  Magnetoelectric coupling terms are derived in piezoelectric/magnetostrictive
(multiferroic) thin film heterostructures using Landau-Ginzburg free energy
expansions in terms of strain and by considering strain boundary conditions
between the two materials. Then, a general effective medium method for solving
for the complete electromagnetic susceptibility tensor of such heterostructures
is used to calculate the ferromagnetic resonance frequency in a
BaTiO$_3$/NiFe$_2$O$_4$ superlattice. This method differs from existing methods
for treating magnetoelectric heterostructures since the magnetic and electric
dipolar fields are not assumed constant but vary from one film to another. The
ferromagnetic resonance frequency shift is calculated as a function of applied
electric field and is compared to some experimental results.
