  We study magnetic state and electron transport properties of composite
multiferroic system consisting of a granular ferromagnetic thin film placed
above the ferroelectric substrate. Ferroelectricity and magnetism in this case
are coupled by the long-range Coulomb interaction. We show that magnetic state
and magneto-transport strongly depend on temperature, external electric field,
and electric polarization of the substrate. Ferromagnetic order exists at
finite temperature range around ferroelectric Curie point. Outside the region
the film is in the superparamagnetic state. We demonstrate that magnetic phase
transition can be driven by an electric field and magneto-resistance effect has
two maxima associated with two magnetic phase transitions appearing in the
vicinity of the ferroelectric phase transition. We show that positions of these
maxima can be shifted by the external electric field and that the magnitude of
the magneto-resistance effect depends on the mutual orientation of external
electric field and polarization of the substrate.
