Charge-Induced Spin Torque in Anomalous Hall Ferromagnets

We demonstrate that spin-orbit coupled electrons in a magnetically doped system exert a spin torque on the local magnetization, without a flowing current, when the chemical potential is modulated in a magnetic field. The spin torque is proportional to the anomalous Hall conductivity, and its effective field strength may overcome the Zeeman field. Using this effect, the direction of the local magnetization is switched by gate control in a thin film. This charge-induced spin torque is essentially an equilibrium effect, in contrast to the conventional current-induced spin-orbit torque, and, thus, devices using this operating principle possibly have higher efficiency than the conventional ones. In addition to a comprehensive phenomenological derivation, we present a physical understanding based on a model of a Dirac-Weyl semimetal, possibly realized in a magnetically doped topological insulator. The effect might be realized also in nanoscale transition materials, complex oxide ferromagnets, and dilute magnetic semiconductors.