Voltage Dependence of Spin Transfer Torque In Magnetic Tunnel junctions

Theoretical investigations of spin transfer torque in magnetic tunnel junctions using the tight-binding model in the framework of nonequilibrium Green functions formalism are presented. We show that the behavior of the spin transfer torque as a function of applied voltage can vary over a wide range depending on the band parameters of the ferromagnetic electrodes and the insulator that comprise the magnetic tunnel junction. The behavior of both the parallel and perpendicular components of the spin torque is addressed. This behavior is explained in terms of the spin and charge current dependence and on the interplay between evanescent states in the insulator and the Fermi surfaces of ferromagnetic electrodes comprising the junction. The origin of the perpendicular (field-like) component of spin transfer torque at zero bias, i.e., exchange coupling through the barrier between ferromagnetic electrodes is discussed.