Spin-filtering effect and proximity effect in normal metal/ferromagnetic insulator/normal metal/superconductor junctions

Taking into account the thickness of the ferromagnetic insulator (FI), the spin-filtering effect and proximity effect in normal metal/ferromagnetic insulator/normal metal/superconductor (NM/FI/NM/SC) junctions are studied based on an extended Blonder-Tinkham-Klapwijk (BTK) theory. It is shown that a spin-dependent energy shift during the tunneling process induces splitting of the sub-energy gap conductance peaks and the spin polarization in the ferromagnetic insulator causes an imbalance of the peak heights. Different from the ferromagnet the spin-filtering effect of the FI cannot cause the reversion of the normalized conductance in NM/FI/NM/SC junctions.