Josephson current in a superconductor-ferromagnet junction with two noncollinear magnetic domains

We study the Josephson effect in a superconductor-ferromagnet-superconductor (SFS) junction with ferromagnetic domains of noncollinear magnetization. As a model for our study we consider a diffusive junction with two ferromagnetic domains along the junction. The superconductor is assumed to be close to the critical temperature T-c, and the linearized Usadel equations predict a sinusoidal current-phase relation. We find analytically the critical current as a function of domain lengths and of the angle between the orientations of their magnetizations. As a function of those parameters, the junction may undergo transitions between 0 and pi phases. We find that the presence of domains reduces the range of junction lengths at which the pi phase is observed. For the junction with two domains of the same length, the pi phase totally disappears as soon as the misorientation angle exceeds pi/2. We further comment on the possible implication of our results for experimentally observable 0-pi transitions in SFS junctions.