Electric Field-Induced Skyrmion Crystals via Charged Monopoles in Insulating Helimagets

TL;DR

This paper demonstrates that electric fields can induce skyrmion crystal phases in insulating helimagnets by leveraging the charge of hedgehog defects, which are monopole excitations influenced by the orbital magnetoelectric effect.

Contribution

It reveals a novel mechanism where electric fields control skyrmion phases via charged monopoles in insulating helimagnets, based on the Witten effect and Berry phase gauge fields.

Findings

Electric fields induce skyrmion crystal phases.

Hedgehogs carry a quantized electric charge.

Orbital magnetoelectric effect influences monopole charge.

Abstract

Electrons propagating in a magnetically ordered medium experience an additional gauge field associated with the Berry phase of their spin following the local magnetic texture. In contrast to the usual electromagnetic field, this gauge field admits monopole excitations, corresponding to hedgehog defects of the magnetic order. In an insulator, these hedgehogs carry a well-defined electric charge allowing for them to be controlled by electric fields. One particularly robust mechanism that contributes to the charge is the orbital magnetoelectric effect, captured by a $\theta$ angle, which leads to a charge of $e\theta/2\pi$ on hedgehogs. This is a direct consequence of the Witten effect for magnetic monopoles in a $\theta$ medium. A physical consequence is that external electric fields can induce skyrmion crystal phases in insulating helimagnets.