Instability of planar vortices in the two-dimensional easy-plane Heisenberg model with distance-dependent interactions

Abstract

It is known that magnetic vortices in two-dimensional Heisenberg models with easy-plane anisotropy exhibit an instability depending on the anisotropy strength. In this paper, we study the statistic behavior of the two-dimensional easy-plane Heisenberg models with distance-dependent interactions ${J}_{xy}(r)$ and ${J}_{z}(r)$ for in-plane and out-of-plane components. We develop analytical and numerical methods for accurate determination of critical anisotropy, above which out-of-plane vortices become stable. In particular, we explore the vortex formation of the Gaussian-type interaction model and determine the critical anisotropy accurately for square, hexagonal, and triangular lattices.