We study theoretically the dc Josephson tunnel current for a junction of two proximity S/F bilayers of a massive superconductor (S) / a thin ferromagnet (F) separated by an insulating (I) barrier. The dependence of the critical current on the relative orientation of the F layers magnetization is analyzed within the microscopic theory of the proximity effect for an S/F bilayer. We demonstrate that for the S/F-I-F/S contact critical current can reverse its sign (π-state of the junction) for the parallel orientation of the F layers magnetization, wile for antiparallel alignment an enhancement of the critical current takes place. The results provide a new effect of the interplay between superconductivity and ferromagnetism in hybrid structures.
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