Theory of current-driven dynamics of spin textures on a surface of topological insulators

Spin-transfer torque is one of the important physical quantities to understand for successful application of topological insulators to spintronics. In this paper, we present analytical expressions of the spin-transfer torques on a surface of a magnetic topological insulator by including the higher-order contributions of momentum, $k^2$-term and the hexagonal warping. We obtain six different types of the spin-transfer torque including both the field-like and the damping-like torques; the four of them appear only when the higher-order momentum contributions are included. In addition, we discuss the dynamics of magnetic skyrmions driven by the spin-transfer torques on the surface of the topological insulator. Unlike the skyrmion dynamics in conventional metals, we find that the dynamics significantly depends on the internal structure of magnetic textures.