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We investigate the Josephson transport through ferromagnetic insulators (FIs)by taking into account the band structure of FIs explicitly. Using therecursive Green's function method, we found the formation of a pi-junction insuch systems. Moreover the atomic-scale 0-pi oscillation is induced byincreasing the thickness of FI and its oscillation period is universal, i.e.,just single atomic layer. Based on these results, we show that stable pi-statecan be realized in junctions based on high-Tc superconductors withLa$_2$BaCuO$_5$ barrier. Such FI-based Josephson junctions may become anelement in the architecture of future quantum computers.

Theory of quantum transport in Josephson junctions with a ferromagnetic insulator