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We study the Josephson effect in asuperconductor--ferromagnet--superconductor (SFS) junction with ferromagneticdomains of non-collinear magnetization. As a model for our study we consider adiffusive junction with two ferromagnetic domains along the junction. Thesuperconductor is assumed to be close to the critical temperature $T_c$, andthe linearized Usadel equations predict a sinusoidal current-phase relation. Wefind analytically the critical current as a function of domain lengths and ofthe angle between the orientations of their magnetizations. As a function ofthose parameters, the junction may undergo transitions between 0 and $\pi$phases. We find that the presence of domains reduces the range of junctionlengths at which the $\pi$ phase is observed. For the junction with two domainsof the same length, the $\pi$ phase totally disappears as soon as themisorientation angle exceeds $\pi/2$. We further comment on possibleimplication of our results for experimentally observable 0--$\pi$ transitionsin SFS junctions.Comment: 9 pages, 4 figures, minor changes, references adde

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