Role of magnetic scattering in 0-π transitions in a superconductor/ferromagnetic metal/superconductor junction

We study the influence of magnetic scattering on the Josephson critical current, I-c in a superconductor/ferromagnetic metal/superconductor (SFS) junction by a tunneling Hamiltonian approach. An analytical formula of I-c is given in the fourth order perturbation theory as regards the tunneling matrix element. The I-c exhibits the damped oscillatory dependence on the thickness of the ferromagnetic metal, d, and shows the transition between 0- and pi-states with d. When the superconducting transition temperature is comparable to the ferromagnetic Curie temperature, the period of oscillation is obviously changed by increasing temperature, T, due to the magnetic scattering, which induces the 0-pi transition with T. The magnetic scattering provides rich variety of Josephson effect in the SFS junction. Our results present an appropriate condition of a superconductor and a ferromagnetic metal to control the 0- and the pi-states.