Odd spin-triplet superconductivity in a multilayered superconductor-ferromagnet Josephson junction

We study the dc Josephson effect in a diffusive multilayered SF'FF'S structure, where S is a superconductor and F and F' are different ferromagnets. We assume that the exchange energies in the F' and F layers are different (h and H, respectively) and the middle F layer consists of two layers with parallel or antiparallel magnetization vectors M. The M vectors in the left and right F' layers are generally not collinear to those in the F layer. In the limit of a weak proximity effect we use a linearized Usadel equation. Solving this equation, we calculate the Josephson critical current for arbitrary temperatures, arbitrary thicknesses of the F' and F layers (L-h and L-H) in the case of parallel and antiparallel M orientations in the F layer. The part of the critical current I-cSR formed by the short-range singlet and S=0 triplet condensate components decays on a short length xi(H)=root D/H, whereas the part I-cLR due to the long-range triplet |S|=1 component decreases with increasing L-H on the length xi(N)=root D/pi T. Our results are in a qualitative agreement with the experiment [T. S. Khaire, M. A. Khasawneh, W. P. Pratt, Jr., and N. O. Birge, Phys. Rev. Lett. 104, 137002 (2010)].