Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field

TL;DR

This paper models frustrated ferromagnets at low magnetic fields, revealing stable Skyrmions with discrete symmetries and analyzing spin wave propagation without a spectral gap, connecting low and high field regimes.

Contribution

It introduces a gauged sigma model formulation for low-field frustrated ferromagnets, constructing stable Skyrmions and analyzing spin wave behavior across magnetic field regimes.

Findings

Stable Skyrmions with discrete symmetries are constructed.

Spin waves propagate without a spectral gap at low fields.

Skyrmions connect continuously to high-field solutions, gaining axial symmetry.

Abstract

A continuum model of frustrated ferromagnets is analyzed in detail in the regime of low applied magnetic field, $H_0<1/4$, where the ground state is a spatially varying conical spiral. By changing variables to a corotating spin field, the model is reformulated as a gauged sigma model in a fixed background gauge, allowing the construction of stable isolated Skyrmions, and stable multi-Skyrmion clusters, which approach the conical ground state at spatial infinity. Owing to the spatial anisotropy induced by the ground state, these Skyrmions exhibit only discrete symmetries, and are of neither N\'eel nor Bloch type. These Skyrmions are continuously connected to the more familar solutions in the high field regime ($H_0>1/4$), acquiring axial symmetry in the limit $H_0\rightarrow 1/4$. The propagation of small amplitude spin waves through the conical ground state is also analyzed and is found to depend strongly on both $H_0$ and propagation direction relative to the ground state. In contrast to spin waves in the high field regime ($H_0>1/4$) there is no spectral gap: waves may propagate with any angular frequency.