  We study in this paper effects of Dzyaloshinskii-Moriya (DM) magnetoelectric
coupling between ferroelectric and magnetic layers in a superlattice formed by
alternate magnetic and ferroelectric films.Magnetic films are films of simple
cubic lattice with Heisenberg spins interacting with each other via an exchange
$J$ and a DM interaction with the ferroelectric interface. Electrical
polarizations of $\pm{1}$ are assigned at simple cubic lattice sites in the
ferroelectric films.We determine the ground-state (GS) spin configuration in
the magnetic film. In zero field, the GS is periodically non collinear and in
an applied field $\mathbf H$ perpendicular to the layers, it shows the
existence of skyrmions at the interface. Using the Green's function method we
study the spin waves (SW) excited in a monolayer and also in a bilayer
sandwiched between ferroelectric films, in zero field. We show that the DM
interaction strongly affects the long-wave length SW mode. We calculate also
the magnetization at low temperature $T$. We use next Monte Carlo simulations
to calculate various physical quantities at finite temperatures such as the
critical temperature, the layer magnetization and the layer polarization, as
functions of the magnetoelectric DM coupling and the applied magnetic
field.Phase transition to the disordered phase is studied in detail.
