Competition between Pi-coupling and FFLO modulation in SF/SF atomic thickness bilayers

We present the detailed theoretical study of a heterostructure comprising of two coupled ferromagnetic superconducting layers. Our model may be also applicable to the layered superconductors with alternating interlayer coupling in a parallel magnetic field. It is demonstrated that such systems exhibit a competition between the nonuniform Larkin-Ovchinnikov-Fulde-Ferrel (FFLO) state and the superconducting state where the sign of the superconducting order parameter is opposite in adjacent layers. We determine the complete temperature-field phase diagram both in the cases of low and strong interlayer coupling. In the former we obtain a new Pi-phase inserted within the FFLO phase and located close to the usual tricritical point, whereas in the latter the bilayer in the state reveals a very high paramagnetic limit and the phenomenon of field-induced superconductivity.