Spin transfer torque enhancement in dual spin valves in the ballistic regime

The spin transfer torque in an all-metal dual spin valve, in which two antiparallel-aligned pinned ferromagnetic layers are on the two sides of a free ferromagnetic layer with two thin normal metal spacers in between, is studied in the ballistic regime. It is argued that, similar to the results in the diffusive regime, the spin transfer torque is dramatically enhanced in comparison to that in a conventional spin valve in the ballistic regime. Within the Slonczewski approach, an analytical expression of the torque on the free magnetic layer is obtained, which may serve as a theoretical model for the micromagnetic simulation of the spin dynamics in a dual spin valve. Depending on the orientation of the free layer and the degree of electron polarization, the spin transfer torque enhancement could be tenfold. The general cases when transmission and reflection probabilities of the free layer are different from zero or one are also numerically calculated.