Proximity effects in normal mental/spin-splitting material/superconductor junctions

We extend the Blonder, Tinkham and Klapwijk (BTK) theory to the studyof the coexistence between ferromagnetism and s-wavesuperconductivity in ferromagnet/superconductor (F/S) structures. Itis found that the ferromagnetism and s-wave superconductivity cancoexist near the F/S interface, which is induced by proximityeffects. On the F side, the density of states (DOS) exhibits somesuperconducting-like properties, and it displays a damped oscillationfrom `0' to `$pi$' states with increasing either the thickness of Ffilm or the exchange energy. We also study the influences of thespin-polarized exchange splitting in the F and the spin-degeneracy byRashba spin--orbit coupling (RSOC) in the two-dimensional electrongas (2DGE) on the proximity effects. It is shown that the case ofRashba spin-degeneracy is very different from that of thespin-polarized exchange splitting.