Strong Spin-Orbit Torque effect on magnetic defects due to topological surface state electrons in Bi$_{2}$Te$_{3}$

TL;DR

This study demonstrates a strong spin-orbit torque effect on magnetic impurities in Bi$_{2}$Te$_{3}$ surface states, revealing impurity-specific responses and optimal conditions for magnetic control in topological insulators.

Contribution

It provides first-principles calculations of spin-orbit torque on various magnetic impurities in Bi$_{2}$Te$_{3}$, highlighting the impact of resonant scattering and identifying Mn as the most effective impurity.

Findings

Mn impurities exhibit the strongest torque response.

Resonant scattering significantly influences torque magnitude.

Resistivity and Joule heating are quantified as functions of torque.

Abstract

We investigate the spin-orbit torque exerted on the magnetic moments of the transition-metal impurities Cr, Mn, Fe and Co, embedded in the surface of the topological insulator Bi$_{2}$Te$ _{3} $, in response to an electric field and a consequent electrical current flow in the surface. The multiple scattering problem of electrons off impurity atoms is solved by first-principles calculations within the full-potential relativistic Korringa-Kohn-Rostoker (KKR) Green function method, while the spin-orbit torque calculations are carried out by combining the KKR method with the semiclassical Boltzmann transport equation. We analyze the correlation of the spin-orbit torque to the spin accumulation and spin flux in the defects. We compare the torque on different magnetic impurities and unveil the effect of resonant scattering. In addition, we calculate the resistivity and the Joule heat as a function of the torque in these systems. We predict that the Mn/Bi$_{2}$Te$_{3}$ is optimal among the studied systems.