Interference phenomena in Josephson junctions with ferromagnetic bilayers: Spin-triplet correlations and resonances

We study the Josephson effect in planar SF1F2S junctions that consist of conventional s-wave superconductors (S) connected by two metallic monodomain ferromagnets (F1 and F2) with an arbitrary transparency of interfaces. We solve the scattering problem in the clean limit based on the Bogoliubov-de Gennes equation for both spinsinglet and odd in frequency spin-triplet pairing correlations. We calculate numerically the Josephson currentphase relation I(phi). While the first harmonic of I(phi) is completely generated by spin-singlet and short-range spin-triplet superconducting correlations, for noncollinear magnetizations of ferromagnetic layers the second harmonic has an additional long-range spin-triplet component. Therefore, for a strong ferromagnetic influence, the long-range spin-triplet contribution to the second harmonic dominates. We find an exception due to the geometric resonance for equal ferromagnetic layers when the first harmonic is strongly enhanced. Both first and second harmonic amplitudes oscillate with ferromagnetic layer thicknesses due to 0-pi transitions. We study the influence of interface transparencies and find additional resonances for finite transparency of the interface between ferromagnetic layers.