The Riccati formulation of the quasiclassical theory of nonequilibrium superconductors is developed for spin-dependent scattering near magnetic interfaces. We derive boundary conditions for the Riccati distribution functions at a spin-active interface. The boundary conditions are formulated in terms of an interface $S$-matrix describing the reflection and transmission of the normal-state conduction electrons by the interface. The $S$-matrix describes the effects of spin filtering and spin mixing (spin rotation) by a ferromagnetic interface. The boundary conditions for the Riccati equations are applicable to a wide range of nonequilibrium transport properties of hybrid systems of superconducting and magnetic materials. As an application we calculate the spin and charge conductance of a normal metal-ferromagnet-superconductor (NFS) point contact; the spin mixing angle that parameterizes the $S$-matrix is determined from experimental measurements of the peak in the subgap differential conductance of the NFS point contact. We also use the new boundary conditions to derive the effects of spin mixing on the phase-modulated thermal conductance of a superconducting-ferromagnetic-superconducting (SFS) point contact. For high-transparency (metallic ferromagnet) “$\pi$” junctions, the phase modulation of the thermal conductance is dramatically different from that of nonmagnetic, “0” junctions. For low-transparency (insulating ferromagnet) SFS tunnel junctions with weak spin-mixing resonant transmission of quasiparticles with energies just above the gap edge leads to an increase of the thermal conductance, compared to the normal-state conductance at $T_c$, over a broad temperature range when the superconducting phase bias is $\varphi \gtrsim \pi ∕2$.

• Received 4 April 2004

DOI:https://doi.org/10.1103/PhysRevB.70.134510