Supercurrent in long SFFS junctions with antiparallel domain configuration

We calculate the current-phase relation of a long Josephson junction consisting of two ferromagnetic domains with an equal but opposite magnetization h, sandwiched between two superconductors. In the clean limit, the current-phase relation is obtained with the help of the Eilenberger equation. In general, the supercurrent oscillations are nonsinusoidal and their amplitude decays algebraically when the exchange field is increased. If the two domains have the same size, the amplitude is independent of h, due to an exact cancellation of the phases acquired in each ferromagnetic domain. These results change drastically in the presence of disorder. We explicitly study two cases: fluctuations of the domain size (in the framework of the Eilenberger equation) and impurity scattering (using the Usadel equation). In both cases, the current-phase relation becomes sinusoidal and the amplitude of the supercurrent oscillations is exponentially suppressed with h, even if the domains are identical on average.