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Temperature induced transition of thin superconductor-ferromagnet-normal(S/F/N) metal hybrid structure to in-plane Fulde-Ferrel-Larkin-Ovchinnikov(FFLO) state is accompanied by vanishing of effective inverse magnetic fieldpenetration depth $\Lambda^{-1}$ (Phys. Rev. Lett. 121, 077002 (2018)). Here weshow that $\Lambda^{-1}$ goes to zero only in limit of zero magnetic field $H\to 0$ and at any finite parallel $H$ or in-plane current $I$ it is finite andpositive in FFLO state which implies diamagnetic response. We demonstrate that$\Lambda^{-1}$ has a nonmonotonic dependence on $H$ and $I$ not only in theparameter range corresponding to the FFLO phase domain but also in itsvicinity. We find that for S/F/N/F/S structures with certain thicknesses of Flayers there is temperature, current and magnetic field driven transition toand out of FFLO phase with a simultaneous jump of $\Lambda^{-1}$.

Tuning in-plane FFLO state in superconductor-ferromagnet-normal metal hybrid structure by magnetic field or current