Magnetoelectric effect and orbital magnetization in skyrmion crystals: Detection and characterization of skyrmions

TL;DR

This paper proposes new electrical and magnetic measurements, including orbital magnetization, Hall conductivity, and magnetoelectric effects, to detect and characterize skyrmions without real-space imaging, and predicts how these vary with skyrmion helicity.

Contribution

It introduces a method to identify skyrmions through bulk and edge observables and predicts a magnetoelectric effect dependent on skyrmion helicity, advancing skyrmion detection techniques.

Findings

Orbital magnetization and Hall conductivity measure skyrmion properties.

Magnetoelectric effect varies with skyrmion helicity, distinguishing Bloch and Neel skyrmions.

Predicted observables enable experimental detection and characterization of skyrmions.

Abstract

Skyrmions are small magnetic quasiparticles, which are uniquely characterized by their topological charge and their helicity. In this Rapid Communication, we show via calculations how both properties can be determined without relying on real-space imaging. The orbital magnetization and topological Hall conductivity measure the arising magnetization due to the circulation of electrons in the bulk and the occurrence of topologically protected edge channels due to the emergent field of a skyrmion crystal. Both observables quantify the topological Hall effect and distinguish skyrmions from antiskyrmions by sign. Additionally, we predict a magnetoelectric effect in skyrmion crystals, which is the generation of a magnetization (polarization) by application of an electric (magnetic) field. This effect is quantified by spin toroidization and magnetoelectric polarizability. The dependence of the transverse magnetoelectric effect on the skyrmion helicity fits that of the classical toroidal moment of the spin texture and allows to differentiate skyrmion helicities: it is largest for Bloch skyrmions and zero for Neel skyrmions. We predict distinct features of the four observables that can be used to detect and characterize skyrmions in experiments.