Mutual conversion between a magnetic Neel hopfion and a Neel toron

TL;DR

This study demonstrates the mutual conversion between Neel-type hopfions and torons in magnetic materials under external magnetic fields, revealing their stability, transformation conditions, and excitation modes, advancing understanding of 3D magnetic textures.

Contribution

It introduces a numerical method to convert and distinguish Neel-type hopfions and torons, revealing their stability and excitation behaviors under magnetic fields.

Findings

Neel-type hopfions are stable without external fields.

Hopfions transform into Neel-type torons at about 20 mT.

Different excitation modes observed under in-plane microwave fields.

Abstract

Three-dimensional (3D) magnetic textures attract great attention from researchers due to their fascinating structures and dynamic behaviors. Magnetic hopfion is a prominent example of 3D magnetic textures. Here, we numerically study the mutual conversion between a Neel-type hopfion and a Neel-type toron under an external magnetic field. We also investigate the excitation modes of hopfions and torons in a film with strong perpendicular magnetic anisotropy. It is found that the Neel-type hopfion could be a stable state in the absence of the external magnetic field, and its diameter varies with the out-of-plane magnetic field. The Neel-type hopfion may transform to a Neel-type toron at an out-of-plane magnetic field of about 20 mT, where the cross section structure is a Neel-type skyrmion. The hopfion and toron show different excitation modes in the presence of an in-plane microwave magnetic field. Our results provide a method to realize the conversion between a Neel-type hopfion and a Neel-type toron, which also gives a way to distinguish Bloch-type and Neel-type hopfions.