Spin Transfer Torque with Spin Diffusion in Magnetic Tunnel Junctions
  Spin transport in magnetic tunnel junctions in the presence of spin diffusion is considered theoretically. Combining ballistic tunneling across the barrier and diffusive transport in the electrodes, we solve the spin dynamics equation in the metallic layers. We show that spin diffusion mixes the transverse spin current components and dramatically modifies the bias dependence of the effective spin transfer torque. This leads to a significant linear bias dependence of the out-of-plane torque, as well as a non-conventional thickness dependence of both spin torque components. 
A Manchon, R. Matsumoto, H. Jaffres, J. Grollier
cond-mat.mes-hall cond-mat.mtrl-sci