Three-dimensional dynamics of a magnetic hopfion driven by spin transfer torque
Hopfion is a three-dimensional (3D) topological soliton with novel spin structure that would enable exotic dynamics. The three spatial dimensions endow hopfions with diverse configurations such as rings, links, and knots that can be classified by the Hopf index QH. Although hopfions were first studied in the contents of field theories, they turn out to emerge in various physical systems and are closely related to many physical phenomena such as vorton, low-energy limit Yang-Mills theory, vortex ring, ball lightning, etc. Very recently, magnetic hopfions have been theoretically proposed in frustrated magnets and confined chiral magnetic heterostructures, further stimulating the study of hopfion from a new respect. To unravel the dynamics of the magnetic hopfion, it is important to study its most essential motion driven by the spin transfer torque (STT) under electric current. Similar to magnetic skyrmion, its two-dimensional counterpart, magnetic hopfion may attract great attention from the field of topological spintronics.
Figure 1. Spin structure of a QH=1magnetic hopfion. At the initial state, the torus midplane lies in the xy plane. (a) Iso-spin surfaces with Sz=0 form a torus. (b) and (c) are the cross sections of hopfion onto xy and yz planes, respectively.
Recently, Dr. Yizhou Liu and Prof. Xiufeng Han from the M02 group at the Institute of Physics, Chinese Academy of Sciences, in collaboration with Prof. Jiadong Zang and Dr. Wentao Hou at the University of New Hampshire, study the 3D spin dynamics of a magnetic hopfion with unit Hopf index in a frustrated magnet. Attributed to 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 non-adiabatic STT parameter and the damping parameter. The theory built upon spin Berry phase and generalized Thiele's approach gives out simple equations of motion reproducing numerical results. A phenomenological analysis also reveals the vital role of skyrmion-antiskyrmion pair in hopfion dynamics and makes connection of soliton dynamics across dimensionality. Since the theory is built on the collective coordinates that is independent of details of spin interactions, it suggests the universality of the reported dynamics in all existing and forthcoming hopfion models, not only in magnetism, but also in other physical systems. Such peculiar 3D dynamics of magnetic hopfion could shed light on understanding the universal physics of hopfions in different systems. The rich dynamics hosted by a hopfion further foreshadows more exotic dynamics for hopfions with higher QH and their potentials in 3D spintronic applications [Three-Dimensional Dynamics of a Magnetic Hopfion Driven by Spin Transfer Torque, Y. Z. Liu, W. T. Hou, X. F. Han, and J. D. Zang, Phys. Rev. Lett. 124 (2020) 127204].
Figure 2. The entangled longitudinal motion, transverse motion [(a), (b)], rotation [(c), (d)], and dilation (e) of hopfion. (f) illustrates the connection between the dynamics of a hopfion and the dynamics of the skyrmion-antiskyrmion pairs.
The work was supported by the Ministry of Science and Technology of China [No. 2017YFA0206200], the National Science Foundation [NSFC No.51831012, 11804380], and the Chinese Academy of Sciences [QYZDJ-SSW-SLH016].