Skyrmions and Hopfions in 3D Frustrated Magnets

TL;DR

This paper introduces a model of 3D frustrated magnets that hosts Skyrmions and Hopfions, exploring their relation through an interpolating non-linear sigma model and analyzing soliton energies and configurations.

Contribution

It presents a new frustrated magnetic model that supports 3D Skyrmions and Hopfions, connecting these topological structures via an interpolating continuum model.

Findings

The model reduces to known Skyrme and Hopfion host systems at parameter limits.

3D Skyrmions are identified and compared to rational map solutions.

Soliton energies obey a linear BPS bound in the interpolating model.

Abstract

A model of an inversion-symmetric frustrated spin system is introduced which hosts three-dimensional extensions of magnetic Skyrmions. In the continuum approximation this model reduces to a non-linear sigma model on a squashed sphere which has a natural interpolating parameter. At one limit of the parameter the model reduces to a frustrated magnetic system earlier considered by Sutcliffe as a host to Hopfions, and in the other limit it becomes very similar to the 3D Skyrme model. To better understand the relation between Hopfions and 3D Skyrmions a model interpolating between the Faddeev-Niemi model and the Skyrme model is reconsidered and it is shown that energies of the solitons obey a linear BPS bound. The 3D Skyrmions in the frustrated magnetic model are found and compared to the rational map ansatz.