Long-range spin-triplet proximity effect in Josephson junctions with multilayered ferromagnets

We study theoretically the Josephson effect and pairing correlations in planar SF1F2S junctions that consist of conventional superconductors (S) connected through two metallic monodomain ferromagnets (F1 and F2) with transparent interfaces. We solve self-consistently the Eilenberger equations for arbitrary orientation of in-plane magnetizations in the clean limit and for moderate disorder in ferromagnets. Both singlet and triplet pair amplitudes and the Josephson current-phase relations are calculated numerically. It is shown that for equally thick ferromagnetic layers (symmetric junctions) the long-range spin-triplet correlations are not dominant: For thin ferromagnetic layers all amplitudes are equally large, while for thick layers the long range triplet amplitude is very small. It is shown that for noncollinear magnetizations the long-range proximity effect can be dominant in highly non-symmetric SF1F2S junctions with particularly thin F1 and thick F2 ferromagnetic layers. We find that dominant triplet correlations in Josephson junctions with ferromagnetic bilayer always give dominant second harmonics in current-phase relations at low temperatures.