71 research outputs found
Stochastic vortex dynamics in two-dimensional easy-plane ferromagnets: Multiplicative versus additive noise
We study how thermal fluctuations affect the dynamics of vortices in the
two-dimensional classical, ferromagnetic, anisotropic Heisenberg model
depending on their additive or multiplicative character. Using a collective
coordinate theory, we analytically show that multiplicative noise, arising from
fluctuations in the local field term of the Landau-Lifshitz equations, and
Langevin-like additive noise both have the same effect on vortex dynamics
(within a very plausible assumption consistent with the collective coordinate
approach). This is a non-trivial result, as multiplicative and additive noises
usually modify the dynamics quite differently. We also carry out numerical
simulations of both versions of the model finding that they indeed give rise to
very similar vortex dynamics.Comment: 10 pages, 6 figure
Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model
We study the effects of finite temperature on the dynamics of non-planar
vortices in the classical, two-dimensional anisotropic Heisenberg model with
XY- or easy-plane symmetry. To this end, we analyze a generalized
Landau-Lifshitz equation including additive white noise and Gilbert damping.
Using a collective variable theory with no adjustable parameters we derive an
equation of motion for the vortices with stochastic forces which are shown to
represent white noise with an effective diffusion constant linearly dependent
on temperature. We solve these stochastic equations of motion by means of a
Green's function formalism and obtain the mean vortex trajectory and its
variance. We find a non-standard time dependence for the variance of the
components perpendicular to the driving force. We compare the analytical
results with Langevin dynamics simulations and find a good agreement up to
temperatures of the order of 25% of the Kosterlitz-Thouless transition
temperature. Finally, we discuss the reasons why our approach is not
appropriate for higher temperatures as well as the discreteness effects
observed in the numerical simulations.Comment: 12 pages, 8 figures, accepted for publication in European Physical
Journal B (uses EPJ LaTeX
Switching between different vortex states in 2-dimensional easy-plane magnets due to an ac magnetic field
Using a discrete model of 2-dimensional easy-plane classical ferromagnets, we
propose that a rotating magnetic field in the easy plane can switch a vortex
from one polarization to the opposite one if the amplitude exceeds a threshold
value, but the backward process does not occur. Such switches are indeed
observed in computer simulations.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let
Topological phase separation in 2D quantum lattice Bose-Hubbard system away from half-filling
We suppose that the doping of the 2D hard-core boson system away from
half-filling may result in the formation of multi-center topological
inhomogeneity (defect) such as charge order (CO) bubble domain(s) with Bose
superfluid (BS) and extra bosons both localized in domain wall(s), or a {\it
topological} CO+BS {\it phase separation}, rather than an uniform mixed CO+BS
supersolid phase. Starting from the classical model we predict the properties
of the respective quantum system. The long-wavelength behavior of the system is
believed to remind that of granular superconductors, CDW materials, Wigner
crystals, and multi-skyrmion system akin in a quantum Hall ferromagnetic state
of a 2D electron gas. To elucidate the role played by quantum effects and that
of the lattice discreteness we have addressed the simplest nanoscopic
counterpart of the bubble domain in a checkerboard CO phase of 2D hc-BH square
lattice. It is shown that the relative magnitude and symmetry of
multi-component order parameter are mainly determined by the sign of the
and transfer integrals. In general, the topologically inhomogeneous phase
of the hc-BH system away from the half-filling can exhibit the signatures both
of , and symmetry of the off-diagonal order.Comment: 12 pages, 6 figure
Dynamics of topological solitons in two-dimensional ferromagnets
Dynamical topological solitons are studied in classical two-dimensional
Heisenberg easy-axis ferromagnets. The properties of such solitons are treated
both analytically in the continuum limit and numerically by spin dynamics
simulations of the discrete system. Excitation of internal mode causes orbital
motion. This is confirmed by simulations.Comment: LaTeX, 15 pages, 6 figure
Topological phase separation in 2D hard-core Bose-Hubbard system away from half-filling
We suppose that the doping of the 2D hard-core boson system away from
half-filling may result in the formation of multi-center topological defect
such as charge order (CO) bubble domain(s) with Bose superfluid (BS) and extra
bosons both localized in domain wall(s), or a {\it topological} CO+BS {\it
phase separation}, rather than an uniform mixed CO+BS supersolid phase.
Starting from the classical model we predict the properties of the respective
quantum system. The long-wavelength behavior of the system is believed to
remind that of granular superconductors, CDW materials, Wigner crystals, and
multi-skyrmion system akin in a quantum Hall ferromagnetic state of a 2D
electron gas.Comment: 6 pages, 1 figur
Brownian dynamics approach to interacting magnetic moments
The question how to introduce thermal fluctuations in the equation of motion
of a magnetic system is addressed. Using the approach of the
fluctuation-dissipation theorem we calculate the properties of the noise for
both, the fluctuating field and fluctuating torque (force) representation. In
contrast to earlier calculations we consider the general case of a system of
interacting magnetic moments without the assumption of axial symmetry. We show
that the interactions do not result in any correlations of thermal fluctuations
in the field representation and that the same widely used formula can be used
in the most general case. We further prove that close to the equilibrium where
the fluctuation-dissipation theorem is valid, both, field and torque (force)
representations coincide, being different far away from it
Noise-induced switching between vortex states with different polarization in classical two-dimensional easy-plane magnets
In the 2-dimensional anisotropic Heisenberg model with XY-symmetry there are
non-planar vortices which exhibit a localized structure of the z-components of
the spins around the vortex center. We study how thermal noise induces a
transition of this structure from one polarization to the opposite one. We
describe the vortex core by a discrete Hamiltonian and consider a stationary
solution of the Fokker-Planck equation. We find a bimodal distribution function
and calculate the transition rate using Langer's instanton theory (1969). The
result is compared with Langevin dynamics simulations for the full many-spin
model.Comment: 15 pages, 4 figures, Phys. Rev. B., in pres
Low Temperature Static and Dynamic Behavior of the Two-Dimensional Easy-Axis Heisenberg Model
We apply the self-consistent harmonic approximation (SCHA) to study static
and dynamic properties of the two-dimensional classical Heisenberg model with
easy-axis anisotropy. The static properties obtained are magnetization and spin
wave energy as functions of temperature, and the critical temperature as a
function of the easy-axis anisotropy. We also calculate the dynamic correlation
functions using the SCHA renormalized spin wave energy. Our analytical results,
for both static properties and dynamic correlation functions, are compared to
numerical simulation data combining cluster-Monte Carlo algorithms and Spin
Dynamics. The comparison allows us to conclude that far below the transition
temperature, where the SCHA is valid, spin waves are responsible for all
relevant features observed in the numerical simulation data; topological
excitations do not seem to contribute appreciably. For temperatures closer to
the transition temperature, there are differences between the dynamic
correlation functions from SCHA theory and Spin Dynamics; these may be due to
the presence of domain walls and solitons.Comment: 12 pages, 14 figure
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