Magnetoelectric classification of skyrmions

TL;DR

This paper introduces a comprehensive classification framework for magnetic skyrmions based on their magnetoelectric multipoles, enabling electric field control of their magnetic properties in insulating materials.

Contribution

The authors develop a general theory linking skyrmion topology and geometry to their magnetoelectric multipoles, providing a new way to manipulate and characterize skyrmions electrically.

Findings

Magnetoelectric multipoles are uniquely determined by skyrmion topology and helicity.

Linear magnetoelectric response measurements can characterize skyrmions.

The formalism applies to skyrmions, anti-skyrmions, and magnetic bimerons.

Abstract

We develop a general theory to classify magnetic skyrmions and related spin textures in terms of their magnetoelectric multipoles. Since magnetic skyrmions are now established in insulating materials, where the magnetoelectric multipoles govern the linear magnetoelectric response, our classification provides a recipe for manipulating the magnetic properties of skyrmions using applied electric fields. We apply our formalism to skyrmions and anti-skyrmions of different helicities, as well as to magnetic bimerons, which are topologically, but not geometrically, equivalent to skyrmions. We show that the non-zero components of the magnetoelectric multipole and magnetoelectric response tensors are uniquely determined by the topology, helicity and geometry of the spin texture. Therefore, we propose straightforward linear magnetoelectric response measurements as an alternative to Lorentz microscopy for characterizing insulating skyrmionic textures.