Hopfion rings in chiral magnets*

Magnetic solitons are localized magnetization field configurations in crystals that possess properties similar to those of ordinary particles, allowing them to move and interact with each other and the environment. This characteristic makes them promising candidates for information transfer and data storage applications. Most known magnetic solitons exhibit quasi-two-dimensional configurations, such as skyrmions in 2D materials and skyrmion strings in bulk samples.

We present the experimental discovery of 3D topological magnetic solitons, also known as hopfions. Hopfions can be understood as closed twisted skyrmion strings, which, in the simplest case, form toroidal or ring-like structures localized in a small volume of the magnetic sample. We observed hopfions linked with skyrmion strings in B20-type FeGe plates through high-resolution transmission electron microscopy. In this talk, I will discuss several aspects of hopfion rings, including the diversity of configurations of hopfion rings linked with one or a few skyrmion strings, a highly reproducible protocol for hopfion ring nucleation, the hopfion ring zero modes, and the topological analysis of these configurations.