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First order $0$ - $π$ phase transitions in superconductor/ferromagnet/superconductor trilayers

We study the thermodynamics of the diffusive SFS trilayer composed of thin superconductor (S) and ferromagnet (F) layers. On the basis the self-consistent solutions of nonlinear Usadel equations in the F and S layers we obtain the Ginzburg--Landau expansion and compute the condensation free energy and entropy of the $0$ (even) and $π$ (odd) order parameter configurations. The first order $0-π$ transition as a function of temperature $T$ occurs, which is responsible for a jump of the averaged magnetic field penetration depth $λ(T)$ recently observed on experiments [N.Pompeo, et. al., Phys. Rev. B 90, 064510 (2014)]. The generalized Ginzburg-Landau functional was proposed to describe SFS trilayer for arbitrary phase difference between the superconducting order parameters in the S layers. The temperature dependence of the SFS Josephson junction critical current demonstrates the strong anharmonicity of the corresponding current--phase relation in the vicinity of the $0-π$ transition. In rf SQUID, coexistence of stable and metastable $0$ and $π$ states provides integer and half--integer fluxoid configurations.