Spin-transfer torque in double tunnel junctions with ferromagnetic barriers and nonmagnetic electrodes

Abstract

Spin and charge transport in a double planar tunnel junction with two ferromagnetic barriers and nonmagnetic electrodes is analysed theoretically. Tunnelling current and both in-plane and normal (out-of-plane) components of the spin-transfer torque exerted on ferromagnetic barriers are determined in the free-electron-like model in the coherent tunnelling limit. It is shown that the bias voltage dependence of the current and both components of the torque are nonmonotonic. The current and in-plane torque can be enhanced due to the resonant tunnelling through resonance states located below the Fermi level. These states also lead to oscillations of the current and torque with the thickness of the central layer. The normal torque can change sign with increase of the bias or the thickness of the central layer, which is due to the position change of the resonance states and the spin-splitting of these states. When electrons tunnel via the resonant states, the angular dependence of the torque can deviate strongly from the sinusoidal dependence observed in single junction with ferromagnetic electrodes and nonmagnetic barrier. The maximum of spin torque in the double junction with ferromagnetic barriers is often shifted from the configuration with perpendicular orientation of magnetic moments toward the configurations close to the antiparallel configuration.