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

The spin transfer torque in all-metal dual spin valve, in which two antiparallelly aligned pinned ferromagnetic layers are on the two sides of a free ferromagnetic layer with two thin nonmagnetic spacers in between, is studied in the ballistic regime. It is argued that, similar to the results in the diffusion regime, the spin transfer torque is dramatically enhanced in comparison to that in a conventional spin valve although no spin accumulation exists at the magnetic-nonmagnetic interfaces. Within the Slonczewski's 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 dual spin valve. Depending on the orientation of free layer and the degree of electron polarization, the spin transfer torque enhancement could be tens times. The general cases when transmission and reflection probabilities of free layer are different from zero or one are also numerically calculated.