Charge transport and quantum phase transitions in singlet-superconductor/ferromagnet/singlet-superconductor junctions

We study the Josephson current, IJ, in a junction consisting of two s-wave superconductors that are separated by a ferromagnetic barrier possessing magnetic and nonmagnetic scattering potentials, g and Z, respectively. We discuss the general dependence of IJ on g, Z, and the phase difference � between the two superconductors. Moreover, we compute the critical current, Ic, for given g and Z, and show that it possesses two lines of nonanalyticity in the �g,Z� plane. We identify those regions in the �g,Z� plane where the Josephson current changes sign with increasing temperature without a change in the relative phase between the two superconductors, i.e., without a transition between the 0 and � states of the junction. Finally, we show that by changing the relative phase �, it is possible to tune the junction through a first-order quantum phase transition in which the spin polarization of the two superconductors’ combined ground state changes from �Sz�=0 to �Sz�=1/ 2