Three-dimensional current-induced magnetic hopfion dynamics

Magnetic hopfions are three-dimensional (3D) topological spin textures characterized by the Hopf invariant. As manifesting by their 3D real-space topologies, magnetic hopfions may exhibit interesting dynamics. Here, we study the current-induced dynamics of a magnetic hopfion in 3D space. The current mainly drives a translational hopfion motion. Depending on the applied current direction, hopfion also shows different moving patterns. We then analyze the equation of motion and find these current-induced dynamics further reflect the 3D nature of hopfion. Such 3D hopfion dynamics may shed light on the study of novel 3D topological spin textures and provides a new pathway to the development of 3D spintronics.