperature dependence can be explained by
the reduction of a magnon excitation gap due to the self-energy corrections. | 2112.12967v2 |
2021-12-10 | Enhanced Planar Antenna Efficiency Through Magnetic Thin-Films | This work proposes to use magnetic material as the substrate of planar
antennas to overcome the platform effect caused by the conducting ground plane.
The upper bound of the radiation efficiency of an electric-current-driven
low-profile antenna is theoretically derived, which is inversely proportional
to the Gilbert damping factor of the magnetic material. Meanwhile, the
improvement of radiation due to the use of magnetic material is demonstrated by
a three-dimensional (3D) multiphysics and multiscale time-domain model. The
simulation results match the theoretical derivation, showing 25% radiation
efficiency from a planar antenna backed by a FeGaB thin film with 2.56 um
thickness. Furthermore, for conductive ferromagnetic materials, it is shown
that the eddy current loss can be well suppressed by laminating the thin film
into multiple layers. The radiation efficiency of the modeled antenna with a
conductive ferromagnetic substrate is improved from 2.2% to 11.8% by dividing
the substrate into 10 layers, with a ferromagnetic material fill factor of 93%. | 2201.04932v1 |
2022-03-07 | Ultrafast optical observation of spin-pumping induced dynamic exchange coupling in ferromagnetic semiconductor/metal bilayer | Spin angular momentum transfer in magnetic bilayers offers the possibility of
ultrafast and low-loss operation for next-generation spintronic devices. We
report the field- and temperature- dependent measurements on the magnetization
precessions in Co$_2$FeAl/(Ga,Mn)As by time-resolved magneto-optical Kerr
effect (TRMOKE). Analysis of the effective Gilbert damping and phase shift
indicates a clear signature of an enhanced dynamic exchange coupling between
the two ferromagnetic (FM) layers due to the reinforced spin pumping at
resonance. The temperature dependence of the dynamic exchange-coupling reveals
a primary contribution from the ferromagnetism in (Ga,Mn)As. | 2203.03225v2 |
2022-04-21 | Transport theory for topological Josephson junctions with a Majorana qubit | We construct a semiclassical theory for the transport of topological
junctions starting from a microscopic Hamiltonian that comprehensively includes
the interplay among the Majorana qubit, the Josephson phase, and the
dissipation process. With the path integral approach, we derive a set of
semiclassical equations of motion that can be used to calculate the time
evolution of the Josephson phase and the Majorana qubit. In the equations we
reveal rich dynamical phenomena such as the qubit induced charge pumping, the
effective spin-orbit torque, and the Gilbert damping. We demonstrate the
influence of these dynamical phenomena on the transport signatures of the
junction. We apply the theory to study the Shapiro steps of the junction, and
find the suppression of the first Shapiro step due to the dynamical feedback of
the Majorana qubit. | 2204.09923v1 |
2022-04-22 | A short-circuited coplanar waveguide for low-temperature single-port ferromagnetic resonance spectroscopy set-up to probe the magnetic properties of ferromagnetic thin films | A coplanar waveguide shorted in one end is proposed, designed, and
implemented successfully to measure the properties of magnetic thin films as a
part of the vector network analyzer ferromagnetic resonance (VNA-FMR)
spectroscopy set-up. Its simple structure, potential applications and easy
installation inside the cryostat chamber made it advantageous especially for
low-temperature measurements. It provides a wide band of frequencies in the
gigahertz range essential for FMR measurements. Our spectroscopy set-up with
short-circuited coplanar waveguide has been used to extract Gilbert damping
coefficient and effective magnetization values for standard ferromagnetic thin
films like Py and Co. The thickness and temperature dependent studies of those
magnetic parameters have also been done here for the afore mentioned magnetic
samples. | 2204.10596v2 |
2022-11-04 | Derivation of Interacting Two-Qubit Dynamics from Spin-Boson Model | We derive damping equations of motion for interacting two-spin states from a
spin-boson model in order to examine qubit dynamics in quantum computers. On
the basis of the composite operator method, we develop the Caldeira-Leggett
approach for open quantum systems so that the entanglement dynamics originated
from the two-spin correlation can be taken. We demonstrate numerical results
for time dependence on the two-spin dynamics. We find that the relaxation of
the total spin is described by a quantum version of the Landau-Lifshitz-Gilbert
equation for magnetic materials. We also find that a two-spin composite mode
keeps oscillation even after the total spin has been fully relaxed. We thus
conclude that the two-spin correlation due to the presence of the composite
mode is stable against dissipation. We consider the mechanism of why the
correlation is maintained. | 2211.02490v1 |
2023-02-06 | Global solutions of the Landau--Lifshitz--Baryakhtar equation | The Landau--Lifshitz--Baryakhtar (LLBar) equation is a generalisation of the
Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch equations which takes
into account contributions from nonlocal damping and is valid at moderate
temperature below the Curie temperature. Therefore, it is used to explain some
discrepancies between the experimental observations and the known theories in
various problems on magnonics and magnetic domain-wall dynamics. In this paper,
the existence and uniqueness of global weak, strong, and regular solutions to
LLBar equation are proven. H\"older continuity of the solution is also
discussed. | 2302.02556v3 |
2023-03-22 | Twisted bilayer graphene reveals its flat bands under spin pumping | The salient property of the electronic band structure of twisted bilayer
graphene (TBG), at the so-called magic angle (MA), is the emergence of flat
bands around the charge neutrality point. These bands are associated with the
observed superconducting phases and the correlated insulating states. Scanning
tunneling microscopy combined with angle resolved photoemission spectroscopy
are usually used to visualize the flatness of the band structure of TBG at the
MA. Here, we theoretically argue that spin pumping (SP) provides a direct probe
of the flat bands of TBG and an accurate determination of the MA. We consider a
junction separating a ferromagnetic insulator and a heterostructure of TBG
adjacent to a monolayer of a transition metal dichalcogenide. We show that the
Gilbert damping of the ferromagnetic resonance experiment, through this
junction, depends on the twist angle of TBG, and exhibits a sharp drop at the
MA. We discuss the experimental realization of our results which open the way
to a twist switchable spintronics in twisted van der Waals heterostructures. | 2303.12380v2 |
2023-05-01 | Coherent and incoherent magnons induced by strong ultrafast demagnetization in thin permalloy films | Understanding spin dynamics on femto- and picosecond timescales offers new
opportunities for faster and more efficient spintronic devices. Here, we
experimentally investigate the coherent spin dynamics after ultrashort laser
excitation by time-resolved magneto optical Kerr effect (TR-MOKE) in thin
Ni80Fe20 films. We provide a detailed study of the magnetic field and pump
fluence dependence of the coherent precessional dynamics. We show that the
coherent precession lifetime increases with the applied external magnetic field
which cannot be understood by viscous Gilbert damping of the coherent magnons.
Instead, it can be explained by nonlinear magnon interactions and by the change
in the fraction of incoherent magnons. This interpretation is in agreement with
the observed trends of the coherent magnon amplitude and lifetime as a function
of the exciting laser fluence. Our results provide a new insight into the
magnetization relaxation processes in ferromagnetic thin films, which is of
great importance for further spintronic applications. | 2305.00814v2 |
2023-07-15 | Switching current distributions in ferromagnetic anomalous Josephson junctions | We investigate the switching current distributions of ferromagnetic anomalous
Josephson junctions subjected to a linearly increasing bias current. Our study
uncovers a significant correlation between the position of the switching
current distributions and crucial system parameters, such as the strength of
the spin-orbit coupling and the Gilbert damping parameter. This indicates that
these parameters can be directly determined through experimental measurements.
By conducting a comprehensive analysis of the interplay among noise,
magnetization, phase dynamics, and the statistical properties of the switching
current distribution, we deepen our understanding of these intriguing cryogenic
spintronics devices. These findings hold potential for applications in the
field of quantum computing architectures and information processing
technologies. | 2307.07751v2 |
2023-07-26 | Oscillatory Edge Modes in Two Dimensional Spin-Torque Oscillator Arrays | Spin torque oscillators (STOs) are dissipative magnetic systems that provide
a natural platform for exploring non-Hermitian phenomena. We theoretically
study a two-dimensional (2d) array of STOs and show that its dynamics can be
mapped to a 2d, non-Hermitian Su-Schrieffer-Heeger (SSH) model. We calculate
the energy spectrum and identify the one-dimensional (1d) edge states of our
model, corresponding to auto-oscillation of STOs on the boundary of the system
while the bulk oscillators do not activate. We show that tuning the Gilbert
damping, injected spin current, and coupling between STOs allows for exploring
the edge state properties under different parameter regimes. Furthermore, this
system admits 1d edge states with non-uniform probability density, and we
explore their properties in systems of different sizes. Additional symmetry
analysis indicates that these states are not topologically protected but are
nevertheless confined to the edge of the system, as the bulk is protected by
PT-symmetry. These results indicate that 2d arrays of STOs may be useful to
explore novel edge state behavior in dissipative systems. | 2307.13876v1 |
2024-04-01 | Harnessing Interlayer Magnetic Coupling for Efficient, Field-Free Current-Induced Magnetization Switching in a Magnetic Insulator | Owing to the unique features of low Gilbert damping, long spin-diffusion
lengths and zero Ohmic losses, magnetic insulators are promising candidate
materials for next-generation spintronic applications. However, due to the
localized magnetic moments and the complex metal-oxide interface between
magnetic insulators and heavy metals, spin-functional Dzyaloshinskii-Moriya
interactions or spin Hall and Edelstein effects are weak, which diminishes the
performance of these typical building blocks for spintronic devices. Here, we
exploit the exchange coupling between metallic and insulating magnets for
efficient electrical manipulation of heavy metal/magnetic insulator
heterostructures. By inserting a thin Co layer, we enhance the spin-orbit
torque efficiency by more than 20 times, which significantly reduces the
switching current density. Moreover, we demonstrate field-free current-induced
magnetization switching caused by a symmetry-breaking non-collinear magnetic
texture. Our work launches magnetic insulators as an alternative platform for
low-power spintronic devices. | 2404.00845v1 |
2003-10-18 | Experiment and Dynamic Simulations of Radiation Damping of Laser-polarized liquid 129Xe at low magnetic field in a flow system | Radiation damping is generally observed when the sample with high spin
concentration and high gyro-magnetic ratio is placed in a high magnetic field.
However, we firstly observed liquid state 129Xe radiation damping using
laser-enhanced nuclear polarization at low magnetic field in a flow system in
which the polarization enhancement factor for the liquid state 129Xe was
estimated to be 5000, and furthermore theoretically simulated the envelopes of
the 129Xe FID and spectral lineshape in the presence of both relaxation and
radiation damping with different pulse flip angles and ratios of T2*/Trd. The
radiation damping time constant Trd of 5 ms was derived based on the
simulations. The reasons of depolarization and the further possible
improvements were also discussed. | 0310435v1 |
2009-08-04 | Time domain detection of pulsed spin torque damping reduction | Combining multiple ultrafast spin torque impulses with a 5 nanosecond
duration pulse for damping reduction, we observe time-domain precession which
evolves from an initial 1 ns duration transient with changing precessional
amplitude to constant amplitude oscillations persisting for over 2 ns. These
results are consistent with relaxation of the transient trajectories to a
stable orbit with nearly zero damping. We find that in order to observe
complete damping cancellation and the transient behavior in a time domain
sampling measurement, a short duration, fast rise-time pulse is required to
cancel damping without significant trajectory dephasing. | 0908.0481v1 |
2014-08-15 | Linear hyperbolic equations with time-dependent propagation speed and strong damping | We consider a second order linear equation with a time-dependent coefficient
c(t) in front of the "elastic" operator. For these equations it is well-known
that a higher space-regularity of initial data compensates a lower
time-regularity of c(t).
In this paper we investigate the influence of a strong dissipation, namely a
friction term which depends on a power of the elastic operator.
What we discover is a threshold effect. When the exponent of the elastic
operator in the friction term is greater than 1/2, the damping prevails and the
equation behaves as if the coefficient c(t) were constant. When the exponent is
less than 1/2, the time-regularity of c(t) comes into play. If c(t) is regular
enough, once again the damping prevails. On the contrary, when c(t) is not
regular enough the damping might be ineffective, and there are examples in
which the dissipative equation behaves as the non-dissipative one. As expected,
the stronger is the damping, the lower is the time-regularity threshold.
We also provide counterexamples showing the optimality of our results. | 1408.3499v1 |
2017-01-12 | Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent | The blow-up for semilinear wave equations with the scale invariant damping
has been well-studied for sub-Fujita exponent. However, for super-Fujita
exponent, there is only one blow-up result which is obtained in 2014 by
Wakasugi in the case of non-effective damping. In this paper we extend his
result in two aspects by showing that: (I) the blow-up will happen for bigger
exponent, which is closely related to the Strauss exponent, the critical number
for non-damped semilinear wave equations; (II) such a blow-up result is
established for a wider range of the constant than the known non-effective one
in the damping term. | 1701.03232v3 |
2018-11-29 | The Lugiato-Lefever equation with nonlinear damping caused by two photon absorption | In this paper we investigate the effect of nonlinear damping on the
Lugiato-Lefever equation $$ \i \partial_t a = -(\i-\zeta) a - da_{xx}
-(1+\i\kappa)|a|^2a +\i f $$ on the torus or the real line. For the case of the
torus it is shown that for small nonlinear damping $\kappa>0$ stationary
spatially periodic solutions exist on branches that bifurcate from constant
solutions whereas all nonconstant solutions disappear when the damping
parameter $\kappa$ exceeds a critical value. These results apply both for
normal ($d<0$) and anomalous ($d>0$) dispersion. For the case of the real line
we show by the Implicit Function Theorem that for small nonlinear damping
$\kappa>0$ and large detuning $\zeta\gg 1$ and large forcing $f\gg 1$ strongly
localized, bright solitary stationary solutions exists in the case of anomalous
dispersion $d>0$. These results are achieved by using techniques from
bifurcation and continuation theory and by proving a convergence result for
solutions of the time-dependent Lugiato-Lefever equation. | 1811.12200v3 |
2020-07-16 | Linearized wave-damping structure of Vlasov-Poisson in $\mathbb R^3$ | In this paper we study the linearized Vlasov-Poisson equation for localized
disturbances of an infinite, homogeneous Maxwellian background distribution in
$\mathbb R^3_x \times \mathbb R^3_v$. In contrast with the confined case
$\mathbb T^d _x \times \mathbb R_v ^d$, or the unconfined case $\mathbb R^d_x
\times \mathbb R^d_v$ with screening, the dynamics of the disturbance are not
scattering towards free transport as $t \to \pm \infty$: we show that the
electric field decomposes into a very weakly-damped Klein-Gordon-type evolution
for long waves and a Landau-damped evolution. The Klein-Gordon-type waves
solve, to leading order, the compressible Euler-Poisson equations linearized
about a constant density state, despite the fact that our model is
collisionless, i.e. there is no trend to local or global thermalization of the
distribution function in strong topologies. We prove dispersive estimates on
the Klein-Gordon part of the dynamics. The Landau damping part of the electric
field decays faster than free transport at low frequencies and damps as in the
confined case at high frequencies; in fact, it decays at the same rate as in
the screened case. As such, neither contribution to the electric field behaves
as in the vacuum case. | 2007.08580v1 |
2020-11-16 | Technology to Counter Online Flaming Based on the Frequency-Dependent Damping Coefficient in the Oscillation Model | Online social networks, which are remarkably active, often experience
explosive user dynamics such as online flaming, which can significantly impact
the real world. However, countermeasures based on social analyses of the
individuals causing flaming are too slow to be effective because of the
rapidity with which the influence of online user dynamics propagates. A
countermeasure technology for the flaming phenomena based on the oscillation
model, which describes online user dynamics, has been proposed; it is an
immediate solution as it does not depend on social analyses of individuals.
Conventional countermeasures based on the oscillation model assume that the
damping coefficient is a constant regardless of the eigenfrequency. This
assumption is, however, problematic as the damping coefficients are, in
general, inherently frequency-dependent; the theory underlying the dependence
is being elucidated. This paper discusses a design method that uses the damping
coefficient to prevent flaming under general conditions considering the
frequency-dependence of the damping coefficient and proposes a countermeasure
technology for the flaming phenomena. | 2011.08117v1 |
2024-02-09 | Damping of density oscillations from bulk viscosity in quark matter | We study the damping of density oscillations in the quark matter phase that
might occur in compact stars. To this end we compute the bulk viscosity and the
associated damping time in three-flavor quark matter, considering both
nonleptonic and semileptonic electroweak processes. We use two different
equations of state of quark matter, more precisely, the MIT bag model and
perturbative QCD, including the leading order corrections in the strong
coupling constant. We analyze the dependence of our results on the density,
temperature and value of strange quark mass in each case. We then find that the
maximum of the bulk viscosity is in the range of temperature from 0.01 to 0.1
MeV for frequencies around 1 kHz, while the associated minimal damping times of
the density oscillations at those temperatures might be in the range of few to
hundreds milliseconds. Our results suggest that bulk viscous damping might be
relevant in the post-merger phase after the collision of two neutron stars if
deconfined matter is achieved in the process. | 2402.06595v1 |
2007-01-12 | Non-equilibrium Lorentz gas on a curved space | The periodic Lorentz gas with external field and iso-kinetic thermostat is
equivalent, by conformal transformation, to a billiard with expanding
phase-space and slightly distorted scatterers, for which the trajectories are
straight lines. A further time rescaling allows to keep the speed constant in
that new geometry. In the hyperbolic regime, the stationary state of this
billiard is characterized by a phase-space contraction rate, equal to that of
the iso-kinetic Lorentz gas. In contrast to the iso-kinetic Lorentz gas where
phase-space contraction occurs in the bulk, the phase-space contraction rate
here takes place at the periodic boundaries. | 0701024v1 |
2007-06-04 | Generation of microwave radiation in planar spin-transfer devices | Current induced precession states in spin-transfer devices are studied in the
case of large easy plane anisotropy (present in most experimental setups). It
is shown that the effective one-dimensional planar description provides a
simple qualitative understanding of the emergence and evolution of such states.
Switching boundaries are found analytically for the collinear device and the
spin-flip transistor. The latter can generate microwave oscillations at zero
external magnetic field without either special functional form of spin-transfer
torque, or ``field-like'' terms, if Gilbert constant corresponds to the
overdamped planar regime. | 0706.0529v1 |
2008-09-16 | Stochastic dynamics of magnetization in a ferromagnetic nanoparticle out of equilibrium | We consider a small metallic particle (quantum dot) where ferromagnetism
arises as a consequence of Stoner instability. When the particle is connected
to electrodes, exchange of electrons between the particle and the electrodes
leads to a temperature- and bias-driven Brownian motion of the direction of the
particle magnetization. Under certain conditions this Brownian motion is
described by the stochastic Landau-Lifshitz-Gilbert equation. As an example of
its application, we calculate the frequency-dependent magnetic susceptibility
of the particle in a constant external magnetic field, which is relevant for
ferromagnetic resonance measurements. | 0809.2611v1 |
2009-04-05 | Projective Space Codes for the Injection Metric | In the context of error control in random linear network coding, it is useful
to construct codes that comprise well-separated collections of subspaces of a
vector space over a finite field. In this paper, the metric used is the
so-called "injection distance", introduced by Silva and Kschischang. A
Gilbert-Varshamov bound for such codes is derived. Using the code-construction
framework of Etzion and Silberstein, new non-constant-dimension codes are
constructed; these codes contain more codewords than comparable codes designed
for the subspace metric. | 0904.0813v2 |
2009-05-28 | Hamilton cycles in random geometric graphs | We prove that, in the Gilbert model for a random geometric graph, almost
every graph becomes Hamiltonian exactly when it first becomes 2-connected. This
answers a question of Penrose. We also show that in the k-nearest neighbor
model, there is a constant \kappa\ such that almost every \kappa-connected
graph has a Hamilton cycle. | 0905.4650v2 |
2011-06-28 | Stability of precessing domain walls in ferromagnetic nanowires | We show that recently reported precessing solution of Landau-Lifshitz-Gilbert
equations in ferromagnetic nanowires is stable under small perturbations of
initial data, applied field and anisotropy constant. Linear stability is
established analytically, while nonlinear stability is verified numerically. | 1106.5808v2 |
2013-05-25 | Thermally-Assisted Spin-Transfer Torque Dynamics in Energy Space | We consider the general Landau-Lifshitz-Gilbert theory underlying the
magnetization dynamics of a macrospin magnet subject to spin-torque effects and
thermal fluctuations. Thermally activated dynamical properties are analyzed by
averaging the full magnetization equations over constant- energy orbits. After
averaging, all the relevant dynamical scenarios are a function of the ratio
between hard and easy axis anisotropies. We derive analytically the range of
currents for which limit cycles exist and discuss the regimes in which the
constant energy orbit averaging technique is applicable. | 1305.5945v2 |
2017-03-05 | On the VC-Dimension of Binary Codes | We investigate the asymptotic rates of length-$n$ binary codes with
VC-dimension at most $dn$ and minimum distance at least $\delta n$. Two upper
bounds are obtained, one as a simple corollary of a result by Haussler and the
other via a shortening approach combining Sauer-Shelah lemma and the linear
programming bound. Two lower bounds are given using Gilbert-Varshamov type
arguments over constant-weight and Markov-type sets. | 1703.01586v2 |
2018-09-22 | Optimizing a Generalized Gini Index in Stable Marriage Problems: NP-Hardness, Approximation and a Polynomial Time Special Case | This paper deals with fairness in stable marriage problems. The idea studied
here is to achieve fairness thanks to a Generalized Gini Index (GGI), a
well-known criterion in inequality measurement, that includes both the
egalitarian and utilitarian criteria as special cases. We show that determining
a stable marriage optimizing a GGI criterion of agents' disutilities is an
NP-hard problem. We then provide a polynomial time 2-approximation algorithm in
the general case, as well as an exact algorithm which is polynomial time in the
case of a constant number of non-zero weights parametrizing the GGI criterion. | 1809.08453v1 |
2023-05-31 | Codes from Goppa codes | On a Goppa code whose structure polynomial has coefficients in the symbol
field, the Frobenius acts. Its fixed codewords form a subcode. Deleting the
naturally occurred redundance, we obtain a new code. It is proved that these
new codes approach the Gilbert-Varshamov bound. It is also proved that these
codes can be decoded within $O(n^2(\logn)^a)$ operations in the symbol field,
which is usually much small than the location field, where $n$ is the codeword
length, and $a$ a constant determined by the polynomial factorization
algorithm. | 2305.19565v5 |
2019-12-09 | Analytical solution of linearized equations of the Morris-Lecar neuron model at large constant stimulation | The classical biophysical Morris-Lecar model of neuronal excitability
predicts that upon stimulation of the neuron with a sufficiently large constant
depolarizing current there exists a finite interval of the current values where
periodic spike generation occurs. Above the upper boundary of this interval,
there is four-stage damping of the spike amplitude: 1) minor primary damping,
which reflects a typical transient to stationary dynamic state, 2) plateau of
nearly undamped periodic oscillations, 3) strong damping, and 4) reaching a
constant asymptotic value of the neuron potential. We have shown that in the
vicinity of the asymptote the Morris-Lecar equations can be reduced to the
standard equation for exponentially damped harmonic oscillations. Importantly,
all coefficients of this equation can be explicitly expressed through
parameters of the original Morris-Lecar model, enabling direct comparison of
the numerical and analytical solutions for the neuron potential dynamics at
later stages of the spike amplitude damping. | 1912.04083v4 |
2011-03-08 | Application of Explicit Symplectic Algorithms to Integration of Damping Oscillators | In this paper an approach is outlined. With this approach some explicit
algorithms can be applied to solve the initial value problem of $n-$dimensional
damped oscillators. This approach is based upon following structure: for any
non-conservative classical mechanical system and arbitrary initial conditions,
there exists a conservative system; both systems share one and only one common
phase curve; and, the value of the Hamiltonian of the conservative system is,
up to an additive constant, equal to the total energy of the non-conservative
system on the aforementioned phase curve, the constant depending on the initial
conditions. A key way applying explicit symplectic algorithms to damping
oscillators is that by the Newton-Laplace principle the nonconservative force
can be reasonably assumed to be equal to a function of a component of
generalized coordinates $q_i$ along a phase curve, such that the damping force
can be represented as a function analogous to an elastic restoring force
numerically in advance. Two numerical examples are given to demonstrate the
good characteristics of the algorithms. | 1103.1455v1 |
2014-05-12 | Global Existence and Nonlinear Diffusion of Classical Solutions to Non-Isentropic Euler Equations with Damping in Bounded Domain | We considered classical solutions to the initial boundary value problem for
non-isentropic compressible Euler equations with damping in multi-dimensions.
We obtained global a priori estimates and global existence results of classical
solutions to both non-isentropic Euler equations with damping and their
nonlinear diffusion equations under small data assumption. We proved the
pressure and velocity decay exponentially to constants, while the entropy and
density can not approach constants. Finally, we proved the pressure and
velocity of the non-isentropic Euler equations with damping converge
exponentially to those of their nonlinear diffusion equations when the time
goes to infinity. | 1405.2842v3 |
2019-10-24 | The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions | In this paper, we study the initial value problem for semilinear wave
equations with the time-dependent and scale-invariant damping in two
dimensions. Similarly to the one dimensional case by Kato, Takamura and Wakasa
in 2019, we obtain the lifespan estimates of the solution for a special
constant in the damping term, which are classified by total integral of the sum
of the initial position and speed. The key fact is that, only in two space
dimensions, such a special constant in the damping term is a threshold between
"wave-like" domain and "heat-like" domain. As a result, we obtain a new type of
estimate especially for the critical exponent. | 1910.11692v2 |
2020-08-06 | Quantum sensing of open systems: Estimation of damping constants and temperature | We determine quantum precision limits for estimation of damping constants and
temperature of lossy bosonic channels. A direct application would be the use of
light for estimation of the absorption and the temperature of a transparent
slab. Analytic lower bounds are obtained for the uncertainty in the estimation,
through a purification procedure that replaces the master equation description
by a unitary evolution involving the system and ad hoc environments. For zero
temperature, Fock states are shown to lead to the minimal uncertainty in the
estimation of damping, with boson-counting being the best measurement
procedure. In both damping and temperature estimates, sequential
pre-thermalization measurements, through a stream of single bosons, may lead to
huge gain in precision. | 2008.02728v1 |
2020-11-15 | A Random Matrix Theory Approach to Damping in Deep Learning | We conjecture that the inherent difference in generalisation between adaptive
and non-adaptive gradient methods in deep learning stems from the increased
estimation noise in the flattest directions of the true loss surface. We
demonstrate that typical schedules used for adaptive methods (with low
numerical stability or damping constants) serve to bias relative movement
towards flat directions relative to sharp directions, effectively amplifying
the noise-to-signal ratio and harming generalisation. We further demonstrate
that the numerical damping constant used in these methods can be decomposed
into a learning rate reduction and linear shrinkage of the estimated curvature
matrix. We then demonstrate significant generalisation improvements by
increasing the shrinkage coefficient, closing the generalisation gap entirely
in both logistic regression and several deep neural network experiments.
Extending this line further, we develop a novel random matrix theory based
damping learner for second order optimiser inspired by linear shrinkage
estimation. We experimentally demonstrate our learner to be very insensitive to
the initialised value and to allow for extremely fast convergence in
conjunction with continued stable training and competitive generalisation. | 2011.08181v5 |
2021-06-07 | Voltage-control of damping constant in magnetic-insulator/topological-insulator bilayers | The magnetic damping constant is a critical parameter for magnetization
dynamics and the efficiency of memory devices and magnon transport. Therefore,
its manipulation by electric fields is crucial in spintronics. Here, we
theoretically demonstrate the voltage-control of magnetic damping in ferro- and
ferrimagnetic-insulator (FI)/topological-insulator (TI) bilayers. Assuming a
capacitor-like setup, we formulate an effective dissipation torque induced by
spin-charge pumping at the FI/TI interface as a function of an applied voltage.
By using realistic material parameters, we find that the effective damping for
a FI with 10nm thickness can be tuned by one order of magnitude under the
voltage with 0.25V. Also, we provide perspectives on the voltage-induced
modulation of the magnon spin transport on proximity-coupled FIs. | 2106.03332v1 |
2023-01-22 | Boundary stabilization of a vibrating string with variable length | We study small vibrations of a string with time-dependent length $\ell(t)$
and boundary damping. The vibrations are described by a 1-d wave equation in an
interval with one moving endpoint at a speed $\ell'(t)$ slower than the speed
of propagation of the wave c=1. With no damping, the energy of the solution
decays if the interval is expanding and increases if the interval is shrinking.
The energy decays faster when the interval is expanding and a constant damping
is applied at the moving end. However, to ensure the energy decay in a
shrinking interval, the damping factor $\eta$ must be close enough to the
optimal value $\eta=1$, corresponding to the transparent condition. In all
cases, we establish lower and upper estimates for the energy with explicit
constants. | 2301.09086v1 |
2022-08-03 | On ergodic invariant measures for the stochastic Landau-Lifschitz-Gilbert equation in 1D | We establish existence of an ergodic invariant measure on
$H^1(D,\mathbb{R}^3)\cap L^2(D,\mathbb{S}^2)$ for the stochastic
Landau-Lifschitz-Gilbert equation on a bounded one dimensional interval $D$.
The conclusion is achieved by employing the classical Krylov-Bogoliubov
theorem. In contrast to other equations, verifying the hypothesis of the
Krylov-Bogoliubov theorem is not a standard procedure. We employ rough paths
theory to show that the semigroup associated to the equation has the Feller
property in $H^1(D,\mathbb{R}^3)\cap L^2(D,\mathbb{S}^2)$. It does not seem
possible to achieve the same conclusion by the classical Stratonovich calculus.
On the other hand, we employ the classical Stratonovich calculus to prove the
tightness hypothesis. The Krein-Milman theorem implies existence of an ergodic
invariant measure. In case of spatially constant noise, we show that there
exists a unique Gibbs invariant measure and we establish the qualitative
behaviour of the unique stationary solution. In absence of the anisotropic
energy and for a spatially constant noise, we are able to provide a path-wise
long time behaviour result: in particular, every solution synchronises with a
spherical Brownian motion and it is recurrent for large times | 2208.02136v2 |
2008-07-23 | Damped driven coupled oscillators: entanglement, decoherence and the classical limit | The interaction of (two-level) Rydberg atoms with dissipative QED cavity
fields can be described classically or quantum mechanically, even for very low
temperatures and mean number of photons, provided the damping constant is large
enough. We investigate the quantum-classical border, the entanglement and
decoherence of an analytically solvable model, analog to the atom-cavity
system, in which the atom (field) is represented by a (driven and damped)
harmonic oscillator. The maximum value of entanglement is shown to depend on
the initial state and the dissipation-rate to coupling-constant ratio. While in
the original model the atomic entropy never grows appreciably (for large
dissipation rates), in our model it reaches a maximum before decreasing.
Although both models predict small values of entanglement and dissipation, for
fixed times of the order of the inverse of the coupling constant and large
dissipation rates, these quantities decrease faster, as a function of the ratio
of the dissipation rate to the coupling constant, in our model. | 0807.3715v1 |
1999-08-26 | Oscillator Strengths and Damping Constants for Atomic Lines in the J and H Bands | We have built a line list in the near-infrared J and H bands (1.00-1.34,
1.49-1.80 um) by gathering a series of laboratory and computed line lists.
Oscillator strengths and damping constants were computed or obtained by fitting
the solar spectrum.
The line list presented in this paper is, to our knowledge, the most complete
one now available, and supersedes previous lists. | 9908296v1 |
1998-07-02 | Linear systems with adiabatic fluctuations | We consider a dynamical system subjected to weak but adiabatically slow
fluctuations of external origin. Based on the ``adiabatic following''
approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the
strength of fluctuations and 1/|\mu| refers to the time scale of evolution of
the unperturbed system to obtain a linear differential equation for the average
solution. The theory is applied to the problems of a damped harmonic oscillator
and diffusion in a turbulent fluid. The result is the realization of
`renormalized' diffusion constant or damping constant for the respective
problems. The applicability of the method has been critically analyzed. | 9807031v1 |
2004-09-15 | Rippled Cosmological Dark Matter from Damped Oscillating Newton Constant | Let the reciprocal Newton 'constant' be an apparently non-dynamical
Brans-Dicke scalar field damped oscillating towards its General Relativistic
VEV. We show, without introducing additional matter fields or dust, that the
corresponding cosmological evolution averagely resembles, in the Jordan frame,
the familiar dark radiation -> dark matter -> dark energy domination sequence.
The fingerprints of our theory are fine ripples, hopefully testable, in the FRW
scale factor; they die away at the General Relativity limit. The possibility
that the Brans-Dicke scalar also serves as the inflaton is favorably examined. | 0409059v2 |
2009-08-31 | Rigorous Theory of Optical Trapping by an Optical Vortex Beam | We propose a rigorous theory for the optical trapping by optical vortices,
which is emerging as an important tool to trap mesoscopic particles. The common
perception is that the trapping is solely due to the gradient force, and may be
characterized by three real force constants. However, we show that the optical
vortex trap can exhibit complex force constants, implying that the trapping
must be stabilized by ambient damping. At different damping levels, particle
shows remarkably different dynamics, such as stable trapping, periodic and
aperiodic orbital motions. | 0908.4504v1 |
2009-10-24 | Two bodies gravitational system with variable mass and damping-antidamping effect due to star wind | We study two-bodies gravitational problem where the mass of one of the bodies
varies and suffers a damping-antidamping effect due to star wind during its
motion. A constant of motion, a Lagrangian and a Hamiltonian are given for the
radial motion of the system, and the period of the body is studied using the
constant of motion of the system. An application to the comet motion is given,
using the comet Halley as an example. | 0910.4684v2 |
2012-03-02 | Damping-Antidamping Effect on Comets Motion | We make an observation about Galilean transformation on a 1-D mass variable
systems which leads us to the right way to deal with mass variable systems.
Then using this observation, we study two-bodies gravitational problem where
the mass of one of the bodies varies and suffers a damping-antidamping effect
due to star wind during its motion. For this system, a constant of motion, a
Lagrangian and a Hamiltonian are given for the radial motion, and the period of
the body is studied using the constant of motion of the system. Our theoretical
results are applied to Halley's comet. | 1203.0495v2 |
2012-03-09 | Collective Light Emission of a Finite Size Atomic Chain | Radiative properties of collective electronic states in a one dimensional
atomic chain are investigated. Radiative corrections are included with
emphasize put on the effect of the chain size through the dependence on both
the number of atoms and the lattice constant. The damping rates of collective
states are calculated in considering radiative effects for different values of
the lattice constant relative to the atomic transition wave length. Especially
the symmetric state damping rate as a function of the number of the atoms is
derived. The emission pattern off a finite linear chain is also presented. The
results can be adopted for any chain of active material, e.g., a chain of
semiconductor quantum dots or organic molecules on a linear matrix. | 1203.2094v1 |
2022-11-18 | Energy decay estimates for an axially travelling string damped at one end | We study the small vibrations of an axially travelling string with a
dashpoint damping at one end. The string is modelled by a wave equation in a
time-dependent interval with two endpoints moving at a constant speed $v$. For
the undamped case, we obtain a conserved functional equivalent to the energy of
the solution. We derive precise upper and lower estimates for the exponential
decay of the energy with explicit constants. These estimates do not seem to be
reported in the literature even for the non-travelling case $v=0$. | 2211.10537v1 |
2023-04-19 | Inviscid damping of monotone shear flows for 2D inhomogeneous Euler equation with non-constant density in a finite channel | We prove the nonlinear inviscid damping for a class of monotone shear flows
with non-constant background density for the two-dimensional ideal
inhomogeneous fluids in $\mathbb{T}\times [0,1]$ when the initial perturbation
is in Gevrey-$\frac{1}{s}$ ($\frac{1}{2}<s<1$) class with compact support. | 2304.09841v2 |
2023-07-27 | Best Ulam constants for damped linear oscillators with variable coefficients | This study uses an associated Riccati equation to study the Ulam stability of
non-autonomous linear differential vector equations that model the damped
linear oscillator. In particular, the best (minimal) Ulam constants for these
non-autonomous linear differential vector equations are derived. These robust
results apply to vector equations with solutions that blow up in finite time,
as well as to vector equations with solutions that exist globally on
$(-\infty,\infty)$. Illustrative, non-trivial examples are presented,
highlighting the main results. | 2307.15103v1 |
2005-07-15 | A Theory of Physical Quantum Computation: The Quantum Computer Condition | In this paper we present a new unified theoretical framework that describes
the full dynamics of quantum computation. Our formulation allows any questions
pertaining to the physical behavior of a quantum computer to be framed, and in
principle, answered. We refer to the central organizing principle developed in
this paper, on which our theoretical structure is based, as the *Quantum
Computer Condition* (QCC), a rigorous mathematical statement that connects the
irreversible dynamics of the quantum computing machine, with the reversible
operations that comprise the quantum computation intended to be carried out by
the quantum computing machine. Armed with the QCC, we derive a powerful result
that we call the *Encoding No-Go Theorem*. This theorem gives a precise
mathematical statement of the conditions under which fault-tolerant quantum
computation becomes impossible in the presence of dissipation and/or
decoherence. In connection with this theorem, we explicitly calculate a
universal critical damping value for fault-tolerant quantum computation. In
addition we show that the recently-discovered approach to quantum error
correction known as "operator quantum error-correction" (OQEC) is a special
case of our more general formulation. Our approach furnishes what we will refer
to as "operator quantum fault-tolerance" (OQFT). In particular, we show how the
QCC allows one to derive error thresholds for fault tolerance in a completely
general context. We prove the existence of solutions to a class of
time-dependent generalizations of the Lindblad equation. Using the QCC, we also
show that the seemingly different circuit, graph- (including cluster-) state,
and adiabatic paradigms for quantum computing are in fact all manifestations of
a single, universal paradigm for all physical quantum computation. | 0507141v2 |
2018-12-22 | Spin dynamics of $3d$ and $4d$ impurities embedded in prototypical topological insulators | Topological insulators are insulating bulk materials hosting conducting
surface states. Their magnetic doping breaks time-reversal symmetry and
generates numerous interesting effects such as dissipationless transport.
Nonetheless, their dynamical properties are still poorly understood. Here, we
perform a systematic investigation of transverse spin excitations of $3d$ and
$4d$ single impurities embedded in two prototypical topological insulators
(Bi$_2$Te$_3$ and Bi$_2$Se$_3$). The impurity-induced states within the bulk
gap of the topological insulators are found to have a drastic impact on the
spin excitation spectra, resulting in very high lifetimes reaching up to
${microseconds}$. An intuitive picture of the spin dynamics is obtained by
mapping onto a generalized Landau-Lifshitz-Gilbert phenomenological model. The
first quantity extracted from this mapping procedure is the magnetic anisotropy
energy, which is then compared to the one provided by the magnetic force
theorem. This uncovers some difficulties encountered with the latter, which can
provide erroneous results for impurities with a high density of states at the
Fermi energy. Moreover, the Gilbert damping and nutation tensors are obtained.
The nutation effects can lead to a non-negligible shift in the spin excitation
resonance in the high-frequency regime. Finally, we study the impact of the
surface state on the spin dynamics, which may be severely altered due to the
repositioning of the impurity-induced state in comparison to the bulk case. Our
systematic investigation of this series of magnetic impurities sheds light on
their spin dynamics within topological insulators, with implications for
available and future experimental studies as, for instance, on the viability of
using such impurities for solid-state qubits. | 1812.09596v1 |
2019-11-02 | Soft contribution to the damping rate of a hard photon in a weakly magnetized hot medium | We consider weakly magnetized hot QED plasma comprising electrons and
positrons. There are three distinct dispersive (longitudinal and two
transverse) modes of a photon in a thermo-magnetic medium. At lowest order in
coupling constant, photon is damped in this medium via Compton scattering and
pair creation process. We evaluate the damping rate of hard photon by
calculating the imaginary part of the each transverse dispersive modes in a
thermo-magnetic QED medium. We note that one of the fermions in the loop of
one-loop photon self-energy is considered as soft and the other one is hard.
Considering the resummed fermion propagator in a weakly magnetized medium for
the soft fermion and the Schwinger propagator for hard fermion, we calculate
the soft contribution to the damping rate of hard photon. In weak field
approximation the thermal and thermo-magnetic contributions to damping rate get
separated out for each transverse dispersive mode. The total damping rate for
each dispersive mode in presence of magnetic field is found to be reduced than
that of the thermal one. This formalism can easily be extended to QCD plasma. | 1911.00744v2 |
2023-06-05 | Damping of coronal oscillations in self-consistent 3D radiative MHD simulations of the solar atmosphere | Oscillations are abundant in the solar corona. Coronal loop oscillations are
typically studied using highly idealised models of magnetic flux tubes. In
order to improve our understanding of coronal oscillations, it is necessary to
consider the effect of realistic magnetic field topology and density
structuring. We analyse the damping of coronal oscillations using a
self-consistent 3D radiation-MHD simulation of the solar atmosphere spanning
from the convection zone into the corona, the associated oscillation
dissipation and heating, and finally the physical processes responsible for the
damping and dissipation. The simulated corona formed in such a model does not
depend on any prior assumptions about the shape of the coronal loops. We find
that the bundle of magnetic loops shows damped transverse oscillations in
response to perturbations in two separate instances with oscillation periods of
177 s and 191 s, velocity amplitudes of 10 km/s and 16 km/s and damping times
of 176 s and 198 s, respectively. The coronal oscillations lead to the
development of velocity shear in the simulated corona resulting in the
formation of vortices seen in the velocity field caused by the Kelvin-Helmholtz
instability, contributing to the damping and dissipation of the transverse
oscillations. The oscillation parameters and evolution observed are in line
with the values typically seen in observations of coronal loop oscillations.
The dynamic evolution of the coronal loop bundle suggests the models of
monolithic and static coronal loops with constant lengths might need to be
re-evaluated by relaxing the assumption of highly idealised waveguides. | 2306.02770v1 |
2013-08-16 | Quantum Gilbert-Varshamov Bound Through Symplectic Self-Orthogonal Codes | It is well known that quantum codes can be constructed through classical
symplectic self-orthogonal codes. In this paper, we give a kind of
Gilbert-Varshamov bound for symplectic self-orthogonal codes first and then
obtain the Gilbert-Varshamov bound for quantum codes. The idea of obtaining the
Gilbert-Varshamov bound for symplectic self-orthogonal codes follows from
counting arguments. | 1308.3578v1 |
2009-01-15 | The sound damping constant for generalized theories of gravity | The near-horizon metric for a black brane in Anti-de Sitter (AdS) space and
the metric near the AdS boundary both exhibit hydrodynamic behavior. We
demonstrate the equivalence of this pair of hydrodynamic systems for the sound
mode of a conformal theory. This is first established for Einstein's gravity,
but we then show how the sound damping constant will be modified, from its
Einstein form, for a generalized theory. The modified damping constant is
expressible as the ratio of a pair of gravitational couplings that are
indicative of the sound-channel class of gravitons. This ratio of couplings
differs from both that of the shear diffusion coefficient and the shear
viscosity to entropy ratio. Our analysis is mostly limited to conformal
theories but suggestions are made as to how this restriction might eventually
be lifted. | 0901.2191v1 |
2009-12-01 | Approximate Sparse Recovery: Optimizing Time and Measurements | An approximate sparse recovery system consists of parameters $k,N$, an
$m$-by-$N$ measurement matrix, $\Phi$, and a decoding algorithm, $\mathcal{D}$.
Given a vector, $x$, the system approximates $x$ by $\widehat x
=\mathcal{D}(\Phi x)$, which must satisfy $\| \widehat x - x\|_2\le C \|x -
x_k\|_2$, where $x_k$ denotes the optimal $k$-term approximation to $x$. For
each vector $x$, the system must succeed with probability at least 3/4. Among
the goals in designing such systems are minimizing the number $m$ of
measurements and the runtime of the decoding algorithm, $\mathcal{D}$.
In this paper, we give a system with $m=O(k \log(N/k))$
measurements--matching a lower bound, up to a constant factor--and decoding
time $O(k\log^c N)$, matching a lower bound up to $\log(N)$ factors.
We also consider the encode time (i.e., the time to multiply $\Phi$ by $x$),
the time to update measurements (i.e., the time to multiply $\Phi$ by a
1-sparse $x$), and the robustness and stability of the algorithm (adding noise
before and after the measurements). Our encode and update times are optimal up
to $\log(N)$ factors. | 0912.0229v1 |
2011-08-29 | Magnetization Dynamics, Throughput and Energy Dissipation in a Universal Multiferroic Nanomagnetic Logic Gate with Fan-in and Fan-out | The switching dynamics of a multiferroic nanomagnetic NAND gate with
fan-in/fan-out is simulated by solving the Landau-Lifshitz-Gilbert (LLG)
equation while neglecting thermal fluctuation effects. The gate and logic wires
are implemented with dipole-coupled 2-phase (magnetostrictive/piezoelectric)
multiferroic elements that are clocked with electrostatic potentials of ~50 mV
applied to the piezoelectric layer generating 10 MPa stress in the
magnetostrictive layers for switching. We show that a pipeline bit throughput
rate of ~ 0.5 GHz is achievable with proper magnet layout and sinusoidal
four-phase clocking. The gate operation is completed in 2 ns with a latency of
4 ns. The total (internal + external) energy dissipated for a single gate
operation at this throughput rate is found to be only ~ 1000 kT in the gate and
~3000 kT in the 12-magnet array comprising two input and two output wires for
fan-in and fan-out. This makes it respectively 3 and 5 orders of magnitude more
energy-efficient than complementary-metal-oxide-semiconductor-transistor (CMOS)
based and spin-transfer-torque-driven nanomagnet based NAND gates. Finally, we
show that the dissipation in the external clocking circuit can always be
reduced asymptotically to zero using increasingly slow adiabatic clocking, such
as by designing the RC time constant to be 3 orders of magnitude smaller than
the clocking period. However, the internal dissipation in the device must
remain and cannot be eliminated if we want to perform fault-tolerant classical
computing.
Keywords: Nanomagnetic logic, multiferroics, straintronics and spintronics,
Landau-Lifshitz-Gilbert equation. | 1108.5758v1 |
2013-04-23 | L2/L2-foreach sparse recovery with low risk | In this paper, we consider the "foreach" sparse recovery problem with failure
probability $p$. The goal of which is to design a distribution over $m \times
N$ matrices $\Phi$ and a decoding algorithm $\algo$ such that for every
$\vx\in\R^N$, we have the following error guarantee with probability at least
$1-p$ \[\|\vx-\algo(\Phi\vx)\|_2\le C\|\vx-\vx_k\|_2,\] where $C$ is a constant
(ideally arbitrarily close to 1) and $\vx_k$ is the best $k$-sparse
approximation of $\vx$.
Much of the sparse recovery or compressive sensing literature has focused on
the case of either $p = 0$ or $p = \Omega(1)$. We initiate the study of this
problem for the entire range of failure probability. Our two main results are
as follows: \begin{enumerate} \item We prove a lower bound on $m$, the number
measurements, of $\Omega(k\log(n/k)+\log(1/p))$ for $2^{-\Theta(N)}\le p <1$.
Cohen, Dahmen, and DeVore \cite{CDD2007:NearOptimall2l2} prove that this bound
is tight. \item We prove nearly matching upper bounds for \textit{sub-linear}
time decoding. Previous such results addressed only $p = \Omega(1)$.
\end{enumerate}
Our results and techniques lead to the following corollaries: (i) the first
ever sub-linear time decoding $\lolo$ "forall" sparse recovery system that
requires a $\log^{\gamma}{N}$ extra factor (for some $\gamma<1$) over the
optimal $O(k\log(N/k))$ number of measurements, and (ii) extensions of Gilbert
et al. \cite{GHRSW12:SimpleSignals} results for information-theoretically
bounded adversaries. | 1304.6232v1 |
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