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 the localized states that exist in parallel to the itinerant states we propose an approximate scheme in which we calculate the conductance of only the barrier region. While we do not take explicit account of either of the effects mentioned above, we do calculate the tunnelling through all the states that exist at the electrode-barrier interfaces by placing reservoirs directly across the barriers. To calculate the current and magnetoresistance for magnetic tunnel junctions (the junction magnetoresistance (JMR)) we have used the lattice model developed by Caroli et al. The propagators, density of states and hopping integrals entering the expressions for the current are determined by using the spin polarized scalar-relativistic screened Korringa-Kohn-Rostoker method that has been adapted to layered structures. By using vacuum as the insulating barrier we have determined with no adjustable parameters the JMR in the linear response region of tunnel junctions with fcc Co(100), fccNi(100) and bcc Fe(100) as electrodes. The JMR ratios that we find for these metal/vacuum/metal junctions are comparable with those measured with alumina as the insulating barrier. For vacuum barriers we find that tunnelling currents have minority- spin polarization whereas the tunnelling currents for th se electrodes have been observed to be positively (majority) polarized for alumina barriers and minority polarized for SrTiO 3 barriers. In addition to determining the JMR ratios in linear response we have also determined how the magnetoresistance of magnetic tunnel junctions varies with a finite voltage bias applied across the junction. In particular we have found how the shape of the potential barrier is altered by the applied bias and how this affects the current. Comparisons with data as they become available will eventually determine whether our approximate scheme or the ballistic Landauer-Büttiker approach is better able to represent the features of the electronic structure that control tunnelling in magnetic tunnel junctions.