Stable topological textures in a classical 2D Heisenberg model

TL;DR

This paper demonstrates the existence of stable topological soliton textures (skyrmions) in a classical 2D Heisenberg ferromagnet with uniaxial anisotropy, analyzing their phase diagram and energy characteristics.

Contribution

It identifies conditions for stable skyrmions with various topological charges in a classical 2D Heisenberg model, including phase diagram and energy behavior analysis.

Findings

Stable skyrmions exist for topological charge $ u \\geq 1$ under certain conditions.

Threshold number of bound magnons depends on anisotropy and topological charge.

Energy per topological charge is minimized at intermediate charges $ u=2$ or 3.

Abstract

We show that stable localized topological soliton textures (skyrmions) with $\pi_2$ topological charge $\nu \geq 1$ exist in a classical 2D Heisenberg model of a ferromagnet with uniaxial anisotropy. For this model the soliton exist only if the number of bound magnons exceeds some threshold value $N_{\rm cr}$ depending on $\nu $ and the effective anisotropy constant $K_{\rm eff}$. We define soliton phase diagram as the dependence of threshold energies and bound magnons number on anisotropy constant. The phase boundary lines are monotonous for both $\nu=1$ and $\nu >2$, while the solitons with $\nu=2$ reveal peculiar nonmonotonous behavior, determining the transition regime from low to high topological charges. In particular, the soliton energy per topological charge (topological energy density) achieves a minimum neither for $\nu=1$ nor high charges, but rather for intermediate values $\nu=2$ or $\nu=3$.