Multi-orbit tight binding calculations for spin transfer torque in magnetic tunneling junctions

We investigate the spin transfer torque (STT) with multi-orbit tight binding model in the magnetic tunneling junctions (MTJs). So far, most of the theoretical works based on the non-equilibrium Keldysh Green's function method employ a single band model for the simplicity, except a few first principle studies. Even though the single band model captures main physics of STT in MTJ, multi-band calculation reveals new features of the STT that depend on band parameters, such as insulator bandgap, inter-band hopping energy of the ferromagnetic layer. We find that the sign change of perpendicular torkance with bandgap of the insulator layer, and when we allow the inter-band hopping, the bias dependences of perpendicular STT are dramatically changed, while no noticeable changes in parallel STT are found.