Classical Spin Dynamics in the Two-Dimensional Anisotropic Heisenberg Model

Abstract

Properties of vortices and dynamic correlation functions have been studied for the two-dimensional classical ferromagnetic Heisenberg model with easy-plane anisotropy, as a function of the anisotropy parameter λ = J_z/J_x. Continuum limit equations of motion exhibit two types of static vortex solutions, with and without out-of-plane spin components. We have studied numerically the stability of these solutions and have found that for λ ≲ 0.7 only the planar vortex (zero out-of-plane spin components) is stable, and for λ ≳ 0.8 only the vortex with nonzero out-of-plane spin components is stable. Approximate spin configurations for nonzero-velocity vortices are presented. A vortex ideal gas phenomenology is used to calculate the dynamic correlation function S (q,ω). Above the Kosterlitz-Thouless transition temperature, the calculation predicts a Gaussian central peak for the out-of-plane correlations and a squared Lorentzian for the in-plane correlations. These results are compared with results of a Monte Carlo-Molecular Dynamics simulation.

Supported by CNP_q (Brazil).