Crossover from clean to dirty limit in Josephson junctions with inhomogeneous ferromagnet

We study the Josephson effect and pairing correlations in SFFS junctions with two metallic monodomain ferromagnets with transparent and spin-inactive interfaces. We solve the Eilenberger equations self-consistently for arbitrary relative orientation of magnetizations of the two F layers in the clean limit and for moderate disorder in ferromagnets. Spatial variation of singlet and odd-frequency triplet pair amplitudes, as well as the Josephson current-phase relations, are calculated for different values of the ferromagnetic layer thickness and the angle between in-plane magnetizations. In the clean limit we find that both spin singlet and triplet pair amplitudes in F layers show a similar oscillatory decay with distance from the SF interfaces. For the singlet pair amplitude this decay gets faster as the impurity-scattering rate in ferromagnets is increased while the triplet amplitudes remain practically unaffected. In the dirty limit, the singlet amplitude penetrates into the ferromagnet over a short length scale determined by the exchange energy, while the triplet amplitudes are not suppressed and consequently they are long-ranged.