Angular dependence of spin transfer torque on magnetic tunnel junctions with synthetic ferrimagnetic free layer

Based on a spin-polarized free-electron model, spin and charge transports are analyzed in magnetic tunnel junctions with synthetic ferrimagnetic layers in the ballistic regime, and the spin transfer torque is derived. We characterize the synthetic ferrimagnetic free layer by extending an arbitrary direction of magnetizations of the two free layers forming the synthetic ferrimagnetic free layer. The synthetic ferrimagnetic configuration exerts the approximately optimum torque for small magnetization angle of the first layer relative to that of the pinned layer. For approximately anti-parallel magnetization of the first layer to that of the pinned layer, the parallel magnetization of two magnetic layers is favorable for magnetization reversal rather than the synthetic ferrimagnetic configuration.