Alternative mechanism of the sign-reversal effect in superconductor-ferromagnet-superconductor Josephson junctions

We consider a simple model of a multidomain superconductor-ferromagnet-superconductor (SFS) Josephson junction. Sign-alternating magnetization $M$ in domains leads to a spatial modulation of the phase difference $\phi (x)$. Due to this modulation the Josephson critical current $I_{c}$ may have a different sign depending on the ratio of the magnetic flux in a domain, 4$\pi Ma(2d_{F}),$ to the magnetic flux quantum. This phase modulation, but not a nonmonotonic dependence of the local critical current density $j_{c}$, may be the reason for oscillations of the current $I_{c}$ {\bf \}as a function of the F layer thickness $2d_{F} $ or temperature, observed in experiments.