Multiple Reflection Effect on Spin-Transfer Torque Dynamics in Spin Valves with a Single or Dual Polarizer

Abstract

In this paper, spin-dependent multiple reflection effect on spin-transfer torque (STT) has been theoretically and numerically studied in a spin valve nanopillar with a single or dual spin-polarizer. By using a scattering matrix method, we formulate an analytical expression of STT that contains the multiple interfacial reflection effect. It is found that the multiple reflections could enhance the STT efficiency and reduce the critical switching current. The STT efficiency depends on the spin polarization of both the free layer and polarizer. In the nanopillars with a dual spin polarizer, the multiple reflections would cause an asymmetric frequency dependence on the applied current, albeit exactly the same parameters are used in all three ferromagnetic layers, indicating that the frequency in the negative current varies much faster than that in the positive case.