Magnetoelectric classification of skyrmions

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.

arXiv comment6 pages, 4 figures

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Cited by in corpus (6)

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• Emergent Magneto-multipoles and Nonlinear Responses of a Magnetic Hopfion
• Designer Meron Lattice on the Surface of a Topological Insulator
• Skyrmion crystal under $D_{3h}$ point group: Role of out-of-plane Dzyaloshinskii-Moriya interaction
• Magnetoelectricity induced by rippling of magnetic nanomembranes and wires
• Modern triad for magnetic material science: geometric shape, electronic bands and spin textures