Adiabatic quantum pumping, magnification effects and quantum size effects of spin-torque in magnetic tunnel junctions

We study the adiabatic quantum pumping and quantum size effects of spin-torque in a magnetic tunnel junction within a scattering matrix approach. Quantum size effects are predicted in the presence of a dc bias as a function of the thickness of the normal metal layer inserted between two magnetic layers and of the fixed magnetic layer. In the presence of ac voltages, the results for the spin-torque show a peculiar magnification effect and advantages of spin-torque pumping in actual devices are also discussed.