Non-Abelian Vortices in Magnets

TL;DR

This paper demonstrates the theoretical existence and classification of non-Abelian vortices in magnetic materials, highlighting their potential for topologically protected information storage and their relation to known Abelian magnetic structures.

Contribution

It introduces the concept of non-Abelian vortices in magnets, providing a topological classification and discussing their advantages over Abelian structures for information encoding.

Findings

Non-Abelian vortices can exist in magnetic materials.

They are topologically distinct from Abelian vortices, merons, and skyrmions.

Non-Abelian vortices can carry topologically protected information.

Abstract

We show that non-Abelian vortices can exist in magnetic materials. These are singularity-free textures, are described by spin-lattice and field theory models, and we demonstrate that typical magnetic materials can be quite suitable for their realization and observation. We give a topological classification of these vortices and reveal their connection with Abelian topological structures, such as usual vortices, merons and skyrmions. We also describe how non-Abelian magnetic vortices can carry topologically protected information and present reasons for the advantage of such information carriers, as compared to Abelian entities.