What is the value of the superconducting gap of a F / S / F trilayer ?

– Based on the model of F/S/F trilayer with atomic thickness [A. Buzdin and M. Daumens, cond-mat/0305320] we discuss the relative roles of pair-breaking and proximity effects, as a function of the exchange field, of disorder and of a finite thickness in the su-perconducting layer. The exchange field can be small (weak ferromagnets) or large (strong ferromagnets) compared to the superconducting gap. With weak ferromagnets we show the existence of a reentrant superconducting gap for the F/S/F trilayer with atomic thickness in the parallel alignment (equivalent to the F/S bilayer). Qualitatively small disorder is equivalent to reducing the value of the hopping parameters. In the presence of a finite thickness in the superconducting layer the superconducting gap in the antiparallel alignment is larger than in the parallel alignment, meaning that pair breaking dominates over the proximity effect. Introduction. – Superconductivity and ferromagnetism are antagonist states of matter: in a superconductor electrons are bound into Cooper pairs whereas one spin population is favored in ferromagnetism. Many interesting phenomena take place in mesoscopic devices when superconductors are connected to ferromagnets. For example the superconducting pair amplitude induced in a ferromagnet oscillates in space [1,2,3,4] and these oscillations can give rise to the π-coupling. The π-coupling manifests itself in superconductor / ferromagnet (S/F) multilayers as oscillations of the superconducting critical temperature with the thickness of the ferromagnetic layers [5, 6, 7]. S/F/S π-junctions have been recently probed with various experimental techniques [8, 9, 10]. The proximity effect in F/S/F trilayers has recently focused a renewed interest. It was established long ago that with insulating ferromagnets the superconducting transition temperature is larger in the antiparallel alignment because of the exchange field induced in the S layer [11] that tends to dissociate Cooper pairs. Following this theoretical prediction two experiments were performed, one with metallic ferromagnets [12] and the other with insulating