Anomalous and spin Hall effects in a magnetic tunnel junction with Rashba spin-orbit coupling

Anomalous and spin Hall effects are investigated theoretically for a magnetic tunnel junction where the applied voltage produces a Rashba spin-orbit coupling within the tunneling barrier layer. The ferromagnetic electrodes are the source of the spin-polarized current. The tunneling electrons experience a spin-orbit coupling inside the barrier due to the applied electrical field. Charge and spin Hall currents are calculated as functions of the position inside the barrier and the angle between the magnetizations of the electrodes. We find that both charge and spin Hall currents are located inside the barrier near the interfaces. The dependence of the currents on magnetic configuration of the magnetic tunnel junction makes possible the manipulation by the Hall currents via rotation of the magnetization of the electrodes.