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

## TL;DR

This paper derives analytical expressions for spin-transfer torques on topological insulator surfaces, including higher-order effects, and explores how these torques influence magnetic skyrmion dynamics, revealing unique behavior compared to conventional metals.

## Contribution

The paper introduces new analytical formulas for spin-transfer torques incorporating higher-order momentum terms and hexagonal warping, advancing understanding of spin dynamics on topological insulator surfaces.

## Key findings

- Six types of spin-transfer torque identified, including four new ones from higher-order effects.
- Skyrmion dynamics depend strongly on internal magnetic structure, unlike in metals.
- Higher-order momentum contributions significantly alter torque behavior.

## Abstract

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.