Three-Dimensional Dynamics of a Magnetic Hopfion Driven by Spin Transfer Torque.

Magnetic hopfion is a three-dimensional (3D) topological soliton with novel spin structure that would enable exotic dynamics. Here, we study the current-driven 3D dynamics of a magnetic hopfion with a unit Hopf index in a frustrated magnet. Attributed to the spin Berry phase and symmetry of the hopfion, the phase space entangles multiple collective coordinates, thus the hopfion exhibits rich dynamics including longitudinal motion along the current direction, transverse motion perpendicular to the current direction, rotational motion, and dilation. Furthermore, the characteristics of hopfion dynamics is determined by the ratio between the nonadiabatic spin transfer torque parameter and the damping parameter. Such peculiar 3D dynamics of magnetic hopfion could shed light on understanding the universal physics of hopfions in different systems and boost the prosperous development of 3D spintronics.