Electric-current-assisted nucleation of zero-field hopfion rings

TL;DR

This paper presents a simple electric-current-assisted method to nucleate stable magnetic hopfions in chiral magnets, independent of sample shape, supported by micromagnetic simulations and a new topological classification framework.

Contribution

It introduces a novel, shape-independent nucleation protocol for magnetic hopfions and provides a comprehensive topological classification framework.

Findings

Hopfions can be nucleated using electric current without special sample geometry.

The generated hopfions are highly stable under various magnetic fields.

Theoretical framework classifies hopfions, skyrmions, and merons via homotopy groups.

Abstract

Magnetic hopfions are three-dimensional topological solitons -- knotted, vortex-like spin configurations. In chiral magnets, hopfions can appear as isolated structures or they can be linked to skyrmion strings. Previous studies employed a sophisticated protocol and a special sample geometry to nucleate such hopfions linked to one or a few skyrmion strings. Here, we introduce an electric-current-assisted nucleation protocol that is simple and independent of the sample shape and size. The resulting hopfions exhibit extraordinary stability in the presence of both positive and negative magnetic fields, in perfect agreement with micromagnetic simulations. We also present a comprehensive framework for classifying hopfions, skyrmions, and merons by deriving the corresponding homotopy group.