Dirac Spin-Orbit Torques at the Surface of Topological Insulators

TL;DR

This paper investigates the unique spin-orbit torques at the surfaces of topological insulators, revealing their distinct symmetry and anisotropy, with implications for magnetization control and switching.

Contribution

It provides a theoretical analysis of Dirac spin-orbit torques using advanced formalisms, highlighting their unique symmetry and anisotropic properties compared to Rashba systems.

Findings

Dirac torques have different symmetry than Rashba torques.

Damping torque vanishes when magnetization is in-plane.

Numerical simulations show impact on magnetization switching.

Abstract

We address the nature of spin-orbit torques at the magnetic surfaces of topological insulators, using both Kubo formula and Keldysh formalism. Through the analysis of the derived spin-charge equations, we find that the so-called Dirac torques possess a different symmetry compared to their Rashba counterpart, as well as a high anisotropy as a function of the magnetization direction. In particular, the damping torque vanishes when the magnetization lies in the plane of the topological insulator surface. This peculiarity has important consequences in terms of magnetization dynamics and switching, as demonstrated numerically via a macrospin model.