On the calculation of the magnetoresistance of tunnel junctions with parallel paths of conduction

At the interfaces between the metallic electrodes and barrier in magnetic tunnel junctions it is possible for localized states to form which are orthogonal to the itinerant states for the junction, as well as resonant states that can form at the interfaces. These states form highly conducting paths across the barrier when their orbitals point directly into the barrier; these paths are in addition to those formed by the itinerant states across the entire junction. Most calculations of transport in magnetic tunnel junctions are made with the assumptions that the transverse momentum of the tunnelling electrons is conserved, in which case the itinerant electron states remain orthogonal to localized states. In principle it is possible to include diffuse scattering in both the bulk of the electrodes and the barrier so that the transverse momentum is not conserved, as well as the processes that couple localized states at the electrode–barrier interface to the itinerant states in the bulk of the electrodes. However, including these effects leads to lengthy calculations. Therefore, to assess the conduction across the barrier through th