Theoretical study on the perpendicular anisotropic magnetoresistance using Rashba-type ferromagnetic model

We investigated the anisotropic magnetoresistance (AMR) effects in ferromagnetic-metal multi-layers stacked on non-magnetic insulators in the context of microscopic theory. We represented this situation with tight-binding models that included the exchange and Rashba fields, where the Rashba field was assumed to originate from spin-orbit interactions as junction effects with the insulator. To describe the AMR ratios, the DC conductivity was calculated based on the Kubo formula. As a result, we showed that the Rashba field induced both perpendicular and in-plane AMR effects and that the perpendicular AMR effect rapidly decayed with increasing film thickness.