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.

中文翻译：

---

自旋传递转矩驱动的磁悬浮轴承的三维动力学

磁跳跃是一种具有新颖自旋结构的三维（3D）拓扑孤子，它将实现奇异的动力学。在这里，我们研究了沮丧的磁体中具有单位Hopf指数的磁Hopfion的电流驱动3D动力学。由于自旋贝里相位和跳跃的对称性，相空间纠缠了多个集合坐标，因此跳跃表现出丰富的动力学特性，包括沿当前方向的纵向运动，垂直于当前方向的横向运动，旋转运动和膨胀。此外，跳变动力学的特性由非绝热自旋传递扭矩参数和阻尼参数之间的比率确定。