Generation of magnetic chiral solitons, skyrmions, and hedgehogs with electric fields

TL;DR

This paper demonstrates how electric fields can induce and control topological spin textures like skyrmions and hedgehogs in magnetic materials by modifying Dzyaloshinskii-Moriya interactions, using numerical simulations and machine learning.

Contribution

It introduces a method to generate and manipulate topological spin textures via electric-field-induced DMI changes, including the creation of 3D hedgehog structures in spin models.

Findings

Electric fields can create and annihilate topological spin textures.

Electric-field-induced DMI leads to the emergence of skyrmion and hedgehog states.

A simple 3D spin model hosting hedgehog structures was constructed.

Abstract

Electric-field controls of Dzyaloshinskii-Moriya interactions (DMIs) have recently been discussed from the microscopic viewpoint. Since the DMI plays a critical role in generating topological spin textures (TSTs) such as the chiral soliton, the magnetic skyrmion, and the magnetic hedgehog, electric-field controls of these TSTs have become an important issue. This paper shows that such electric-field-induced DMI indeed creates and annihilates TSTs by numerically solving the Landau-Lifshitz-Gilbert (LLG) equation for many-body spin systems at finite temperatures. We show that when a strong electric field is applied in a proper way to one- or two-dimensional ferromagnets, the Hamiltonians are changed into the well-known spin models for the chiral soliton or the skyrmion lattice, and the TST states emerge. We utilize a machine-learning method to count the number of generated TSTs. In the three-dimensional (3D) case, we demonstrate the electric-field induction of a magnetic hedgehog structure as follows: Applying a strong enough electric field along a proper direction to a skyrmion-string state (a triple-$\boldsymbol{q}$ state) at low but finite temperatures, we find that the field-induced DMI can drive a quadruple-$\boldsymbol{q}$ state with hedgehog-antihedgehog pairs. This result indicates that we have succeeded in constructing a simple 3D short-range interacting spin model hosting a magnetic hedgehog structure.