Fundamental theory of current-induced motion of magnetic skyrmions

Magnetic skyrmions are topological spin textures that appear in magnets with broken spatial inversion symmetry as a consequence of competition between the (anti)ferromagnetic exchange interactions and the Dzyaloshinskii-Moriya interactions in a magnetic field. In the research of spintronics, the current-driven dynamics of skyrmions has been extensively studied aiming at their applications to next-generation spintronic devices. However, current-induced skyrmion motion exhibits diverse behaviors depending on various factors and conditions such as the type of skyrmion, driving mechanism, system geometry, direction of applied current, and type of the magnet. While this variety attracts enormous research interest of fundamental science and enriches their possibilities of technical applications, it is, at the same time, a source of difficulty and complexity that hinders their comprehensive understandings. In this article, we discuss fundamental and systematic theoretical descriptions of current-induced motion of skyrmions driven by the spin-transfer torque and the spin-orbit torque. Specifically, we theoretically describe the behaviors of current-driven skyrmions depending on the factors and conditions mentioned above by means of analyses using the Thiele equation. Furthermore, the results of the analytical theory are visually demonstrated and quantitatively confirmed by micromagnetic simulations using the Landau-Lifshitz-Gilbert-Slonczewski equation. In particular, we discuss dependence of the direction and velocity of motion on the type of skyrmion (Bloch type and Néel type) and its helicity, the system geometry (thin plate and nanotrack), the direction of applied current (length and width direction of the nanotrack) and its spin-polarization orientation, and the type of magnet (ferromagnet and antiferromagnet). The comprehensive theory provided by this article is expected to contribute significantly to research on the manipulation and control of magnetic skyrmions by electric currents for future spintronics applications.