Higher-dimensional magnetic Skyrmions

TL;DR

This paper extends the theory of magnetic Skyrmions from two to three dimensions using a higher-dimensional framework with an $S^3$ target space, potentially realizable via synthetic dimensions in condensed matter physics.

Contribution

It introduces a higher-dimensional Skyrmion theory with an $S^3$ target space and explores its spectrum with and without the Skyrme term, revealing new stable and unstable solitons.

Findings

Identified a Skyrmion and sphaleron in the basic theory.

Including the Skyrme term yields a metastable Skyrmion and a stable large Skyrmion.

Proposed physical realization using synthetic dimensions.

Abstract

We propose a generalization of the theory of magnetic Skyrmions in chiral magnets in two dimensions to a higher-dimensional theory with magnetic Skyrmions in three dimensions and an $S^3$ target space, requiring a 4-dimensional magnetization vector. A physical realization of our theory could be made using a synthetic dimension, recently promoted and realized in condensed matter physics. In the simplest incarnation of the theory, we find a Skyrmion and a sphaleron - the latter being an unstable soliton. Including also the Skyrme term in the theory enriches the spectrum to a small metastable Skyrmion, an unstable sphaleron and a large stable Skyrmion.