Spin transfer torque and tunneling magnetoresistance dependences on finite bias voltages and insulator barrier energy

We investigate the dependence of perpendicular and parallel spin transfer torque (STT) and tunneling magnetoresistance (TMR) on the insulator barrier energy of the magnetic tunnel junction (MTJ). We employed the single orbit tight binding model combined with the Keldysh non-equilibrium Green's function method in order to calculate the perpendicular and parallel STT and the TMR in the MTJ with finite bias voltages. The dependences of the STT and TMR on the insulator barrier energy are calculated for semi-infinite half metallic ferromagnetic electrodes. We find a perfect linear relation between the parallel STT and the tunneling current for a wide range of insulator barrier energy. Furthermore, the TMR also depends on the insulator barrier energy, contradicting Julliere's simple model.