Magnetic hopfions are three-dimensional topological solitons with a nontrivial Hopf index. Here, we theoretically investigated the spin excitation spectrum and revealed corresponding spin-wave modes of a magnetic hopfion. Compared with skyrmion tubes, the hopfions have distinctly less resonance peaks due to the suppression of vertical spin-wave modes by the internal topological defect. We also found that breathing and rotating modes could hybridize in hopfions under z-direction excitations and, thus, characterized the five individual resonance modes by a set of number pair (b, r). The results provide a fundamental understanding of the spin-wave modes of magnetic hopfions and open a route to detect and manipulate 3D topological solitons using microwave magnetic fields.

We theoretically investigate the micromagnetic dynamics and spin configurations in a CoFeB/Pt nanodisk with varying effective anisotropy constant (K) and radius (R). It is found that skyrmion and skyrmionium could be stabilized well in a certain region of the phase diagram of topological structures, and their formations physically originated from the competition between exchange interactions and anisotropy contributions. Furthermore, we achieve the transition between the skyrmion and the skyrmionium through fine tuning the magnetic anisotropy. Our results reveal the specific conditions needed to form the equilibrium states of skyrmions and skyrmionium and have significance for the development of skyrmion-based devices.

Magnetic skyrmions have attracted enormous research interest across a wide range of fields, from condensed matter physics to material science, since the first observation in 2009. Abundant theoretical, computational, and experimental studies have contributed to this emerging interdiscipline: skyrmionics. Especially, great expectations have been placed on exploiting the physics and dynamics of magnetic skyrmions as potential information carriers. In this topical review, we particularly focus on the computational studies of skyrmions during the last decade. After briefly introducing the mechanism of micromagnetic simulations, we review and discuss the manipulation of skyrmions, i. e., their creation, transformation, motion, and spin excitation, by both traditional and advanced methods, including electric currents, magnetic fields, spin waves, microwaves, etc. We take magnetic skyrmion as a typical example, while other skyrmion-related magnetic structures such as skyrmioniums and skyrmion tubes are also slightly involved. Through this review, we hope to give some insights into the further development of magnetic skyrmions in spintronics.

Spin waves (SWs) have been proven effective in driving the magnetic skyrmion motion, while the physical correlation between skyrmion velocity and the resonance frequency of local magnetization remains unknown. Here, we theoretically investigate the skyrmion motion in a magnetic Co/Pt nanotrack with the perpendicular magnetic anisotropy, which is driven by SWs. The results show that magnetic skyrmions move along the propagation direction of SWs in a specific frequency range (50–175 GHz). It is evidenced that there is a linear relationship between the response resonance frequency (fr) of local magnetization and the skyrmion velocity (v), and the motion of skyrmions could also be manipulated by controlling the amplitude and location of the exciting source. The present study provides a fundamental insight into understanding the intrinsic physics of SW-driven skyrmion-based devices.

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