  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.
