# Microscopic theory of electrically induced spin torques in magnetic Weyl semimetals

## TL;DR

This paper develops a microscopic theory of electrically induced spin torques in magnetic Weyl semimetals, revealing the dominance of spin-orbit torque proportional to axial current and linking charge-induced torque to the chiral anomaly.

## Contribution

It provides a systematic calculation of all first-order current- and charge-induced spin torques in magnetic Weyl semimetals, highlighting the role of the chiral anomaly.

## Key findings

- Spin-transfer torque and β-term are absent.
- Spin-orbit torque is proportional to axial current density.
- Charge-induced spin torque originates from the chiral anomaly.

## Abstract

We theoretically study electrical responses of magnetization in Weyl semimetals. The Weyl semimetal is a new class of topological semimetals, possessing hedgehog type spin textures in momentum space. Because of this peculiar spin texture, an interplay of electron transport and spin dynamics might provide new method to electrical control of magnetization. In this paper, we consider the magnetically doped Weyl semimetals, and systematically study current- and charge-induced spin torque exerted on the local magnetization in three-dimensional Dirac-Weyl metals. We determine all current-induced spin torques including spin-orbit torque, spin-transfer torque, and the so-called $\beta$-term, up to first order with respect to spatial and temporal derivation and electrical currents. We find that spin-transfer torque and $\beta$-term are absent while spin-orbit torque is proportional to the axial current density. We also calculate the charge-induced spin torque microscopically. We find the charge-induced spin torque originates from the chiral anomaly due to the correspondence between spin operators and axial current operators in our model.