  The precessing magnetization of a magnetic islands coupled to a quantum spin
Hall edge pumps charge along the edge. Conversely, a bias voltage applied to
the edge makes the magnetization precess. We point out that this device
realizes an adiabatic quantum motor and discuss the efficiency of its operation
based on a scattering matrix approach akin to Landauer-B"uttiker theory.
Scattering theory provides a microscopic derivation of the
Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device,
including spin-transfer torque, Gilbert damping, and Langevin torque. We find
that the device can be viewed as a Thouless motor, attaining unit efficiency
when the chemical potential of the edge states falls into the
magnetization-induced gap. For more general parameters, we characterize the
device by means of a figure of merit analogous to the ZT value in
thermoelectrics.
