Noise-induced switching between vortex states with different polarization in classical two-dimensional easy-plane magnets

TL;DR

This paper investigates how thermal noise causes polarization switching in vortex states of 2D easy-plane magnets, combining theoretical analysis with simulations to understand transition mechanisms.

Contribution

It introduces a discrete Hamiltonian approach and applies Langer's instanton theory to analyze noise-induced vortex polarization transitions.

Findings

Bimodal distribution of vortex core polarization states

Calculated transition rates match Langevin simulation results

Identified the role of thermal noise in vortex state switching

Abstract

In the 2-dimensional anisotropic Heisenberg model with XY-symmetry there are non-planar vortices which exhibit a localized structure of the z-components of the spins around the vortex center. We study how thermal noise induces a transition of this structure from one polarization to the opposite one. We describe the vortex core by a discrete Hamiltonian and consider a stationary solution of the Fokker-Planck equation. We find a bimodal distribution function and calculate the transition rate using Langer's instanton theory (1969). The result is compared with Langevin dynamics simulations for the full many-spin model.