  A theoretical model is presented for low-frequency magnetoelectric (ME)
effects in bilayers of magnetostrictive and piezoelectric phases. A novel
approach, the introduction of an interface coupling parameter k, is proposed
for the consideration of actual boundary conditions at the interface. An
averaging method is used to estimate effective material parameters. Expressions
for ME voltage coefficients are obtained by solving elastostatic and
electrostatic equations. We consider both unclamped and rigidly clamped
bilayers and three different field orientations of importance: (i) longitudinal
fields in which the poling field, bias field and ac fields are all parallel to
each other and perpendicular to the sample plane; (ii) transverse fields for
magnetic fields parallel to each other and perpendicular to electric fields,
and (iii) in-plane longitudinal fields for all the fields parallel to each
other and to the sample plane. The theory predicts a giant ME coupling for
bilayers with cobalt ferrite (CFO), nickel ferrite (NFO), or lanthanum
strontium manganite (LSMO) for the magnetostrictive phase and barium titanate
(BTO) or lead zirconate titanate (PZT) for the piezoelectric phase.
