Spin torque from tunneling through impurities in a magnetic tunnel junction

We calculate the contribution to the spin transfer torque from sequential tunneling through impurities in a magnetic tunnel junction. For a junction with weakly polarized ferromagnetic contacts, the torque is found to be in the plane spanned by the magnetizations of the ferromagnetic contacts and proportional to $\sin \theta$, where $\theta$ is the angle between the magnetic moments. If the polarization is larger, the torque acquires a significant out-of-plane component and a different dependence on $\theta$.