Spin Transfer Torque and Tunneling Magnetoresistance Dependences on the 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 in the magnetic tunnel junction (MTJ). We employed 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 TMR in MTJ with the finite bias voltages. The dependences of STT and TMR on the insulator barrier energy are calculated for the semi-infinite half metallic ferromagnetic electrodes. We find that perfect linear relation between the parallel STT and the tunneling current for the wide range of the insulator barrier energy. Furthermore, the TMR also depends on the insulator barrier energy, which contradicts to the Julliere's simple model.