Josephson current in a superconductor-ferromagnet-superconductor junction with in-plane ferromagnetic domains

We study a diffusive superconductor-ferromagnet-superconductor (SFS) junction with in-plane ferromagnetic domains. Close to the superconducting transition temperature, we describe the proximity effect in the junction with the linearized Usadel equations [Phys. Rev. Lett. 25, 507 (1970)]. We find that properties of such a junction depend on the size of the domains relative to the magnetic coherence length. In the case of large domains, the junction exhibits transitions to the pi state, similar to a single-domain SFS junction. In the case of small domains, the magnetization effectively averages out, and the junction is always in the zero state, similar to a superconductor-normal metal-superconductor junction. In both those regimes, the influence of domain walls may be approximately described as an effective spin-flip scattering. We also study the inhomogeneous distribution of the local current density in the junction. Close to the 0-pi transitions, the directions of the critical current may be opposite in the vicinity of the domain wall and in the middle of the domains.