MRSej, Vol. 6, No.1, pp.103-118, 2004

**NONUNIFORM SUPERCONDUCTING STATES
AND UMKLAPP PROCESSES
IN FERROMAGNET–SUPERCONDUCTOR NANOSTRUCTURES **

M.G. Khusainov

*Kazan state university, Kazan, **Russia *

*Kazan state technical university, branch "Vostok", Chistopol', **Russia *

* *For the layered ferromagnetic metal/superconductor (FM/S) structures new boundary-value problem, which takes into account a competition between the one-dimensional (1D) and three-dimensional (3D) realizations of the Larkin-Ovchinnikov-Fulde-Ferrell states, is derived. Superconductivity in the FM/S structures proves to be a superposition of the BCS pairing with zero total momentum in the S layers and the FFLO paring with nonzero pair momentum **k ** in the FM layers. It is shown that processes of transition and mutual transformation of the BCS and FFLO pairs at the FM/S boundary occur as the Umklapp processes during which the coherent pair momentum k is conserved with exactness up to the reciprocal LOFF lattice vector **G **. These Umklapp processes can occur both in normal (1D states) and in the tangent (3D states) directions with respect to the FM/S interface. It is found that nonmonotonic behavior of the critical temperature *T _{c} * in the FM/S billayers is caused by the oscillations of the Cooper pairs flux through the S/FM boundary due to 3D-1D-3D phase transition cascade and switching between normal and tangent Umklapp processes. For the FM/S superlattices the existence of new $\pi$-magnetic 0$\pi$ and $\pi\pi$ LOFF states, which at certain conditions can have a much higher

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