Tunneling Hamiltonian description of the atomic-scale 0-pi transition in   superconductor/ferromagnetic-insulator junctions
  We show a perturbation theory of the Josephson transport through ferromagnetic insulators (FIs). Recently we have found that the appearance of the atomic scale 0-pi transition in such junctions based on numerical calculations. In order to explore the mechanism of this anomalous transition, we have analytically calculated the Josephson current using the tunneling Hamiltonian theory and found that the spin dependent pi-phase shift in the FI barrier gives the atomic scale 0-pi transition. 
Shiro Kawabata, Yukio Tanaka, Alexander A. Golubov, Andrey S. Vasenko,   Satoshi Kashiwaya, Yasuhiro Asano
cond-mat.mes-hall cond-mat.supr-con quant-ph