NATURE

By

Fengshan Zheng, Nikolai S. Kiselev, Filipp N. Rybakov, Luyan Yang, Wen Shi, Stefan Blügel & Rafal E. Dunin-Borkowski

Published

23 November 2023

Abstract

Magnetic skyrmions and hopfions are topological solitons—well-localized field configurations that have gained considerable attention over the past decade owing to their unique particle-like properties, which make them promising objects for spintronic applications. Skyrmions are two-dimensional solitons resembling vortex-like string structures that can penetrate an entire sample. Hopfions are three-dimensional solitons confined within a magnetic sample volume and can be considered as closed twisted skyrmion strings that take the shape of a ring in the simplest case. Despite extensive research on magnetic skyrmions, the direct observation of magnetic hopfions is challenging and has only been reported in a synthetic material. Here we present direct observations of hopfions in crystals. In our experiment, we use transmission electron microscopy to observe hopfions forming coupled states with skyrmion strings in B20-type FeGe plates. We provide a protocol for nucleating such hopfion rings, which we verify using Lorentz imaging and electron holography. Our results are highly reproducible and in full agreement with micromagnetic simulations. We provide a unified skyrmion–hopfion homotopy classification and offer insight into the diversity of topological solitons in three-dimensional chiral magnets.

Full Text Link

https://www.nature.com/articles/s41586-023-06658-5