Theoretical model of spin transfer torque in multilayers

We present a model of spin transport in a Co/Cu(1 1 1)/Co pseudo-spin-valve (PSV) structure where current is flowing in the current perpendicular-to-plane (CPP) geometry. The model considers ballistic spin-dependent transmission at the two Co–Cu interfaces, as well as diffusive spin relaxation within the Cu spacer and free Co layer. In the latter, the spin relaxation process is composed of the usual longitudinal spin relaxation due to spin flip scattering, as well as transverse spin relaxation due to spin precession. The resulting spin transfer torque exerted on the moments within the free Co layer is composed of two contributions, the main contribution coming from “absorbed” spins in the interfacial regions. The second contribution arises from the relaxation of spin accumulation within the free Co layer. The calculated critical current density for switching is estimated to be approximately between 3.3×10⁷ and 1.1×10⁸ A/cm², which is in agreement with available experimental results.