Theory of nonequilibrium spin transport and spin-transfer torque in superconducting-ferromagnetic nanostructures

Spin transport currents and the spin-transfer torques in voltage-biased superconducting-ferromagnetic nanopillars (SFNFS point contacts) are computed. We develop and implement an algorithm based on the Ricatti formulation of the quasiclassical theory of superconductivity to solve the time-dependent boundary conditions for the nonequilibrium Green's functions for spin transport through the ferromagnetic interfaces. A signature of the nonequilibrium torque is a component perpendicular to the plane spanned by the two ferromagnetic moments. The perpendicular component is absent in normal-metal-ferromagnetic nanopillar contacts but is shown to have the same order of magnitude as the in-plane torque for nonequilibrium SFNFS contacts. The out-of-plane torque is due to the rotation of quasiparticle spin by the exchange fields of the ferromagnetic layers. In the ballistic limit the equilibrium torque is related to the spectrum of spin-polarized Andreev bound states, while the ac component, for small bias voltages, is determined by the nearly adiabatic dynamics of the Andreev bound states. The nonlinear voltage dependence of the nonequilibrium torque, including the subharmonic gap structure and the high-voltage asymptotics, is attributed to the interplay between multiple Andreev reflections, spin filtering, and spin mixing. These properties of spin angular momentum transport may be exploited to control the state of nanomagnets.