An approximate calculation for transport in magnetic tunnel junctions in the presence of localized states

In conventional calculations of transport in magnetic tunnel junctions, one usually assumes that the transverse momentum of the tunnelling electrons is conserved and that the itinerant electron states are orthogonal to localized states. However, in most of the junctions studied, there is diffuse scattering in both the bulk of the electrodes and the barrier so that the transverse momentum is not conserved, and there are processes that couple localized states at the electrode-barrier interface to the itinerant states in the bulk of the electrodes. While it is in principle possible to include these effects, it leads to lengthy calculations. Here we propose an approximate scheme in which we do not take explicit account of either of the effects mentioned above, but in which we calculate the tunnelling through all the states that exist at the electrode-barrier interfaces. We compare the k_∥-resolved density of states and tunnelling currents across a junction in our approximate scheme with that found using the Landauer formalism in the ballistic limit.