Phase transitions in hybrid SFS structures with thin superconducting layers

Calculations of critical temperature $T_{c}$ of the phase transition to superconducting state of a superconductor/ferromagnet/superconductor (SFS) hybrid structure with proximity effect is performed on the base of linearized Usadel equations. It is shown that the proximity effect between $S$ and $F$ metals and the exchange interaction can induce an inhomogeneous superconducting state with longitudinal to layers $\Delta\propto\exp(ipz)$ modulation of the superconductivity order parameter, which is characterized by nonzero value of the wave number $p$, describing the Larkin–Ovchinnikov–Fulde–Ferrell instability. Influence of this instability on transitions between 0- and $\pi$-states of the $SFS$ structure is studied. It is shown that the 0–$\pi$ transition is accompanied by a nonmonotonic dependence of both the critical temperature $T_{c}$ and the effective penetration depth $\Delta$ of the magnetic field into the hybrid structure on the characteristic size of the ferromagnetic region.