Spin Torque in Double Planar Tunnel Junctions

Transport in a double planar tunnel junction with ferromagnetic electrodes is analyzed theoretically in the zero-temperature limit. The in-plane and out-of-plane components of the spin torque exerted on magnetic moment of the central layer are determined as a function of the angle θ between magnetic moments of one of the external electrodes and of the central layer. Two configurations of the magnetic moments of external electrodes are considered, i.e. parallel and antiparallel ones. It is found that both torque components depend strongly on the thickness of the central layer, especially in junctions with a relatively thin central layer, where enhancement of the torque or a change of its sign can be observed for specific layer thicknesses. In junctions with thick central layer and in the limit of small bias voltage applied to the junction, the in-plane torque is generally smaller in the parallel configuration than in the antiparallel one. The opposite relation is observed for the normal torque.