2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125016We study the Josephson effect in a superconductor--ferromagnet--superconductor (SFS) junction with ferromagnetic domains of non-collinear 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 $π$ phases. We find that the presence of domains reduces the range of junction lengths at which the $π$ phase is observed. For the junction with two domains of the same length, the $π$ phase totally disappears as soon as the misorientation angle exceeds $π/2$. We further comment on possible implication of our results for experimentally observable 0--$π$ transitions in SFS junctions.9 pages, 4 figures, minor changes, references addedSuperconductivityMesoscale and Nanoscale Physicstext