Theory of proximity effect in ferromagnet/superconductor heterostructures in the presence of spin dependent interfacial phase shift

We study the proximity effect and charge transport in ferromagnet (F)/superconductor (S) and S/F/I/F/S junctions (where I is insulator) by taking into account simultaneously exchange field in F and spin-dependent interfacial phase shifts (SDIPS) at the F/S interface. We solve the Usadel equations using extended Kupriyanov–Lukichev boundary conditions which include SDIPS, where spin-independent part of tunneling conductance GT and spin-dependent one Gφ coexist. The resulting local density of states (LDOS) in a ferromagnet depends both on the exchange energy Eex and Gφ/GT. We show that the magnitude of zero-temperature gap and the height of zero-energy LDOS have a non-monotonic dependence on Gφ/GT. We also calculate Josephson current in S/F/I/F/S junctions and show that crossover from 0-state to π