  We discuss the properties of a ferromagnet - superconductor heterostructure
on the basis of a Hubbard model featuring exchange splitting in the ferromagnet
and electron - electron attraction in the superconductor. We have solved the
spin - polarized Hartree - Fock - Gorkov equations together with the Maxwell's
equation (Ampere's law) fully self-consistently. We have found that a Proximity
Effect - Fulde - Ferrell - Larkin - Ovchinnikov state is realized in such a
heterostructure. It manifests itself in an oscillatory behavior of the pairing
amplitude in the ferromagnet and spontaneously generated spin polarized current
in the ground state. We argue that it is built up from the Andreev bound
states, whose energy can be tuned by the exchange splitting and hence can
coincide with the Fermi energy giving rise to a current carrying $\pi$-state.
We also suggest experiments to verify these predictions.
