  We study the ground state properties of a ferromagnet-superconductor
heterostructure on the basis of a quasiclassical theory. We have solved the
Eilenberger equations together with Maxwell's equation fully self-consistently
and found that due to the proximity effect a Fulde-Ferrel-Larkin-Ovchinnikov
(FFLO) like state is realized in such system. Moreover this state has
oscillations of the pairing amplitude in either one or two directions,
depending on the exchange splitting and thickness of the ferromagnet. In
particular, using semiclassical arguments (Bohr-Sommerfeld quantization rule)
we show that owing to the presence of the Andreev bound states in the
ferromagnet, a spontaneous current in the ground state is generated as a
hallmark of the FFLO state in the direction parallel to the interface. We also
discuss the effects of the the elastic disorder and finite transparency of the
interface on the properties of the $FFLO$ state in the system.
