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

摘要

It is known that magnetic vortices in two dimensional Heisenberg models witheasy-plane anisotropy exhibit an instability depending on the anisotropystrength. In this paper, we study the statistic behavior of the two-dimensionaleasy-plane Heisenberg models with distance-dependent interactions, $J_{xy}(r)$and $J_z(r)$ for in-plane and out-of-plane components. We develop analyticaland numerical methods for accurate determination of critical anisotropy, abovewhich out-of-plane vortices are stable. In particular, we explore the vortexformation of the Gaussian-type interaction model and determine the criticalanisotropy accurately for square, hexagonal and triangular lattices.