Josephson pi-state in a ferromagnetic insulator

We predict anomalous atomic-scale 0-pi transitions in a Josephson junction with a ferromagnetic-insulator (FI) barrier. The ground state of such junction alternates between 0- and pi-states when thickness of FI is increasing by a single atomic layer. We find that the mechanism of the 0-pi transition can be attributed to thickness-dependent phase-shifts between the wave numbers of electrons and holes in FI. Based on these results, we show that stable pi-state can be realized in junctions based on high-Tc superconductors with La$_2$BaCuO$_5$ barrier.