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2013-11-12
|
Vertex finiteness for splittings of relatively hyperbolic groups
|
Consider a group G and a family $\mathcal{A}$ of subgroups of G. We say that
vertex finiteness holds for splittings of G over $\mathcal{A}$ if, up to
isomorphism, there are only finitely many possibilities for vertex stabilizers
of minimal G-trees with edge stabilizers in $\mathcal{A}$.
We show vertex finiteness when G is a toral relatively hyperbolic group and
$\mathcal{A}$ is the family of abelian subgroups.
We also show vertex finiteness when G is hyperbolic relative to virtually
polycyclic subgroups and $\mathcal{A}$ is the family of virtually cyclic
subgroups; if moreover G is one-ended, there are only finitely many minimal
G-trees with virtually cyclic edge stabilizers, up to automorphisms of G.
|
1311.2835v2
|
2013-11-13
|
Fokker-Planck approach to the theory of magnon-driven spin Seebeck effect
|
Following the theoretical approach by Xiao et al [Phys. Rev. B 81, 214418
(2010)] to the spin Seebeck effect, we calculate the mean value of the total
spin current flowing through a normalmetal/ ferromagnet interface. The spin
current emitted from the ferromagnet to the normal metal is evaluated in the
framework of the Fokker-Planck approach for the stochastic
Landau-Lifshitz-Gilbert equation. We show that the total spin current depends
not only on the temperature difference between the electron and the magnon
baths, but also on the external magnetic field and magnetic anisotropy. Apart
from this, the spin current is shown to saturate with increasing magnon
temperature, and the saturation temperature increases with increasing magnetic
field and/or magnetic anisotropy.
|
1311.3117v1
|
2013-11-20
|
Recent integral cross section validation measurements at the ASP facility
|
This work presents new integral data measured at the ASP 14 MeV neutron
irradiation facility at Aldermaston in the UK, which has recently become
available for fusion-related work through the CCFE materials programme.
Measurements of reaction products from activation experiments using elemental
foils were carried out using gamma spectrometry in a high efficiency,
high-purity germanium (HPGe) detector and associated digital signal processing
hardware. Following irradiation and rapid extraction to the measurement cell,
gamma emissions were acquired with both energy and time bins. Integral cross
section and half-life data have been derived from these measurements. Selected
integral cross section values are presented from the measurement campaigns.
|
1311.5074v1
|
2013-11-25
|
Application of the Moment-SOS Approach to Global Optimization of the OPF Problem
|
Finding a global solution to the optimal power flow (OPF) problem is
difficult due to its nonconvexity. A convex relaxation in the form of
semidefinite programming (SDP) has attracted much attention lately as it yields
a global solution in several practical cases. However, it does not in all
cases, and such cases have been documented in recent publications. This paper
presents another SDP method known as the moment-sos (sum of squares) approach,
which generates a sequence that converges towards a global solution to the OPF
problem at the cost of higher runtime. Our finding is that in the small
examples where the previously studied SDP method fails, this approach finds the
global solution. The higher cost in runtime is due to an increase in the matrix
size of the SDP problem, which can vary from one instance to another. Numerical
experiment shows that the size is very often a quadratic function of the number
of buses in the network, whereas it is a linear function of the number of buses
in the case of the previously studied SDP method.
|
1311.6370v2
|
2013-12-06
|
Lazy Cops and Robbers played on Graphs
|
We consider a variant of the game of Cops and Robbers, called Lazy Cops and
Robbers, where at most one cop can move in any round. We investigate the
analogue of the cop number for this game, which we call the lazy cop number.
Lazy Cops and Robbers was recently introduced by Offner and Ojakian, who
provided asymptotic upper and lower bounds on the lazy cop number of the
hypercube. By investigating expansion properties, we provide asymptotically
almost sure bounds on the lazy cop number of binomial random graphs
$\mathcal{G}(n,p)$ for a wide range of $p=p(n)$. By coupling the probabilistic
method with a potential function argument, we also improve on the existing
lower bounds for the lazy cop number of hypercubes. Finally, we provide an
upper bound for the lazy cop number of graphs with genus $g$ by using the
Gilbert-Hutchinson-Tarjan separator theorem.
|
1312.1750v1
|
2014-01-03
|
Spin-Transfer-Torque Driven Magneto-Logic Gates Using Nano Spin-Valve Pillars
|
We propose model magneto-logic NOR and NAND gates using a spin valve pillar,
wherein the logical operation is induced by spin-polarized currents which also
form the logical inputs. The operation is facilitated by the simultaneous
presence of a constant controlling magnetic field. The same spin-valve assembly
can also be used as a magnetic memory unit. We identify regions in the
parameter space of the system where the logical operations can be effectively
performed. The proposed gates retain the non-volatility of a magnetic random
access memory,(MRAM). We verify the functioning of the gate by numerically
simulating its dynamics, governed by the appropriate Landau-Lifshitz-Gilbert
equation with the spin-transfer torque term. The flipping time for the logical
states is estimated to be within nano seconds.
|
1401.0723v1
|
2014-01-17
|
Diffuse Scattering on Graphs
|
We formulate and analyze difference equations on graphs analogous to
time-independent diffusion equations arising in the study of diffuse scattering
in continuous media. Moreover, we show how to construct solutions in the
presence of weak scatterers from the solution to the homogeneous (background
problem) using Born series, providing necessary conditions for convergence and
demonstrating the process through numerous examples. In addition, we outline a
method for finding Green's functions for Cayley graphs for both abelian and
non-abelian groups. Finally, we conclude with a discussion of the effects of
sparsity on our method and results, outlining the simplifications that can be
made provided that the scatterers are weak and well-separated.
|
1401.4428v2
|
2014-01-25
|
Linear Boolean classification, coding and "the critical problem"
|
The problem of constructing a minimal rank matrix over GF(2) whose kernel
does not intersect a given set S is considered. In the case where S is a
Hamming ball centered at 0, this is equivalent to finding linear codes of
largest dimension. For a general set, this is an instance of "the critical
problem" posed by Crapo and Rota in 1970. This work focuses on the case where S
is an annulus. As opposed to balls, it is shown that an optimal kernel is
composed not only of dense but also of sparse vectors, and the optimal mixture
is identified in various cases. These findings corroborate a proposed
conjecture that for annulus of inner and outer radius nq and np respectively,
the optimal relative rank is given by (1-q)H(p/(1-q)), an extension of the
Gilbert-Varshamov bound H(p) conjectured for Hamming balls of radius np.
|
1401.6528v3
|
2014-01-30
|
Langevin spin dynamics based on ab initio calculations: numerical schemes and applications
|
A method is proposed to study the finite-temperature behaviour of small
magnetic clusters based on solving the stochastic Landau-Lifshitz-Gilbert
equations, where the effective magnetic field is calculated directly during the
solution of the dynamical equations from first principles instead of relying on
an effective spin Hamiltonian. Different numerical solvers are discussed in the
case of a one-dimensional Heisenberg chain with nearest-neighbour interactions.
We performed detailed investigations for a monatomic chain of ten Co atoms on
top of Au(001) surface. We found a spiral-like ground state of the spins due to
Dzyaloshinsky-Moriya interactions, while the finite-temperature magnetic
behaviour of the system was well described by a nearest-neighbour Heisenberg
model including easy-axis anisotropy.
|
1401.7885v2
|
2014-02-25
|
Flux $1/f^α$ noise in 2D Heisenberg spin glasses: effects of weak anisotropic interactions
|
We study the dynamics of a two-dimensional ensemble of randomly distributed
classical Heisenberg spins with isotropic RKKY and weaker anisotropic
dipole-dipole couplings. Such ensembles may give rise to the flux noise
observed in SQUIDs with a $1/f^{\alpha}$ power spectrum ($\alpha \lesssim 1$).
We solve numerically the Landau-Lifshiftz-Gilbert equations of motion in the
dissipationless limit. We find that Ising type fluctuators, which arise from
spin clustering close to a spin-glass critical behavior with $T_c =0$, give
rise to $1/f^{\alpha}$ noise. Even weak anisotropic interactions lead to a
crossover from the Heisenberg-type criticality to the much stronger Ising-type
criticality. The temperature dependent exponent $\alpha(T) \lesssim 1$ grows
and approaches unity when the temperature is lowered. This mechanism acts in
parallel to the spin diffusion mechanism. Whereas the latter is sensitive to
the device geometry, the spin-clustering mechanism is largely geometry
independent.
|
1402.6229v2
|
2014-02-25
|
Spinless Topological Insulators without Time-Reversal Symmetry
|
We explore the 32 crystallographic point groups and identify topological
phases of matter with robust surface modes. For n =3,4 and 6 of the C_{nv}
groups, we find the first-known 3D topological insulators without spin-orbit
coupling, and with surface modes that are protected only by point groups, i.e.,
not needing time-reversal symmetry. To describe these C_{nv} systems, we
introduce the notions of (a) a halved mirror chirality: an integer invariant
which characterizes half-mirror-planes in the 3D Brillouin zone, and (b) a bent
Chern number: the traditional TKNN invariant generalized to bent 2D manifolds.
We find that a Weyl semimetallic phase intermediates two gapped phases with
distinct halved chiralities.
|
1402.6323v1
|
2014-04-08
|
Resonant Spin Wave Excitation by Terahertz Magnetic Near-field Enhanced with Split Ring Resonator
|
Excitation of antiferromagnetic spin waves in HoFeO$_{3}$ crystal combined
with a split ring resonator (SRR) is studied using terahertz (THz)
electromagnetic pulses. The magnetic field in the vicinity of the SRR induced
by the incident THz electric field component excites and the Faraday rotation
of the polarization of a near-infrared probe pulse directly measures
oscillations that correspond to the antiferromagnetic spin resonance mode. The
good agreement of the temperature-dependent magnetization dynamics with the
calculation using the two-lattice Landau-Lifshitz-Gilbert equation confirms
that the spin wave is resonantly excited by the THz magnetic near-field
enhanced at the LC resonance frequency of the SRR, which is 20 times stronger
than the incident magnetic field.
|
1404.2179v1
|
2014-04-09
|
Spin switches for compact implementation of neuron and synapse
|
Nanomagnets driven by spin currents provide a natural implementation for a
neuron and a synapse: currents allow convenient summation of multiple inputs,
while the magnet provides the threshold function. The objective of this paper
is to explore the possibility of a hardware neural network (HNN) implementation
using a spin switch (SS) as its basic building block. SS is a recently proposed
device based on established technology with a transistor-like gain and
input-output isolation. This allows neural networks to be constructed with
purely passive interconnections without intervening clocks or amplifiers. The
weights for the neural network are conveniently adjusted through analog
voltages that can be stored in a non-volatile manner in an underlying CMOS
layer using a floating gate low dropout voltage regulator. The operation of a
multi-layer SS neural network designed for character recognition is
demonstrated using a standard simulation model based on coupled
Landau-Lifshitz-Gilbert (LLG) equations, one for each magnet in the network.
|
1404.2654v2
|
2014-06-30
|
Coercivity reduction in a two-dimensional array of nanoparticles
|
We report on theoretical investigation of the magnetization reversal in
two-dimensional arrays of ferromagnetic nano-particles with parameters of
cobalt. The system was optimized for achieving the lowest coercivity in an
array of particles located in the nodes of triangular, hexagonal and square
grids. Based on the numerical solution of the non-stochastic
Landau-Lifshitz-Gilbert equation we show that each particle distribution type
is characterized with a proper optimal distance, allowing to lower the
coercivity values for approximately 30% compared with the reference value
obtained for a single nano-particle. It was shown that the reduction of
coercivity occurs even if the particle position in the array is not very
precise. In particular, the triangular particle arrangement maintained the same
optimal distance between the particles under up to 20% random displacements of
their position within the array.
|
1406.7786v1
|
2014-07-17
|
Spatial ordering of nano-dislocation loops in ion-irradiated materials
|
Defect microstructures formed in ion-irradiated metals, for example iron or
tungsten, often exhibit patterns of spatially ordered nano-scale dislocation
loops. We show that such ordered dislocation loop structures may form
spontaneously as a result of Brownian motion of loops, biased by the
angular-dependent elastic interaction between the loops. Patterns of spatially
ordered loops form once the local density of loops produced by ion irradiation
exceeds a critical threshold value.
|
1407.4683v1
|
2014-07-22
|
Lattice swelling and modulus change in a helium-implanted tungsten alloy: X-ray micro-diffraction, surface acoustic wave measurements, and multiscale modelling
|
Using X-ray micro-diffraction and surface acoustic wave spectroscopy, we
measure lattice swelling and elastic modulus changes in a W-1%Re alloy after
implantation with 3110 appm of helium. A fraction of a percent observed lattice
expansion gives rise to an order of magnitude larger reduction in the surface
acoustic wave velocity. A multiscale elasticity, molecular dynamics, and
density functional theory model is applied to the interpretation of
observations. The measured lattice swelling is consistent with the relaxation
volume of self-interstitial and helium-filled vacancy defects that dominate the
helium-implanted material microstructure. Molecular dynamics simulations
confirm the elasticity model for swelling. Elastic properties of the implanted
surface layer also change due to defects. The reduction of surface acoustic
wave velocity predicted by density functional theory calculations agrees
remarkably well with experimental observations.
|
1407.6051v1
|
2014-07-26
|
Principles and Parameters: a coding theory perspective
|
We propose an approach to Longobardi's parametric comparison method (PCM) via
the theory of error-correcting codes. One associates to a collection of
languages to be analyzed with the PCM a binary (or ternary) code with one code
words for each language in the family and each word consisting of the binary
values of the syntactic parameters of the language, with the ternary case
allowing for an additional parameter state that takes into account phenomena of
entailment of parameters. The code parameters of the resulting code can be
compared with some classical bounds in coding theory: the asymptotic bound, the
Gilbert-Varshamov bound, etc. The position of the code parameters with respect
to some of these bounds provides quantitative information on the variability of
syntactic parameters within and across historical-linguistic families. While
computations carried out for languages belonging to the same family yield codes
below the GV curve, comparisons across different historical families can give
examples of isolated codes lying above the asymptotic bound.
|
1407.7169v1
|
2014-07-28
|
Eddy current effects in the magnetization dynamics of ferromagnetic metal nanoparticles
|
We develop an analytical model for describing the magnetization dynamics in
ferromagnetic metal nanoparticles, which is based on the coupled system of the
Landau-Lifshitz-Gilbert (LLG) and Maxwell equations. By solving Maxwell's
equations in the quasi-static approximation and finding the magnetic field of
eddy currents, we derive the closed LLG equation for the magnetization that
fully accounts for the effects of conductivity. We analyze the difference
between the LLG equations in metallic and dielectric nanoparticles and show
that these effects can strongly influence the magnetization dynamics. As an
example illustrating the importance of eddy currents, the phenomenon of
precessional switching of magnetization is considered.
|
1407.7466v1
|
2014-08-02
|
Standards for Graph Algorithm Primitives
|
It is our view that the state of the art in constructing a large collection
of graph algorithms in terms of linear algebraic operations is mature enough to
support the emergence of a standard set of primitive building blocks. This
paper is a position paper defining the problem and announcing our intention to
launch an open effort to define this standard.
|
1408.0393v1
|
2014-08-02
|
McCool groups of toral relatively hyperbolic groups
|
The outer automorphism group Out(G) of a group G acts on the set of conjugacy
classes of elements of G. McCool proved that the stabilizer $Mc(c_1,...,c_n)$
of a finite set of conjugacy classes is finitely presented when G is free. More
generally, we consider the group $Mc(H_1,...,H_n)$ of outer automorphisms
$\Phi$ of G acting trivially on a family of subgroups $H_i$, in the sense that
$\Phi$ has representatives $\alpha_i$ with $\alpha_i$ equal to the identity on
$H_i$.
When G is a toral relatively hyperbolic group, we show that these two
definitions lead to the same subgroups of Out(G), which we call "McCool groups"
of G. We prove that such McCool groups are of type VF (some finite index
subgroup has a finite classifying space). Being of type VF also holds for the
group of automorphisms of G preserving a splitting of G over abelian groups.
We show that McCool groups satisfy a uniform chain condition: there is a
bound, depending only on G, for the length of a strictly decreasing sequence of
McCool groups of G. Similarly, fixed subgroups of automorphisms of G satisfy a
uniform chain condition.
|
1408.0418v1
|
2014-08-06
|
The first SPIE software Hack Day
|
We report here on the software Hack Day organised at the 2014 SPIE conference
on Astronomical Telescopes and Instrumentation in Montreal. The first ever Hack
Day to take place at an SPIE event, the aim of the day was to bring together
developers to collaborate on innovative solutions to problems of their choice.
Such events have proliferated in the technology community, providing
opportunities to showcase, share and learn skills. In academic environments,
these events are often also instrumental in building community beyond the
limits of national borders, institutions and projects. We show examples of
projects the participants worked on, and provide some lessons learned for
future events.
|
1408.1278v1
|
2014-08-07
|
A broadband silicon quarter-wave retarder for far-infrared spectroscopic circular dichroism
|
The high brightness, broad spectral coverage and pulsed characteristics of
infrared synchrotron radiation enable time-resolved spectroscopy under
throughput-limited optical systems, as can occur with the high-field magnet
cryostat systems used to study electron dynamics and cyclotron resonance by
far-infrared techniques. A natural extension for magnetospectroscopy is to
sense circular dichroism, i.e. the difference in a material's optical response
for left and right circularly polarized light. A key component for
spectroscopic circular dichroism is an achromatic 1/4 wave retarder functioning
over the spectral range of interest. We report here the development of an
in-line retarder using total internal reflection in high-resistivity silicon.
We demonstrate its performance by distinguishing electronic excitations of
different handednesses for GaAs in a magnetic field. This 1/4 wave retarder is
expected to be useful for far-infrared spectroscopy of circular dichroism in
many materials.
|
1408.1650v1
|
2014-08-12
|
Probing the A1 to L10 Transformation in FeCuPt Using the First Order Reversal Curve Method
|
The A1- L10 phase transformation has been investigated in (001) FeCuPt thin
films prepared by atomic-scale multilayer sputtering and rapid thermal
annealing (RTA). Traditional x-ray diffraction is not always applicable in
generating a true order parameter, due to non-ideal crystallinity of the A1
phase. Using the first-order reversal curve (FORC) method, the A1 and L10
phases are deconvoluted into two distinct features in the FORC distribution,
whose relative intensities change with the RTA temperature. The L10 ordering
takes place via a nucleation-and-growth mode. A magnetization-based phase
fraction is extracted, providing a quantitative measure of the L10 phase
homogeneity.
|
1408.2860v1
|
2014-09-09
|
Magnetization pumping and dynamics in a Dzyaloshinskii-Moriya magnet
|
We formulate a phenomenological description of thin ferromagnetic layers with
inversion asymmetry where the single-domain magnetic dynamics experiences
magnon current-induced torques and leads to magnon-motive forces. We first
construct a phenomenological theory based on irreversible thermodynamics,
taking into account the symmetries of the system. Furthermore, we confirm that
these effects originate from Dzyaloshinskii-Moriya interactions from the
analysis based on the stochastic Landau-Lifshitz-Gilbert equation. Our
phenomenological results generalize to a general form of Dzyaloshinskii-Moriya
interactions and to other systems, such as pyrochlore crystals and chiral
magnets. Possible applications include spin current generation, magnetization
reversal and magnonic cooling.
|
1409.2846v3
|
2014-09-17
|
Communities and Hierarchical Structures in Dynamic Social Networks: Analysis and Visualization
|
Detection of community structures in social networks has attracted lots of
attention in the domain of sociology and behavioral sciences. Social networks
also exhibit dynamic nature as these networks change continuously with the
passage of time. Social networks might also present a hierarchical structure
led by individuals that play important roles in a society such as Managers and
Decision Makers. Detection and Visualization of these networks changing over
time is a challenging problem where communities change as a function of events
taking place in the society and the role people play in it.
In this paper we address these issues by presenting a system to analyze
dynamic social networks. The proposed system is based on dynamic graph
discretization and graph clustering. The system allows detection of major
structural changes taking place in social communities over time and reveals
hierarchies by identifying influential people in a social networks. We use two
different data sets for the empirical evaluation and observe that our system
helps to discover interesting facts about the social and hierarchical
structures present in these social networks.
|
1409.5040v1
|
2014-09-30
|
Free upper boundary value problems for the semi-geostrophic equations
|
The semi-geostrophic system is widely used in the modelling of large-scale
atmospheric flows. In this paper, we prove existence of solutions of the
incompressible semi-geostrophic equations in a fully three-dimensional domain
with a free upper boundary condition.
We show that, using methods similar to those introduced in the pioneering
work of Benamou and Brenier, who analysed the same system but with a rigid
boundary condition, we can prove the existence of solutions for the
incompressible free boundary problem. The proof is based on optimal transport
results as well as the analysis of Hamiltonian ODEs in spaces of probability
measures given by Ambrosio and Gangbo. We also show how these techniques can be
modified to yield the same result also for the compressible version of the
system.
|
1409.8560v3
|
2014-10-21
|
Voltage Induced Dynamical Quantum Phase Transitions in Exciton Condensates
|
We explore non-analytic quantum phase dynamics of dipolar exciton condensates
formed in a system of 1D quantum layers subjected to voltage quenches. We map
the exciton condensate physics on to the pseudospin ferromagnet model showing
an additional oscillatory metastable and paramagnetic phase beyond the
well-known ferromagnetic phase by utilizing a time-dependent, non-perturbative
theoretical model. We explain the coherent phase of the exciton condensate in
quantum Hall bilayers, observed for currents equal to and slightly larger than
the critical current, as a stable time-dependent phase characterized by
persistent charged meron flow in each of the individual layers with a
characteristic AC Josephson frequency. As the magnitude of the voltage quench
is further increased, we find that the time-dependent current oscillations
associated with the charged meron flow decay, resulting in a transient
pseudospin paramagnet phase characterized by partially coherent charge transfer
between layers, before the state relaxes to incoherent charge transfer between
the layers.
|
1410.5564v1
|
2014-10-22
|
Landau-Lifshitz-Bloch equation for exchange coupled grains
|
Heat assisted recording is a promising technique to further increase the
storage density in hard disks. Multilayer recording grains with graded Curie
temperature is discussed to further assist the write process. Describing the
correct magnetization dynamics of these grains, from room temperature to far
above the Curie point, during a write process is required for the calculation
of bit error rates. We present a coarse grained approach based on the
Landau-Lifshitz-Bloch (LLB) equation to model exchange coupled grains with low
computational effort. The required temperature dependent material properties
such as the zero-field equilibrium magnetization as well as the parallel and
normal susceptibilities are obtained by atomistic Landau-Lifshitz-Gilbert (LLG)
simulations. Each grain is described with one magnetization vector. In order to
mimic the atomistic exchange interaction between the grains a special treatment
of the exchange field in the coarse grained approach is presented.
|
1410.6066v2
|
2014-10-22
|
A three-dimensional spin-diffusion model for micromagnetics
|
We implement a finite-element scheme that solves the Landau-Lifshitz-Gilbert
equation coupled to a diffusion equation accounting for spin-polarized
currents. The latter solves for the spin accumulation not only in magnetic
materials but also in nonmagnetic conductors. The presented method incorporates
the model by Slonczewski for the description of spin torque in magnetic
multilayers as well as the model of Zhang and Li for the description of current
driven domain-wall motion. Furthermore it is able to do both resolve the time
evolution of the spin accumulation or treat it in an adiabatic fashion by the
choice of sufficiently large time steps.
|
1410.6067v2
|
2014-11-13
|
Random geometric graphs with general connection functions
|
In the original (1961) Gilbert model of random geometric graphs, nodes are
placed according to a Poisson point process, and links formed between those
within a fixed range. Motivated by wireless ad-hoc networks "soft" or
"probabilistic" connection models have recently been introduced, involving a
"connection function" H(r) that gives the probability that two nodes at
distance r are linked (directly connect). In many applications (not only
wireless networks), it is desirable that the graph is connected, that is every
node is linked to every other node in a multihop fashion. Here, the connection
probability of a dense network in a convex domain in two or three dimensions is
expressed in terms of contributions from boundary components, for a very
general class of connection functions. It turns out that only a few quantities
such as moments of the connection function appear. Good agreement is found with
special cases from previous studies and with numerical simulations.
|
1411.3617v3
|
2014-11-24
|
Enhancement of Spin-transfer torque switching via resonant tunneling
|
We propose the use of resonant tunneling as a route to enhance the
spin-transfer torque switching characteristics of magnetic tunnel junctions.
The proposed device structure is a resonant tunneling magnetic tunnel junction
based on a MgO-semiconductor heterostructure sandwiched between a fixed magnet
and a free magnet. Using the non-equilibrium Green's function formalism coupled
self consistently with the Landau-Lifshitz-Gilbert-Slonczewski equation, we
demonstrate enhanced tunnel magneto-resistance characteristics as well as lower
switching voltages in comparison with traditional trilayer devices. Two device
designs based on MgO based heterostructures are presented, where the physics of
resonant tunneling leads to an enhanced spin transfer torque thereby reducing
the critical switching voltage by up to 44%. It is envisioned that the
proof-of-concept presented here may lead to practical device designs via
rigorous materials and interface studies.
|
1411.6454v1
|
2014-12-22
|
Langevin dynamics for vector variables driven by multiplicative white noise: a functional formalism
|
We discuss general multi-dimensional stochastic processes driven by a system
of Langevin equations with multiplicative white noise. In particular, we
address the problem of how time reversal diffusion processes are affected by
the variety of conventions available to deal with stochastic integrals. We
present a functional formalism to built up the generating functional of
correlation functions without any type of discretization of the Langevin
equations at any intermediate step. The generating functional is characterized
by a functional integration over two sets of commuting variables as well as
Grassmann variables. In this representation, time reversal transformation
became a linear transformation in the extended variables, simplifying in this
way the complexity introduced by the mixture of prescriptions and the
associated calculus rules. The stochastic calculus is codified in our formalism
in the structure of the Grassmann algebra. We study some examples such as
higher order derivatives Langevin equations and the functional representation
of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.
|
1412.7015v2
|
2014-12-30
|
Mapping tori of free group automorphisms, and the Bieri-Neumann-Strebel invariant of graphs of groups
|
Let $G$ be the mapping torus of a polynomially growing automorphism of a
finitely generated free group. We determine which epimorphisms from $G$ to
$\mathbb{Z}$ have finitely generated kernel, and we compute the rank of the
kernel. We thus describe all possible ways of expressing $G$ as the mapping
torus of a free group automorphism. This is similar to the case for 3--manifold
groups, and different from the case of mapping tori of exponentially growing
free group automorphisms. The proof uses a hierarchical decomposition of $G$
and requires determining the Bieri-Neumann-Strebel invariant of the fundamental
group of certain graphs of groups.
|
1412.8582v1
|
2015-01-12
|
Magnetic correlations beyond the Heisenberg model in an Fe monolayer on Rh(001)
|
Motivated by a recent experimental observation of a complex magnetic
structure [Takada et al. 2013 J. Magn. Magn. Mater. 329 95] we present a
theoretical study of the magnetic structure of an Fe monolayer deposited on
Rh(001). We use a classical spin Hamiltonian with parameters obtained from ab
initio calculations and go beyond the usual anisotropic Heisenberg model by
including isotropic biquadratic interactions. Zero-temperature
Landau--Lifshitz--Gilbert spin dynamics simulations lead to a complex collinear
spin configuration that, however, contradicts experimental finding. We thus
conclude that higher order multi-spin interactions are likely needed to account
for the magnetic ordering of the system.
|
1501.02657v1
|
2015-01-22
|
Relativistic dynamical spin excitations of magnetic adatoms
|
We present a first-principles theory of dynamical spin excitations in the
presence of spin-orbit coupling. The broken global spin rotational invariance
leads to a new sum rule. We explore the competition between the magnetic
anisotropy energy and the external magnetic field, as well as the role of
electron-hole excitations, through calculations for 3$d$-metal adatoms on the
Cu(111) surface. The spin excitation resonance energy and lifetime display
non-trivial behavior, establishing the strong impact of relativistic effects.
We legitimate the use of the Landau-Lifshitz-Gilbert equation down to the
atomic limit, but with parameters that differ from a stationary theory.
|
1501.05509v1
|
2015-01-23
|
Tuning Range-Separated Density Functional Theory for Photocatalytic Water Splitting Systems
|
We discuss the system-specific optimization of long-range separated density
functional theory (DFT) for the prediction of electronic properties relevant
for a photocatalytic cycle based on an Ir(III) photosensitizer (IrPS). Special
attention is paid to the charge-transfer properties, which are of key
importance for the photoexcitation dynamics, but and cannot be correctly
described by means of conventional DFT. The optimization of the
range-separation parameter using the $\Delta$SCF method is discussed for IrPS
including its derivatives and complexes with electron donors and acceptors used
in photocatalytic hydrogen production. Particular attention is paid to the
problems arising for a description of medium effects by means of a polarizable
continuum model.
|
1501.05863v2
|
2015-01-26
|
Dynamics of magnon fluid in Dzyaloshinskii-Moriya magnet and its manifestation in magnon-Skyrmion scattering
|
We construct Holstein-Primakoff Hamiltonian for magnons in arbitrary slowly
varying spin background, for a microscopic spin Hamiltonian consisting of
ferromagnetic spin exchange,Dzyaloshinskii-Moriya exchange, and the Zeeman
term. The Gross-Pitaevskii-type equation for magnon dynamics contains several
background gauge fields pertaining to local spin chirality, inhomogeneous
potential, and anomalous scattering that violates the boson number
conservation. Non-trivial corrections to previous formulas derived in the
literature are given. Subsequent mapping to hydrodynamic fields yields the
continuity equation and the Euler equation of the magnon fluid dynamics. Magnon
wave scattering off a localized Skyrmion is examined numerically based on our
Gross-Pitaevskii formulation. Dependence of the effective flux experienced by
the impinging magnon on the Skyrmion radius is pointed out, and compared with
analysis of the same problem using the Landau-Lifshitz-Gilbert equation.
|
1501.06467v1
|
2015-02-05
|
Improved efficiency of heat generation in nonlinear dynamics of magnetic nanoparticles
|
The deterministic Landau-Lifshitz-Gilbert equation has been used to
investigate the nonlinear dynamics of magnetization and the specific loss power
in magnetic nanoparticles with uniaxial anisotropy driven by a rotating
magnetic field. We propose a new type of applied field, which is
"simultaneously rotating and alternating", i.e. the direction of the rotating
external field changes periodically. We show that a more efficient heat
generation by magnetic nanoparticles is possible with this new type of applied
field and we suggest its possible experimental realization in cancer therapy
which requires the enhancement of loss energies.
|
1502.01619v2
|
2015-03-10
|
Microwave-induced dynamic switching of magnetic skyrmion cores in nanodots
|
The nonlinear dynamic behavior of a magnetic skyrmion in circular nanodots
was studied numerically by solving the Landau-Lifshitz-Gilbert equation with a
classical spin model. We show that a skyrmion core reversal can be achieved
within nanoseconds using a perpendicular oscillating magnetic field. Two
symmetric switching processes that correspond to excitations of the breathing
mode and the mixed mode (combination of the breathing mode and a radial
spin-wave mode) are identified. For excitation of the breathing mode, the
skyrmion core switches through nucleation of a new core from a transient
uniform state. In the mixed mode, the skyrmion core reverses with the help of
spins excited both at the edge and core regions. Unlike the magnetic vortex
core reversal, the excitation of radial spin waves does not dominate the
skyrmion core reversal process.
|
1503.02869v1
|
2015-03-23
|
Local dynamics of topological magnetic defects in the itinerant helimagnet FeGe
|
Chiral magnetic interactions induce complex spin textures including helical
and conical spin waves, as well as particle-like objects such as magnetic
skyrmions and merons. These spin textures are the basis for innovative device
paradigms and give rise to exotic topological phenomena, thus being of interest
for both applied and fundamental sciences. Present key questions address the
dynamics of the spin system and emergent topological defects. Here we analyze
the micromagnetic dynamics in the helimagnetic phase of FeGe. By combining
magnetic force microscopy, single-spin magnetometry, and
Landau-Lifschitz-Gilbert simulations we show that the nanoscale dynamics are
governed by the depinning and subsequent motion of magnetic edge dislocations.
The motion of these topologically stable objects triggers perturbations that
can propagate over mesoscopic length scales. The observation of stochastic
instabilities in the micromagnetic structure provides new insight to the
spatio-temporal dynamics of itinerant helimagnets and topological defects, and
discloses novel challenges regarding their technological usage.
|
1503.06622v2
|
2015-04-01
|
Minimum-cost matching in a random graph with random costs
|
Let $G_{n,p}$ be the standard Erd\H{o}s-R\'enyi-Gilbert random graph and let
$G_{n,n,p}$ be the random bipartite graph on $n+n$ vertices, where each $e\in
[n]^2$ appears as an edge independently with probability $p$. For a graph
$G=(V,E)$, suppose that each edge $e\in E$ is given an independent uniform
exponential rate one cost. Let $C(G)$ denote the random variable equal to the
length of the minimum cost perfect matching, assuming that $G$ contains at
least one. We show that w.h.p. if $d=np\gg(\log n)^2$ then w.h.p. ${\bf
E}[C(G_{n,n,p})] =(1+o(1))\frac{\p^2}{6p}$. This generalises the well-known
result for the case $G=K_{n,n}$. We also show that w.h.p. ${\bf E}[C(G_{n,p})]
=(1+o(1))\frac{\p^2}{12p}$ along with concentration results for both types of
random graph.
|
1504.00312v5
|
2015-04-04
|
Graphs, Matrices, and the GraphBLAS: Seven Good Reasons
|
The analysis of graphs has become increasingly important to a wide range of
applications. Graph analysis presents a number of unique challenges in the
areas of (1) software complexity, (2) data complexity, (3) security, (4)
mathematical complexity, (5) theoretical analysis, (6) serial performance, and
(7) parallel performance. Implementing graph algorithms using matrix-based
approaches provides a number of promising solutions to these challenges. The
GraphBLAS standard (istc-bigdata.org/GraphBlas) is being developed to bring the
potential of matrix based graph algorithms to the broadest possible audience.
The GraphBLAS mathematically defines a core set of matrix-based graph
operations that can be used to implement a wide class of graph algorithms in a
wide range of programming environments. This paper provides an introduction to
the GraphBLAS and describes how the GraphBLAS can be used to address many of
the challenges associated with analysis of graphs.
|
1504.01039v2
|
2015-04-08
|
A Global Star Forming Episode in M31 2-4 Gyr Ago
|
We have identified a major global enhancement of star formation in the inner
M31 disk that occurred between 2-4 Gyr ago, producing $\sim$60% of the stellar
mass formed in the past 5 Gyr. The presence of this episode in the inner disk
was discovered by modeling the optical resolved star color-magnitude diagrams
of low extinction regions in the main disk of M31 (3$<$R$<$20 kpc) as part of
the Panchromatic Hubble Andromeda Treasury. This measurement confirms and
extends recent measurements of a widespread star formation enhancement of
similar age in the outer disk, suggesting that this burst was both massive and
global. Following the galaxy-wide burst, the star formation rate of M31 has
significantly declined. We briefly discuss possible causes for these features
of the M31 evolutionary history, including interactions with M32, M33 and/or a
merger.
|
1504.02120v1
|
2015-04-13
|
Ultra-low-energy non-volatile straintronic computing using single multiferroic composites
|
The primary impediment to continued downscaling of traditional charge-based
electronic devices in accordance with Moore's law is the excessive energy
dissipation that takes place in the device during switching of bits. One very
promising solution is to utilize multiferroic heterostructures, comprised of a
single-domain magnetostrictive nanomagnet strain-coupled to a piezoelectric
layer, in which the magnetization can be switched between its two stable states
while dissipating minuscule amount of energy. However, no efficient and viable
means of computing is proposed so far. Here we show that such single
multiferroic composites can act as universal logic gates for computing
purposes, which we demonstrate by solving the stochastic
Landau-Lifshitz-Gilbert (LLG) equation of magnetization dynamics in the
presence of room-temperature thermal fluctuations. The proposed concept can
overwhelmingly simplify the design of large-scale circuits and portend a highly
dense yet an ultra-low-energy computing paradigm for our future information
processing systems.
|
1504.03907v1
|
2015-04-20
|
Electric field-induced magnetization switching in interface-coupled multiferroic heterostructures: A highly-dense, non-volatile, and ultra-low-energy computing paradigm
|
Electric-field induced magnetization switching in multiferroic
magnetoelectric devices is promising for beyond Moore's law computing. We show
here that interface-coupled multiferroic heterostructures, i.e., a
ferroelectric layer coupled with a ferromagnetic layer, are particularly
suitable for highly-dense, non-volatile, and ultra-low-energy computing. By
solving stochastic Landau-Lifshitz-Gilbert equation of magnetization dynamics
in the presence of room-temperature thermal fluctuations, we demonstrate that
error-resilient switching of magnetization is possible in sub-nanosecond delay
while expending a minuscule amount of energy of $\sim$1 attojoule. Such devices
can be operated by drawing energy from the environment without the need for an
external battery.
|
1504.05572v1
|
2015-04-23
|
Quantum Magnets and Matrix Lorenz Systems
|
The Landau--Lifshitz--Gilbert equations for the evolution of the
magnetization, in presence of an external torque, can be cast in the form of
the Lorenz equations and, thus, can describe chaotic fluctuations. To study
quantum effects, we describe the magnetization by matrices, that take values in
a Lie algebra. The finite dimensionality of the representation encodes the
quantum fluctuations, while the non-linear nature of the equations can describe
chaotic fluctuations. We identify a criterion, for the appearance of such
non-linear terms. This depends on whether an invariant, symmetric tensor of the
algebra can vanish or not. This proposal is studied in detail for the
fundamental representation of
$\mathfrak{u}(2)=\mathfrak{u}(1)\times\mathfrak{su}(2)$. We find a knotted
structure for the attractor, a bimodal distribution for the largest Lyapunov
exponent and that the dynamics takes place within the Cartan subalgebra, that
does not contain only the identity matrix, thereby can describe the quantum
fluctuations.
|
1504.06161v1
|
2015-04-26
|
Speed of field driven domain walls in nanowires with large transverse magnetic anisotropy
|
Recent analytical and numerical work on field driven domain wall propagation
in nanowires has shown that for large transverse anisotropy and sufficiently
large applied fields the Walker profile becomes unstable before the breakdown
field, giving way to a slower stationary domain wall. We perform an asymptotic
expansion of the Landau Lifshitz Gilbert equation for large transverse magnetic
anisotropy and show that the asymptotic dynamics reproduces this behavior. At
low applied field the speed increases linearly with the field and the profile
is the classic Landau profile. Beyond a critical value of the applied field the
domain wall slows down. The appearance of a slower domain wall profile in the
asymptotic dynamics is due to a transition from a pushed to a pulled front of a
reaction diffusion equation.
|
1504.06865v1
|
2015-04-27
|
New Reversal Mode in Exchange Coupled Antiferromagnetic/Ferromagnetic Disks: Distorted Viscous Vortex
|
Magnetic vortices have generated intense interest in recent years due to
their unique reversal mechanisms, fascinating topological properties, and
exciting potential applications. Additionally, the exchange coupling of
magnetic vortices to antiferromagnets has also been shown to lead to a range of
novel phenomena and functionalities. Here we report a new magnetization
reversal mode of magnetic vortices in exchange coupled Ir20Mn80/Fe20Ni80
microdots: distorted viscous vortex reversal. Contrary to the previously known
or proposed reversal modes, the vortex is distorted close to the interface and
viscously dragged due to the uncompensated spins of a thin antiferromagnet,
which leads to unexpected asymmetries in the annihilation and nucleation
fields. These results provide a deeper understanding of the physics of exchange
coupled vortices and may also have important implications for applications
involving exchange coupled nanostructures.
|
1504.07121v1
|
2015-05-03
|
Driving magnetic skyrmions with microwave fields
|
We show theoretically by numerically solving the Landau-Lifshitz-Gilbert
equation with a classical spin model on a two-dimensional system that both
magnetic skyrmions and skyrmion lattices can be moved with microwave magnetic
fields. The mechanism is enabled by breaking the axial symmetry of the
skyrmion, for example through application of a static in-plane external field.
The net velocity of the skyrmion depends on the frequency and amplitude of the
microwave fields as well as the strength of the in-plane field. The maximum
velocity is found where the frequency of the microwave coincides with the
resonance frequency of the breathing mode of the skyrmions.
|
1505.00445v2
|
2015-05-04
|
Landau-Lifshitz theory of the thermomagnonic torque
|
We derive the thermomagnonic torque associated with smooth magnetic textures
subjected to a temperature gradient, in the framework of the stochastic
Landau-Lifshitz-Gilbert equation. Our approach captures on equal footing two
distinct contributions: (1) A local entropic torque that is caused by a
temperature dependence of the effective exchange field, the existence of which
had been previously suggested based on numerics and (2) the well-known
spin-transfer torque induced by thermally-induced magnon flow. The dissipative
components of two torques have the same structure, following a common
phenomenology, but opposite signs, with the twice larger entropic torque
leading to a domain-wall motion toward the hotter region. We compare the
efficiency of the torque-driven domain-wall motion with the recently proposed
Brownian thermophoresis.
|
1505.00818v1
|
2015-05-05
|
Three-dimensional Character of the Magnetization Dynamics in Magnetic Vortex Structures - Hybridization of Flexure Gyromodes with Spin Waves
|
Three-dimensional linear spin-wave eigenmodes of a Permalloy disk having
finite thickness are studied by micromagnetic simulations based on the
Landau-Lifshitz-Gilbert equation. The eigenmodes found in the simulations are
interpreted as linear superpositions (hybridizations) of 'approximate'
three-dimensional eigenmodes, which are the fundamental gyromode $G_0$, the
spin-wave modes and the higher-order gyromodes $G_N$ (flexure modes), the
thickness dependence of which is represented by perpendicular standing spin
waves. This hybridization leads to new and surprising dependencies of the mode
frequencies on the disk thickness. The three-dimensional character of the
eigenmodes is essential to explain the recent experimental results on
vortex-core reversal observed in relatively thick Permalloy disks.
|
1505.01148v2
|
2015-05-14
|
A Subset Selection Algorithm for Wireless Sensor Networks
|
One of the main challenges facing wireless sensor networks (WSNs) is the
limited power resources available at small sensor nodes. It is therefore
desired to reduce the power consumption of sensors while keeping the distortion
between the source information and its estimate at the fusion centre (FC) below
a specific threshold. In this paper, given the channel state information at the
FC, we propose a subset selection algorithm of sensor nodes to reduce the
average transmission power of the WSN. We assume the channels between the
source and the sensors to be correlated fading channels, modeled by the
Gilbert-Elliott model. We show that when these channels are known at the FC, a
subset of sensors can be selected by the FC such that the received observations
from this subset is sufficient to estimate the source information at the FC
while maintaining the distortion between source information and its estimate
below a specific threshold. Through analyses, we find the probability
distribution of the size of this subset and provide results to evaluate the
power efficiency of our proposed algorithm.
|
1505.03640v1
|
2015-05-20
|
Effect of Transverse Magnetic Field on Dynamics of Current Driven Domain Wall Motion in the Presence of Spin-Hall Effect
|
Theoretically, we study the dynamics of a current induced domain wall in the
bi-layer structure consists of a ferromagnetic layer and a non-magnetic metal
layer with strong spin-orbit coupling in the presence of spin-Hall effect. The
analytical expressions for the velocity and width of the domain wall interms of
excitation angle are obtained by solving the Landau-Lifshitz-Gilbert equation
with adiabatic, nonadiabatic and spin Hall effect-spin transfer torques using
Schryers and Walker's method. Numerical results show that the occurance of
polarity switching in the domain wall is observed only above the threshold
current density. The presence of transverse magnetic field along with spin Hall
effect-spin transfer torque enchances the value of the threshold current
density, and the corresponding saturated velocity at the threshold current
density is also increased.
|
1505.05249v1
|
2015-05-25
|
New Explicit Binary Constant Weight Codes from Reed-Solomon Codes
|
Binary constant weight codes have important applications and have been
studied for many years. Optimal or near-optimal binary constant weight codes of
small lengths have been determined. In this paper we propose a new construction
of explicit binary constant weight codes from $q$-ary Reed-Solomon codes. Some
of our binary constant weight codes are optimal or new. In particular new
binary constant weight codes $A(64, 10, 8) \geq 4108$ and $A(64, 12, 8) \geq
522$ are constructed. We also give explicitly constructed binary constant
weight codes which improve Gilbert and Graham-Sloane lower bounds in some range
of parameters. An extension to algebraic geometric codes is also presented.
|
1505.06524v4
|
2015-06-01
|
Closing the hierarchy for non-Markovian magnetization dynamics
|
We propose a stochastic approach for the description of the time evolution of
the magnetization of nanomagnets, that interpolates between the
Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch approximations, by
varying the strength of the noise. In addition, we take into account the
autocorrelation time of the noise and explore the consequences, when it is
finite, on the scale of the response of the magnetization, i.e. when it may be
described as colored, rather than white, noise and non-Markovian features
become relevant. We close the hierarchy for the moments of the magnetization,
by introducing a suitable truncation scheme, whose validity is tested by direct
numerical solution of the moment equations and compared to the average deduced
from a numerical solution of the corresponding stochastic Langevin equation. In
this way we establish a general framework, that allows both coarse-graining
simulations and faster calculations beyond the truncation approximation used
here.
|
1506.00544v1
|
2015-06-02
|
Spin Superfluidity in the $ν=0$ Quantum Hall State of Graphene
|
A proposal to detect the purported canted antiferromagnet order for the
$\nu=0$ quantum Hall state of graphene based on a two-terminal spin transport
setup is theoretically discussed. In the presence of a magnetic field normal to
the graphene plane, a dynamic and inhomogeneous texture of the N\'eel vector
lying within the plane should mediate (nearly dissipationless) superfluid
transport of spin angular momentum polarized along the $z$ axis, which could
serve as a strong support for the canted antiferromagnet scenario. Spin
injection and detection can be achieved by coupling two spin-polarized edge
channels of the $|\nu|=2$ quantum Hall state on two opposite ends of the
$\nu=0$ region. A simple kinetic theory and Onsager reciprocity are invoked to
model the spin injection and detection processes, and the transport of spin
through the antiferromagnet is accounted for using the Landau-Lifshitz-Gilbert
phenomenology.
|
1506.01061v1
|
2015-06-05
|
Multi-reference approach to the calculation of photoelectron spectra including spin-orbit coupling
|
X-ray photoelectron spectra provide a wealth of information on the electronic
structure. The extraction of molecular details requires adequate theoretical
methods, which in case of transition metal complexes has to account for effects
due to the multi-configurational and spin-mixed nature of the many-electron
wave function. Here, the Restricted Active Space Self-Consistent Field method
including spin-orbit coupling is used to cope with this challenge and to
calculate valence and core photoelectron spectra. The intensities are estimated
within the frameworks of the Dyson orbital formalism and the sudden
approximation. Thereby, we utilize an efficient computational algorithm that is
based on a biorthonormal basis transformation. The approach is applied to the
valence photoionization of the gas phase water molecule and to the core
ionization spectrum of the $\text{[Fe(H}_2\text{O)}_6\text{]}^{2+}$ complex.
The results show good agreement with the experimental data obtained in this
work, whereas the sudden approximation demonstrates distinct deviations from
experiments.
|
1506.01826v1
|
2015-06-10
|
Parafermionic phases with symmetry-breaking and topological order
|
Parafermions are the simplest generalizations of Majorana fermions that
realize topological order. We propose a less restrictive notion of topological
order in 1D open chains, which generalizes the seminal work by Fendley [J.
Stat. Mech., P11020 (2012)]. The first essential property is that the
groundstates are mutually indistinguishable by local, symmetric probes, and the
second is a generalized notion of zero edge modes which cyclically permute the
groundstates. These two properties are shown to be topologically robust, and
applicable to a wider family of topologically-ordered Hamiltonians than has
been previously considered. An an application of these edge modes, we formulate
a new notion of twisted boundary conditions on a closed chain, which guarantees
that the closed-chain groundstate is topological, i.e., it originates from the
topological manifold of degenerate states on the open chain. Finally, we
generalize these ideas to describe symmetry-breaking phases with a
parafermionic order parameter. These exotic phases are condensates of
parafermion multiplets, which generalizes Cooper pairing in superconductors.
The stability of these condensates are investigated on both open and closed
chains.
|
1506.03455v1
|
2015-06-17
|
Magnetic field control of the spin Seebeck effect
|
The origin of the suppression of the longitudinal spin Seebeck effect by
applied magnetic fields is studied. We perform numerical simulations of the
stochastic Landau-Lifshitz-Gilbert equation of motion for an atomistic spin
model and calculate the magnon accumulation in linear temperature gradients for
different strengths of applied magnetic fields and different length scales of
the temperature gradient. We observe a decrease of the magnon accumulation with
increasing magnetic field and we reveal that the origin of this effect is a
field dependent change of the frequency distribution of the propagating
magnons. With increasing field the magnonic spin currents are reduced due to a
suppression of parts of the frequency spectrum. By comparison with measurements
of the magnetic field dependent longitudinal spin Seebeck effect in YIG thin
films with various thicknesses, we find that our model describes the
experimental data very well, demonstrating the importance of this effect for
experimental systems.
|
1506.05290v1
|
2015-06-18
|
The pion quasiparticle in the low-temperature phase of QCD
|
We investigate the properties of the pion quasiparticle in the
low-temperature phase of two-flavor QCD on the lattice with support from chiral
effective theory. We find that the pion quasiparticle mass is significantly
reduced compared to its value in the vacuum, by contrast with the static
screening mass, which increases with temperature. By a simple argument, near
the chiral limit the two masses are expected to determine the quasiparticle
dispersion relation. Analyzing two-point functions of the axial charge density
at non-vanishing spatial momentum, we find that the predicted dispersion
relation and the residue of the pion pole are simultaneously consistent with
the lattice data at low momentum. The test, based on fits to the correlation
functions, is confirmed by a second analysis using the Backus-Gilbert method.
|
1506.05732v1
|
2015-06-23
|
Bounds on the Parameters of Locally Recoverable Codes
|
A locally recoverable code (LRC code) is a code over a finite alphabet such
that every symbol in the encoding is a function of a small number of other
symbols that form a recovering set. In this paper we derive new finite-length
and asymptotic bounds on the parameters of LRC codes. For LRC codes with a
single recovering set for every coordinate, we derive an asymptotic
Gilbert-Varshamov type bound for LRC codes and find the maximum attainable
relative distance of asymptotically good LRC codes. Similar results are
established for LRC codes with two disjoint recovering sets for every
coordinate. For the case of multiple recovering sets we derive a lower bound on
the parameters using expander graph arguments. Finally, we also derive
finite-length upper bounds on the rate and distance of LRC codes with multiple
recovering sets.
|
1506.07196v2
|
2015-06-24
|
From Random Matrix Theory to Coding Theory: Volume of a Metric Ball in Unitary Group
|
Volume estimates of metric balls in manifolds find diverse applications in
information and coding theory. In this paper, some new results for the volume
of a metric ball in unitary group are derived via various tools from random
matrix theory. The first result is an integral representation of the exact
volume, which involves a Toeplitz determinant of Bessel functions. The
connection to matrix-variate hypergeometric functions and Szeg\H{o}'s strong
limit theorem lead independently from the finite size formula to an asymptotic
one. The convergence of the limiting formula is exceptionally fast due to an
underlying mock-Gaussian behavior. The proposed volume estimate enables simple
but accurate analytical evaluation of coding-theoretic bounds of unitary codes.
In particular, the Gilbert-Varshamov lower bound and the Hamming upper bound on
cardinality as well as the resulting bounds on code rate and minimum distance
are derived. Moreover, bounds on the scaling law of code rate are found.
Lastly, a closed-form bound on diversity sum relevant to unitary space-time
codes is obtained, which was only computed numerically in literature.
|
1506.07259v1
|
2015-06-18
|
Ultra-low-energy computing paradigm using giant spin Hall devices
|
Spin Hall effect converts charge current to spin current, which can exert
spin-torque to switch the magnetization of a nanomagnet. Recently, it is shown
that the ratio of spin current to charge current using spin Hall effect can be
made more than unity by using the areal geometry judiciously, unlike the case
of conventional spin-transfer-torque switching of nanomagnets. This can enable
energy-efficient means to write a bit of information in nanomagnets. Here, we
study the energy dissipation in such spin Hall devices. By solving stochastic
Landau-Lifshitz-Gilbert equation of magnetization dynamics in the presence of
room temperature thermal fluctuations, we show a methodology to simultaneously
reduce switching delay, its variance and energy dissipation, while lateral
dimensions of the spin Hall devices are scaled down.
|
1506.07863v1
|
2015-06-18
|
Separating read and write units in multiferroic devices
|
Strain-mediated multiferroic composites, i.e., piezoelectric-magnetostrictive
heterostructures, hold profound promise for energy-efficient computing in
beyond Moore's law era. While reading a bit of information stored in the
magnetostrictive nanomagnets using a magnetic tunnel junction (MTJ), a material
selection issue crops up since magnetostrictive materials in general cannot be
utilized as the free layer of the MTJ. This is an important issue since we need
to achieve a high magnetoresistance for technological applications. We show
here that magnetically coupling the magnetostrictive nanomagnet and the free
layer e.g., utilizing the magnetic dipole coupling between them can circumvent
this issue. By solving stochastic Landau-Lifshitz-Gilbert equation of
magnetization dynamics in the presence of room-temperature thermal
fluctuations, we show that such design can eventually lead to a superior
energy-delay product.
|
1506.07865v1
|
2015-06-26
|
Estimating the Parameters of the Waxman Random Graph
|
The Waxman random graph is a generalisation of the simple Erd\H{o}s-R\'enyi
or Gilbert random graph. It is useful for modelling physical networks where the
increased cost of longer links means they are less likely to be built, and thus
less numerous than shorter links. The model has been in continuous use for over
two decades with many attempts to select parameters which match real networks.
In most the parameters have been arbitrarily selected, but there are a few
cases where they have been calculated using a formal estimator. However, the
performance of the estimator was not evaluated in any of these cases. This
paper presents both the first evaluation of formal estimators for the
parameters of these graphs, and a new Maximum Likelihood Estimator with $O(n)$
computational time complexity that requires only link lengths as input.
|
1506.07974v2
|
2015-07-07
|
Rayleigh-Jeans condensation of pumped magnons in thin film ferromagnets
|
We show that the formation of a magnon condensate in thin ferromagnetic films
can be explained within the framework of a classical stochastic non-Markovian
Landau-Lifshitz-Gilbert equation where the properties of the random magnetic
field and the dissipation are determined by the underlying phonon dynamics. We
have numerically solved this equation for a tangentially magnetized
yttrium-iron garnet film in the presence of a parallel parametric pumping
field. We obtain a complete description of all stages of the nonequilibrium
time evolution of the magnon gas which is in excellent agreement with
experiments. Our calculation proves that the experimentally observed
condensation of magnons in yttrium-iron garnet at room temperature is a purely
classical phenomenon which should be called Rayleigh-Jeans rather than
Bose-Einstein condensation.
|
1507.01717v2
|
2015-07-07
|
Dynamic Reallocation Problems in Scheduling
|
In this paper we look at the problem of scheduling tasks on a
single-processor system, where each task requires unit time and must be
scheduled within a certain time window, and each task can be added to or
removed from the system at any time. On each operation, the system is allowed
to reschedule any tasks, but the goal is to minimize the number of rescheduled
tasks. Our main result is an allocator that maintains a valid schedule for all
tasks in the system if their time windows have constant size and reschedules
O(1/{\epsilon}*log(1/{\epsilon})) tasks on each insertion as {\epsilon}->0,
where {\epsilon} is a certain measure of the schedule flexibility of the
system. We also show that it is optimal for any allocator that works on
arbitrary instances. We also briefly mention a few variants of the problem,
such as if the tasks have time windows of difference sizes, for which we have
an allocator that we conjecture reschedules only 1 task on each insertion if
the schedule flexibility remains above a certain threshold.
|
1507.01981v2
|
2015-08-03
|
Stable oscillation in spin torque oscillator excited by a small in-plane magnetic field
|
Theoretical conditions to excite self-oscillation in a spin torque oscillator
consisting of a perpendicularly magnetized free layer and an in-plane
magnetized pinned layer are investigated by analytically solving the
Landau-Lifshitz-Gilbert equation. The analytical relation between the current
and oscillation frequency is derived. It is found that a large amplitude
oscillation can be excited by applying a small field pointing to the direction
anti-parallel to the magnetization of the pinned layer. The validity of the
analytical results is confirmed by comparing with numerical simulation, showing
good agreement especially in a low current region.
|
1508.00601v1
|
2015-08-07
|
Spin Dynamics in Driven Composite Multiferroics
|
A spin dynamics approach has been used to study the behavior of the magnetic
spins and the electric pseudo-spins in a 1-D composite multiferroic chain with
a linear magneto-electric coupling at the interface. The response is
investigated with either external magnetic or electric fields driving the
system. The spin dynamics is based on the Landau-Lifshitz-Gilbert equation. A
Gaussian white noise is later added into the dynamic process to include the
thermal effects. The interface requires a closer inspection of the
magneto-electric effects. Thus, we construct a 2-D ladder model to describe the
behavior of the magnetic spins and the electric pseudo-spins with different
magneto-electric couplings.
|
1508.01584v2
|
2015-08-11
|
Analysis of a coupled spin drift-diffusion Maxwell-Landau-Lifshitz system
|
The existence of global weak solutions to a coupled spin drift-diffusion and
Maxwell-Landau-Lifshitz system is proved. The equations are considered in a
two-dimensional magnetic layer structure and are supplemented with
Dirichlet-Neumann boundary conditions. The spin drift-diffusion model for the
charge density and spin density vector is the diffusion limit of a spinorial
Boltzmann equation for a vanishing spin polarization constant. The
Maxwell-Landau-Lifshitz system consists of the time-dependent Maxwell equations
for the electric and magnetic fields and of the Landau-Lifshitz-Gilbert
equation for the local magnetization, involving the interaction between
magnetization and spin density vector. The existence proof is based on a
regularization procedure, $L^2$-type estimates, and Moser-type iterations which
yield the boundedness of the charge and spin densities. Furthermore, the free
energy is shown to be nonincreasing in time if the magnetization-spin
interaction constant in the Landau-Lifshitz equation is sufficiently small.
|
1508.02660v1
|
2015-08-12
|
Bounds for codes on pentagon and other cycles
|
The capacity of a graph is defined as the rate of exponential grow of
independent sets in the strong powers of the graph. In strong power, an edge
connects two sequences if at each position letters are equal or adjacent. We
consider a variation of the problem where edges in the power graphs are removed
among sequences which differ in more than a fraction $\delta$ of coordinates.
For odd cycles, we derive an upper bound on the corresponding rate which
combines Lov\'asz' bound on the capacity with Delsarte's linear programming
bounds on the minimum distance of codes in Hamming spaces. For the pentagon,
this shows that for $\delta \ge {1-{1\over\sqrt{5}}}$ the Lov\'asz rate is the
best possible, while we prove by a Gilbert-Varshamov-type bound that a higher
rate is achievable for $\delta < {2\over 5}$.
Communication interpretation of this question is the problem of sending
quinary symbols subject to $\pm 1\mod 5$ disturbance. The maximal communication
rate subject to the zero undetected-error equals capacity of a pentagon. The
question addressed here is how much this rate can be increased if only a
fraction $\delta$ of symbols is allowed to be disturbed
|
1508.03020v1
|
2015-08-14
|
Smoothed Analysis of Dynamic Networks
|
We generalize the technique of smoothed analysis to distributed algorithms in
dynamic network models. Whereas standard smoothed analysis studies the impact
of small random perturbations of input values on algorithm performance metrics,
dynamic graph smoothed analysis studies the impact of random perturbations of
the underlying changing network graph topologies. Similar to the original
application of smoothed analysis, our goal is to study whether known strong
lower bounds in dynamic network models are robust or fragile: do they withstand
small (random) perturbations, or do such deviations push the graphs far enough
from a precise pathological instance to enable much better performance? Fragile
lower bounds are likely not relevant for real-world deployment, while robust
lower bounds represent a true difficulty caused by dynamic behavior. We apply
this technique to three standard dynamic network problems with known strong
worst-case lower bounds: random walks, flooding, and aggregation. We prove that
these bounds provide a spectrum of robustness when subjected to
smoothing---some are extremely fragile (random walks), some are moderately
fragile / robust (flooding), and some are extremely robust (aggregation).
|
1508.03579v1
|
2015-08-16
|
The Computational Power of Beeps
|
In this paper, we study the quantity of computational resources (state
machine states and/or probabilistic transition precision) needed to solve
specific problems in a single hop network where nodes communicate using only
beeps. We begin by focusing on randomized leader election. We prove a lower
bound on the states required to solve this problem with a given error bound,
probability precision, and (when relevant) network size lower bound. We then
show the bound tight with a matching upper bound. Noting that our optimal upper
bound is slow, we describe two faster algorithms that trade some state
optimality to gain efficiency. We then turn our attention to more general
classes of problems by proving that once you have enough states to solve leader
election with a given error bound, you have (within constant factors) enough
states to simulate correctly, with this same error bound, a logspace TM with a
constant number of unary input tapes: allowing you to solve a large and
expressive set of problems. These results identify a key simplicity threshold
beyond which useful distributed computation is possible in the beeping model.
|
1508.03859v1
|
2015-09-02
|
Topological dynamics and current-induced motion in a skyrmion lattice
|
We study the Thiele equation for current-induced motion in a skyrmion lattice
through two soluble models of the pinning potential. Comprised by a Magnus
term, a dissipative term and a pinning force, Thiele's equation resembles
Newton's law but in virtue of the topological character of the first two, it
differs significantly from Newtonian mechanics and because the Magnus force is
dominant, unlike its mechanical counterpart, the Coriolis force, skyrmion
trajectories do not necessarily have mechanical counterparts. This is important
if we are to understand skykrmion dynamics and tap into its potential for
data-storage technology. We identify a pinning threshold velocity for the
one-dimensional potential and for a two-dimensional potential we find a pinning
point and the skyrmion trajectories toward the point are spirals whose
frequency (compare Kepler's second law) and amplitude decay depends only on the
Gilbert constant and potential at the pinning point.
|
1509.00591v1
|
2015-09-02
|
Thermally-Activated Phase Slips in Superfluid Spin Transport in Magnetic Wires
|
We theoretically study thermally-activated phase slips in superfluid spin
transport in easy-plane magnetic wires within the stochastic
Landau-Lifshitz-Gilbert phenomenology, which runs parallel to the
Langer-Ambegaokar-McCumber-Halperin theory for thermal resistances in
superconducting wires. To that end, we start by obtaining the exact solutions
for free-energy minima and saddle points. We provide an analytical expression
for the phase-slip rate in the zero spin-current limit, which involves detailed
analysis of spin fluctuations at extrema of the free energy. An experimental
setup of a magnetoeletric circuit is proposed, in which thermal phase slips can
be inferred by measuring nonlocal magnetoresistance.
|
1509.00904v1
|
2015-09-11
|
Comparison between a quantum kinetic theory of spin transfer dynamics in Mn doped bulk semiconductors and its Markov limit for non-zero Mn magnetization
|
We investigate the transfer between carrier and Mn spins due to the
s-d-exchange interaction in a Mn doped bulk semiconductor within a microscopic
quantum kinetic theory. We demonstrate that the spin transfer dynamics is
qualitatively different for components of the carrier spin parallel and
perpendicular to the Mn magnetization. From our quantum kinetic equations we
have worked out the corresponding Markov limit which is equivalent to rate
equations based on Fermi's golden rule. The resulting equations resemble the
widely used Landau-Lifshitz-Gilbert-equations, but also describe genuine spin
transfer due to quantum corrections. Although it is known that the Markovian
rate description works well for bulk systems when the initial Mn magnetization
is zero, we find large qualitative deviations from the full quantum kinetic
theory for finite initial Mn magnetizations. These deviations mainly reflect
corrections of higher than leading order in the interaction which are not
accounted for in golden rule-type rates.
|
1509.03479v1
|
2015-09-14
|
Spectral characteristics of time resolved magnonic spin Seebeck effect
|
Spin Seebeck effect (SSE) holds promise for new spintronic devices with
low-energy consumption. The underlying physics, essential for a further
progress, is yet to be fully clarified. This study of the time resolved
longitudinal SSE in the magnetic insulator yttrium iron garnet (YIG) concludes
that a substantial contribution to the spin current stems from small
wave-vector subthermal exchange magnons. Our finding is in line with the recent
experiment by S. R. Boona and J. P. Heremans, Phys. Rev. B 90, 064421 (2014).
Technically, the spin-current dynamics is treated based on the
Landau-Lifshitz-Gilbert (LLG) equation also including magnons back-action on
thermal bath, while the formation of the time dependent thermal gradient is
described self-consistently via the heat equation coupled to the magnetization
dynamics
|
1509.04018v1
|
2015-09-21
|
The pion quasiparticle in the low-temperature phase of QCD
|
We investigate the properties of the pion quasiparticle in the
low-temperature phase of two-flavor QCD on the lattice with support from chiral
effective theory. We find that the pion quasiparticle mass is significantly
reduced compared to its value in the vacuum, in contrast to the static
screening mass, which increases with temperature. By a simple argument, the two
masses are expected to determine the quasiparticle dispersion relation near the
chiral limit. Analyzing two-point functions of the axial charge density at
non-vanishing spatial momentum, we find that the predicted dispersion relation
and the residue of the pion pole are simultaneously consistent with the lattice
data at low momentum. The test, based on fits to the correlation functions, is
confirmed by a second analysis using the Backus-Gilbert method.
|
1509.06241v1
|
2015-10-29
|
On Differentially Private Online Collaborative Recommendation Systems
|
In collaborative recommendation systems, privacy may be compromised, as
users' opinions are used to generate recommendations for others. In this paper,
we consider an online collaborative recommendation system, and we measure
users' privacy in terms of the standard differential privacy. We give the first
quantitative analysis of the trade-offs between recommendation quality and
users' privacy in such a system by showing a lower bound on the best achievable
privacy for any non-trivial algorithm, and proposing a near-optimal algorithm.
From our results, we find that there is actually little trade-off between
recommendation quality and privacy for any non-trivial algorithm. Our results
also identify the key parameters that determine the best achievable privacy.
|
1510.08546v1
|
2015-11-05
|
Non-Markovian magnetization dynamics for uniaxial nanomagnets
|
A stochastic approach for the description of the time evolution of the
magnetization of nanomagnets is proposed, that interpolates between the
Landau-Lifshitz-Gilbert and the Landau-Lifshitz-Bloch approximations, by
varying the strength of the noise. Its finite autocorrelation time, i.e. when
it may be described as colored, rather than white, is, also, taken into account
and the consequences, on the scale of the response of the magnetization are
investigated. It is shown that the hierarchy for the moments of the
magnetization can be closed, by introducing a suitable truncation scheme, whose
validity is tested by direct numerical solution of the moment equations and
compared to the averages obtained from a numerical solution of the
corresponding colored stochastic Langevin equation. This comparison is
performed on magnetic systems subject to both an external uniform magnetic
field and an internal one-site uniaxial anisotropy.
|
1511.01693v1
|
2015-11-06
|
Colored-noise magnetization dynamics: from weakly to strongly correlated noise
|
Statistical averaging theorems allow us to derive a set of equations for the
averaged magnetization dynamics in the presence of colored (non-Markovian)
noise. The non-Markovian character of the noise is described by a finite
auto-correlation time, tau, that can be identified with the finite response
time of the thermal bath to the system of interest. Hitherto, this model was
only tested for the case of weakly correlated noise (when tau is equivalent or
smaller than the integration timestep). In order to probe its validity for a
broader range of auto-correlation times, a non-Markovian integration model,
based on the stochastic Landau-Lifshitz-Gilbert equation is presented.
Comparisons between the two models are discussed, and these provide evidence
that both formalisms remain equivalent, even for strongly correlated noise
(i.e. tau much larger than the integration timestep).
|
1511.02008v1
|
2015-12-17
|
A self-consistent spin-diffusion model for micromagnetics
|
We propose a three-dimensional micromagnetic model that dynamically solves
the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion
equation. In contrast to previous methods, we solve for the magnetization
dynamics and the electric potential in a self-consistent fashion. This
treatment allows for an accurate description of magnetization dependent
resistance changes. Moreover, the presented algorithm describes both spin
accumulation due to smooth magnetization transitions and due to material
interfaces as in multilayer structures. The model and its finite-element
implementation are validated by current driven motion of a magnetic vortex
structure. In a second experiment, the resistivity of a magnetic multilayer
structure in dependence of the tilting angle of the magnetization in the
different layers is investigated. Both examples show good agreement with
reference simulations and experiments respectively.
|
1512.05519v4
|
2015-12-17
|
Statics and field-driven dynamics of transverse domain walls in biaxial nanowires under uniform transverse magnetic fields
|
In this work, we report analytical results on transverse domain wall (TDW)
statics and field-driven dynamics in quasi one-dimensional biaxial nanowires
under arbitrary uniform transverse magnetic fields (TMFs) based on the
Landau-Lifshitz-Gilbert equation. Without axial driving fields, the static TDW
should be symmetric about its center meanwhile twisted in its azimuthal angle
distribution. By decoupling of polar and azimuthal degrees of freedom, an
approximate solution is provided which reproduces these features to a great
extent. When an axial driving field is applied, the dynamical behavior of a TDW
is viewed as the response of its static profile to external excitations. By
means of the asymptotic expansion method, the TDW velocity in traveling-wave
mode is obtained, which provides the extent and boundary of the
"velocity-enhancement" effect of TMFs to TDWs in biaxial nanowires. Finally
numerical simulations are performed and strongly support our analytics.
|
1512.05627v2
|
2015-12-24
|
Eroding dipoles and vorticity growth for Euler flows in $ \scriptstyle{\mathbb{R}}^3$ I. Axisymmetric flow without swirl
|
A review of analyses based upon anti-parallel vortex structures suggests that
structurally stable vortex structures with eroding circulation may offer a path
to the study of rapid vorticity growth in solutions of Euler's equations in $
\scriptstyle{\mathbb{R}}^3$. We examine here the possible formation of such a
structure in axisymmetric flow without swirl, leading to maximal growth of
vorticity as $t^{4/3}$. Our study suggests that the optimizing flow giving the
$t^{4/3}$ growth mimics an exact solution of Euler's equations representing an
eroding toroidal vortex dipole which locally conserves kinetic energy. The
dipole cross-section is a perturbation of the classical Sadovskii dipole having
piecewise constant vorticity, which breaks the symmetry of closed streamlines.
The structure of this perturbed Sadovskii dipole is analyzed asymptotically at
large times, and its predicted properties are verified numerically.
|
1512.07898v1
|
2016-01-11
|
Reliable spin-transfer torque driven precessional magnetization reversal with an adiabatically decaying pulse
|
We show that a slowly decaying current pulse can lead to nearly deterministic
precessional switching in the presence of noise. We consider a biaxial
macrospin, with an easy axis in the plane and a hard axis out-of-the plane,
typical of thin film nanomagnets patterned into asymmetric shapes. Out-of-plane
precessional magnetization orbits are excited with a current pulse with a
component of spin polarization normal to the film plane. By numerically
integrating the stochastic Landau-Lifshitz-Gilbert-Slonczewski equation we show
that thermal noise leads to strong dephasing of the magnetization orbits.
However, an adiabatically decreasing pulse amplitude overwhelmingly leads to
magnetization reversal, with a final state that {\em only} depends on the pulse
polarity, not on the pulse amplitude. We develop an analytic model to explain
this phenomena and to determine the pulse decay time necessary for adiabatic
magnetization relaxation and thus precessional magnetization switching.
|
1601.02336v1
|
2016-01-19
|
Minimal Radius of Magnetic Skyrmions: Statics and Dynamics
|
In a broad range of applied magnetic fields and material parameters isolated
magnetic skyrmions condense into skyrmion lattices. While the geometry of
isolated skyrmions and their lattice counterparts strongly depend on field and
Dzyaloshinski-Moriya interaction, this issue has not been adequately addressed
in previous studies. Meanwhile, this information is extremely important for
applications, because the skyrmion size and the interskyrmion distance have to
be tuned for skyrmion based memory and logic devices. In this investigation we
elucidate the size and density-dependent phase diagram showing traditional
phases in field vs. material parameters space by means of Monte-Carlo
simulations on a discrete lattice. The obtained diagram permits us to establish
that, in contrast to the continuum limit, skyrmions on a discrete lattice
cannot be smaller than some critical size and have a very specific shape. These
minimal skyrmions correspond to the micromagnetic configuration at the energy
barrier between the ferromagnetic and the skyrmionic states. Furthermore, we
use atomistic Landau-Lifshitz-Gilbert simulations to study dynamics of the
skyrmion annihilation. It is shown that this procees consists of two stages:
the continuous skyrmion contraction and its discontinuous annihilation. The
detailed analysis of this dynamical process is given.
|
1601.04898v1
|
2016-01-20
|
Limited-Magnitude Error-Correcting Gray Codes for Rank Modulation
|
We construct Gray codes over permutations for the rank-modulation scheme,
which are also capable of correcting errors under the infinity-metric. These
errors model limited-magnitude or spike errors, for which only
single-error-detecting Gray codes are currently known. Surprisingly, the
error-correcting codes we construct achieve a better asymptotic rate than that
of presently known constructions not having the Gray property, and exceed the
Gilbert-Varshamov bound. Additionally, we present efficient ranking and
unranking procedures, as well as a decoding procedure that runs in linear time.
Finally, we also apply our methods to solve an outstanding issue with
error-detecting rank-modulation Gray codes (snake-in-the-box codes) under a
different metric, the Kendall $\tau$-metric, in the group of permutations over
an even number of elements $S_{2n}$, where we provide asymptotically optimal
codes.
|
1601.05218v3
|
2016-01-20
|
Many-body effects on graphene conductivity: Quantum Monte Carlo calculations
|
Optical conductivity of graphene is studied using Quantum Monte Carlo
calculations. We start from Euclidean current-current correlator and extract
$\sigma (\omega)$ from Green-Kubo relations using Backus-Gilbert method.
Calculations were performed both for long-range interactions and taking into
account only contact term. In both cases we vary interaction strength and study
its influence on optical conductivity. We compare our results with previous
theoretical calculations choosing $\omega \approx \kappa$ thus working in the
region of the plateau in $\sigma(\omega)$ which corresponds to optical
conductivity of Dirac quasiparticles. No dependence of optical conductivity on
interaction strength is observed unless we approach antiferromagnetic phase
transition in case of artificially enhanced contact term. Our results strongly
support previous theoretical studies claimed very weak regularization of
graphene conductivity.
|
1601.05315v2
|
2016-02-01
|
Efficient thermal energy harvesting using nanoscale magnetoelectric heterostructures
|
Thermomechanical cycles with a ferroelectric working substance convert heat
to electrical energy. As shown here, magnetoelectrically coupled
ferroelectric/ferromangtic composites (also called multiferroics) add new
functionalities and allow for an efficient thermal energy harvesting at room
temperature by exploiting the pyroelectric effect. By virtue of the
magnetoelectric coupling, external electric and magnetic fields can steer the
operation of these heat engines. Our theoretical predictions are based on a
combination of Landau-Khalatnikov-Tani approach (with a
Ginzburg-Landau-Devonshire potential) to simulate the ferroelectric dynamics
coupled to the magnetic dynamics. The latter is treated via the
electric-polarization-dependent Landau-Lifshitz-Gilbert equation. Performing an
adapted Olsen cycle we show that a multiferroic working substance is
potentially much more superior to sole ferroelectrics, as far as thermal energy
harvesting using pyroelectric effect is concerned. Our proposal holds promise
not only for low-energy consuming devices but also for cooling technology.
|
1602.00433v1
|
2016-02-04
|
A double oracle approach for minmax regret optimization problems with interval data
|
In this paper, we provide a generic anytime lower bounding procedure for
minmax regret optimization problems. We show that the lower bound obtained is
always at least as accurate as the lower bound recently proposed by Chassein
and Goerigk (2015). This lower bound can be viewed as the optimal value of a
linear programming relaxation of a mixed integer programming formulation of
minmax regret optimization, but the contribution of the paper is to compute
this lower bound via a double oracle algorithm (McMahan et al., 2003) that we
specify. The double oracle algorithm is designed by relying on a game theoretic
view of robust optimization, similar to the one developed by Mastin et al.
(2015), and it can be efficiently implemented for any minmax regret
optimization problem whose standard version is "easy". We describe how to
efficiently embed this lower bound in a branch and bound procedure. Finally, we
apply our approach to the robust shortest path problem. Our numerical results
show a significant gain in the computation times compared to previous
approaches in the literature.
|
1602.01764v3
|
2016-02-10
|
Temperature dependence of the threshold magnetic field for nucleation and domain wall propagation in an inhomogeneous structure with grain boundary
|
In order to study the dependence of the coercive force of sintered magnets on
temperature, nucleation and domain wall propagation at the grain boundary are
studied as rate-determining processes of the magnetization reversal phenomena
in magnets consisting of bulk hard magnetic grains contacting via grain
boundaries of a soft magnetic material. These systems have been studied
analytically for a continuum model at zero temperature (A. Sakuma, et al. J.
Mag. Mag. Mat. {\bf 84} 52 (1990)). In the present study, the temperature
dependence is studied by making use of the stochastic Landau-Lifshitz-Gilbert
equation at finite temperatures. In particular, the threshold fields for
nucleation and domain wall propagation are obtained as functions of ratios of
magnetic interactions and anisotropies of the soft and hard magnets for various
temperatures. It was found that the threshold field for domain wall propagation
is robust against thermal fluctuations, while that for nucleation is fragile.
The microscopic mechanisms of the observed temperature dependence are
discussed.
|
1602.03285v2
|
2016-02-26
|
The magnetic monopole and the separation between fast and slow magnetic degrees of freedom
|
The Landau-Lifshitz-Gilbert (LLG) equation that describes the dynamics of a
macroscopic magnetic moment finds its limit of validity at very short times.
The reason for this limit is well understood in terms of separation of the
characteristic time scales between slow degrees of freedom (the magnetization)
and fast degrees of freedom. The fast degrees of freedom are introduced as the
variation of the angular momentum responsible for the inertia. In order to
study the effect of the fast degrees of freedom on the precession, we calculate
the geometric phase of the magnetization (i.e. the Hannay angle) and the
corresponding magnetic monopole. In the case of the pure precession (the slow
manifold), a simple expression of the magnetic monopole is given as a function
of the slowness parameter, i.e. as a function of the ratio of the slow over the
fast characteristic times.
|
1602.08470v1
|
2016-03-01
|
Instability analysis of spin torque oscillator with an in-plane magnetized free layer and a perpendicularly magnetized pinned layer
|
We study the theoretical conditions to excite a stable self-oscillation in a
spin torque oscillator with an in-plane magnetized free layer and a
perpendicularly magnetized pinned layer in the presence of magnetic field
pointing in an arbitrary direction. The linearized Landau-Lifshitz-Gilbert
(LLG) equation is found to be inapplicable to evaluate the threshold between
the stable and self-oscillation states because the critical current density
estimated from the linearized equation is considerably larger than that found
in the numerical simulation. We derive a theoretical formula of the threshold
current density by focusing on the energy gain of the magnetization from the
spin torque during a time shorter than a precession period. A good agreement
between the derived formula and the numerical simulation is obtained. The
condition to stabilize the out-of-plane self-oscillation above the threshold is
also discussed.
|
1603.00155v2
|
2016-03-02
|
Electric-Field-Induced Spin Resonance in Antiferromagnetic Insulators: Inverse Process of the Dynamical Chiral Magnetic Effect
|
We propose a realization of the electric-field-induced antiferromagnetic
resonance. We consider three-dimensional antiferromagnetic insulators with
spin-orbit coupling characterized by the existence of a topological term called
the $\theta$ term. By solving the Landau-Lifshitz-Gilbert equation in the
presence of the $\theta$ term, we show that, in contrast to conventional
methods using ac magnetic fields, the antiferromagnetic resonance state is
realized by ac electric fields along with static magnetic fields. This
mechanism can be understood as the inverse process of the dynamical chiral
magnetic effect, an alternating current generation by magnetic fields. In other
words, we propose a way to electrically induce the dynamical axion field in
condensed matter. We discuss a possible experiment to observe our proposal,
which utilizes the spin pumping from the antiferromagnetic insulator into a
heavy metal contact.
|
1603.00614v3
|
2016-03-25
|
Microscopic theory of spin-orbit torques and skyrmion dynamics
|
We formulate a general microscopic approach to spin-orbit torques in thin
ferromagnet/heavy-metal bilayers in linear response to electric current or
electric field. The microscopic theory we develop avoids the notion of spin
currents and spin-Hall effect. Instead, the torques are directly related to a
local spin polarization of conduction electrons, which is computed from
generalized Kubo-St\v{r}eda formulas. A symmetry analysis provides a one-to-one
correspondence between polarization susceptibility tensor components and
different torque terms in the Landau-Lifshitz-Gilbert equation for
magnetization dynamics. The spin-orbit torques arising from Rashba or
Dresselhaus type of spin-orbit interaction are shown to have different
symmetries. We analyze these spin-orbit torques microscopically for a generic
electron model in the presence of an arbitrary smooth magnetic texture. For a
model with spin-independent disorder we find a major cancelation of the
torques. In this case the only remaining torque corresponds to the
magnetization-independent Edelstein effect. Furthermore, our results are
applied to analyze the dynamics of a Skyrmion under the action of electric
current.
|
1603.07994v2
|
2016-04-01
|
Modular Anomalies in (2+1) and (3+1)-D Edge Theories
|
The classification of topological phases of matter in the presence of
interactions is an area of intense interest. One possible means of
classification is via studying the partition function under modular transforms,
as the presence of an anomalous phase arising in the edge theory of a
D-dimensional system under modular transformation, or modular anomaly, signals
the presence of a (D+1)-D non-trivial bulk. In this work, we discuss the
modular transformations of conformal field theories along a (2+1)-D and a
(3+1)-D edge. Using both analytical and numerical methods, we show that chiral
complex free fermions in (2+1)-D and (3+1)-D are modular invariant. However, we
show in (3+1)-D that when the edge theory is coupled to a background U(1) gauge
field this results in the presence of a modular anomaly that is the
manifestation of a quantum Hall effect in a (4+1)-D bulk. Using the modular
anomaly, we find that the edge theory of (4+1)-D insulator with spacetime
inversion symmetry(P*T) and fermion number parity symmetry for each spin
becomes modular invariant when 8 copies of the edges exist.
|
1604.00407v1
|
2016-04-12
|
Voltage-driven magnetization switching and spin pumping in Weyl semimetals
|
We demonstrate electrical magnetization switching and spin pumping in
magnetically doped Weyl semimetals. The Weyl semimetal is a new class of
topological semimetals, known to have nontrivial coupling between the charge
and the magnetization due to the chiral anomaly. By solving the
Landau-Lifshitz-Gilbert equation for a multilayer structure of a Weyl
semimetal, an insulator and a metal whilst taking the charge-magnetization
coupling into account, magnetization dynamics is analyzed. It is shown that the
magnetization dynamics can be driven by the electric voltage. Consequently,
switching of the magnetization with a pulsed electric voltage can be achieved,
as well as precession motion with an applied oscillating electric voltage. The
effect requires only a short voltage pulse and may therefore be more
energetically efficient for us in spintronics devices compared to conventional
spin transfer torque switching.
|
1604.03326v1
|
2016-04-29
|
Current induced magnetization dynamics and magnetization switching in superconducting ferromagnetic hybrid (F$|$S$|$F) structures
|
We investigate the current induced magnetization dynamics and magnetization
switching in an unconventional p-wave superconductor sandwiched between two
misaligned ferromagnetic layers by numerically solving Landau-Lifshitz-Gilbert
equation modified with current induced Slonczewski's spin torque term. A
modified form of Ginzburg-Landau free energy functional has been used for this
purpose. We demonstrated the possibility of current induced magnetization
switching in the spin-triplet ferromagnetic superconducting hybrid structures
with strong easy axis anisotropy and the condition for magnetization reversal.
The switching time for such arrangement is calculated and is found to be highly
dependent on the magnetic configuration along with the biasing current. This
study would be useful in designing practical superconducting-spintronic
devices.
|
1604.08704v3
|
2016-05-04
|
Asymptotic behaviors of Landau-Lifshitz flows from $\Bbb R^2$ to Kähler manifolds
|
In this paper, we study the asymptotic behaviors of finite energy solutions
to the Landau-Lifshitz flows from $\Bbb R^2$ into K\"ahler manifolds. First, we
prove that the solution with initial data below the critical energy converges
to a constant map in the energy space as $t\to \infty$ for the compact
Riemannian surface targets. In particular, when the target is a two dimensional
sphere, we prove that the solution to the Landau-Lifshitz-Gilbert equation with
initial data having an energy below $4\pi$ converges to some constant map in
the energy space. Second, for general compact K\"ahler manifolds and initial
data of an arbitrary finite energy, we obtain a bubbling theorem analogous to
the Struwe's results on the heat flows.
|
1605.01245v2
|
2016-05-04
|
Phase transition and uniqueness of levelset percolation
|
The main purpose of this paper is to introduce and establish basic results of
a natural extension of the classical Boolean percolation model (also known as
the Gilbert disc model). We replace the balls of that model by a positive
non-increasing attenuation function $l:(0,\infty) \to (0,\infty)$ to create the
random field $\Psi(y)=\sum_{x\in \eta}l(|x-y|),$ where $\eta$ is a homogeneous
Poisson process in ${\mathbb R}^d.$ The field $\Psi$ is then a random potential
field with infinite range dependencies whenever the support of the function $l$
is unbounded.
In particular, we study the level sets $\Psi_{\geq h}(y)$ containing the
points $y\in {\mathbb R}^d$ such that $\Psi(y)\geq h.$ In the case where $l$
has unbounded support, we give, for any $d\geq 2,$ exact conditions on $l$ for
$\Psi_{\geq h}(y)$ to have a percolative phase transition as a function of $h.$
We also prove that when $l$ is continuous then so is $\Psi$ almost surely.
Moreover, in this case and for $d=2,$ we prove uniqueness of the infinite
component of $\Psi_{\geq h}$ when such exists, and we also show that the
so-called percolation function is continuous below the critical value $h_c$.
|
1605.01275v1
|
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