Stretched exponential relaxation in two-dimensional easy-plane ferromagnets
S. Komineasa, A.R. Bishopa,
F.G. Mertensa aPhysikalisches Institut, Universitaet Bayreuth,
D-95440 Bayreuth, Germany bTheoretical Division and Center for Nonlinear Studies,
Los Alamos National Laboratory, Los Alamos, NM 87545
Abstract
A classical ferromagnet is described in a continuum approximation and
at the microscopic level by the Landau-Lifshitz equation.
In two spatial dimensions, vortices are the topological solutions
of the model in the presence of
easy-plane anisotropy.
We argue that a system of vortices
has an energy landscape whose gross features can be well described.
We investigate numerically the effect of the complex energy landscape
on the relaxation dynamics, namely a characteristic stretched exponential
decrease in the energy and the number of vortices present in the system
as the system relaxes toward the ground state.