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

TL;DR

This paper investigates the stability of vortices in 2D easy-plane Heisenberg models with distance-dependent interactions, developing methods to determine the critical anisotropy for vortex stability across different lattice types.

Contribution

It introduces analytical and numerical techniques to accurately find the critical anisotropy in models with distance-dependent interactions, extending understanding of vortex stability.

Findings

Critical anisotropy values determined for various lattice types.

Analytical and numerical methods developed for stability analysis.

Vortex formation behavior characterized for Gaussian-type 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 are 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.