Magnetic hopfions and their 3-dimensional spin dynamics

Magnetic hopfions are three-dimensional (3D) topological solitons, which may host fascinating physical properties due to their sophisticated 3D real-space topology. Recently, the emergence of magnetic hopfion- related research has stimulated the study of 3D topological solitons. Here we describe how to realize stable magnetic hopfions in solid magnetic systems. The interesting 3D spin dynamics of the simplest non-trivial hopfion will also be discussed. These results pave an avenue for further studies on the universal properties of topological spin textures across dimensionality, and for boosting the advancement of 3D topological spintronics.