We examine superconductivity in layered systems with large Fermi-surface
splitting due to coexisting ferromagnetic layers. In particular, the hybrid
ruthenate-cuprate compound RuSr_2GdCu_2O_8 is examined on the coexistence of
the superconductivity and the ferromagnetism, which has been observed recently.
We calculate critical fields of the superconductivity taking into account the
Fulde-Ferrell-Larkin-Ovchinnikov state in a model with Fermi-surfaces which
shapes are similar to those obtained by a band calculation. It is shown that
the critical field is enhanced remarkably due to a Fermi-surface effect, and
can be high enough to make the coexistence possible in a microscopic scale. We
also clarify the direction of the spatial oscillation of the order parameter,
which may be observed by scanning tunneling microscope experiments.Comment: 4 pages, 4 figures, (Latex, revtex.sty, epsf.sty
