Abstract
We study theoretically the Josephson effect and pairing correlations in planar SF${}_{1}$F${}_{2}$S junctions that consist of conventional superconductors (S) connected by two metallic monodomain ferromagnets (F${}_{1}$ and F${}_{2}$) with transparent interfaces. We obtain both spin-singlet and -triplet pair amplitudes and the Josephson current-phase relations for arbitrary orientation of the magnetizations using the self-consistent solutions of Eilenberger equations in the clean limit and for a moderate disorder in ferromagnets. We find that the long-range triplet correlations cannot prevail in symmetric junctions with equal ferromagnetic layers. Surprisingly, the long-range spin-triplet correlations give the dominant second harmonic in the Josephson current-phase relation of highly asymmetric SF${}_{1}$F${}_{2}$S junctions. The effect is robust against moderate disorder and variations in the layers thickness and exchange energy of ferromagnets.
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