Topological solitons in highly anisotropic two dimensional ferromagnets

TL;DR

This paper investigates topological solitons in highly anisotropic two-dimensional ferromagnets, revealing new behaviors and stability conditions through analytical and numerical methods, especially at high anisotropy levels.

Contribution

It provides a combined analytical and numerical study of solitons in anisotropic ferromagnets, uncovering novel features at high anisotropy levels not present in continuous models.

Findings

Solitons are stable above a critical number of spin deviations.

At high anisotropy, soliton energy becomes non-monotonic with respect to bound magnons.

New soliton behaviors include irregular frequency dependence and stable static states.

Abstract

e study the solitons, stabilized by spin precession in a classical two--dimensional lattice model of Heisenberg ferromagnets with non-small easy--axis anisotropy. The properties of such solitons are treated both analytically using the continuous model including higher then second powers of magnetization gradients, and numerically for a discrete set of the spins on a square lattice. The dependence of the soliton energy $E$ on the number of spin deviations (bound magnons) $N$ is calculated. We have shown that the topological solitons are stable if the number $N$ exceeds some critical value $N_{\rm{cr}}$. For $N < N_{\rm{cr}}$ and the intermediate values of anisotropy constant $K_{\mathrm{eff}} <0.35J$ ($J$ is an exchange constant), the soliton properties are similar to those for continuous model; for example, soliton energy is increasing and the precession frequency $ \omega (N)$ is decreasing monotonously with $N$ growth. For high enough anisotropy $K_{\mathrm{eff}} > 0.6 J$ we found some fundamentally new soliton features absent for continuous models incorporating even the higher powers of magnetization gradients. For high anisotropy, the dependence of soliton energy E(N) on the number of bound magnons become non-monotonic, with the minima at some "magic" numbers of bound magnons. Soliton frequency $\omega (N)$ have quite irregular behavior with step-like jumps and negative values of $\omega $ for some regions of $N$. Near these regions, stable static soliton states, stabilized by the lattice effects, exist.