Numerical study of pi-junction using spin filtering barriers

We numerically investigate the Josephson transport through ferromagnetic insulators (FIs) by taking into account its band structure. By use of the recursive Green's function method, we found the formation of the pi junction in the case of the fully spin-polarized FI (FPFI), e.g., La$_2$BaCuO$_5$. Moreover, the 0-pi transition is induced by increasing the thickness of FPFI. On the other hand, Josephson current through the Eu chalcogenides shows the pi junction behavior in the case of the strong d-f hybridization between the conduction d and the localized f electrons of Eu. Such FI-based Josephson junctions may become a element in the architecture of future quantum information devices.