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 α′ E = δE/δH, where δE is the induced electric field for an applied ac magnetic field δH, 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 (α′ E,L ) in which the poling field E, bias field H and ac fields δE and δH are all parallel to each other and perpendicular to the sample plane; (ii) transverse fields (α′ E,T ) for in-plane H and δH parallel to each other and perpendicular to out-of-plane E and δE, and (iii) in-plane longitudinal fields (α′ E,IL ) 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. Estimates of α′ E are carried out as a function of the interface coupling k and volume fraction v for the piezoelectric phase. In unclamped samples, α′ E increases with increasing k. The strongest coupling occurs for equal volume of the two phases for transverse and longitudinal cases , but a maximum occurs at v=0.1 for the in-plane longitudinal case. Upon clamping the bilayer, the ME effect is strengthened for the longitudinal case and is weakened for the transverse case. Other important results of the theory are as follows. (i) The strongest ME coupling is expected for the inplane longitudinal fields and the weakest coupling for the (out-of-plane) longitudinal case. (ii) In ferrite based composites, α′ E,T and α′ E,IL are a factor of 2-10 higher than α E,L . (iii) The highest ME voltage coefficients are expected for CFO-PZT and the lowest values are for LSMO-PZT. Results of the present model are compared with available data on volume and static magnetic field dependence of α′ E . We infer, from the comparison, ideal interface conditions in NFO-PZT and poor interface coupling for CFO-PZT and LSMO-PZT.

Magnetoelectric interactions in bilayers of magnetostrictive and piezoelectric phases are mediated by mechanical deformation. Here we discuss the theory and companion data for magnetoelectric (ME) coupling at electromechanical resonance (EMR) in a ferrite-lead zirconate titanate (PZT) bilayer. Estimated ME voltage coefficient versus frequency profiles for nickel, cobalt, or lithium ferrite and PZT reveal a giant ME effect at EMR with the highest coupling expected for cobalt ferrite-PZT. Measurements of resonance ME coupling have been carried out on layered and bulk composites of nickel ferrite-PZT. We observe a factor of 40-600 increase in ME voltage coefficient at EMR compared to low frequency values. Theoretical ME voltage coefficients versus frequency profiles are in excellent agreement with data. The resonance ME effect is therefore a novel tool for enhancing the field conversion efficiency in the composites.

A theoretical model is presented for low-frequency magnetoelectric (ME) effects in bilayers of magnetostrictive and piezoelectric phases. An approach is proposed for the consideration of actual boundary conditions at the interface. An averaging method is used to estimate effective material parameters. The model predicts the strongest ME effect in cobalt ferrite-lead zirconate titanate (PZT) among ferrite based composites. The ME voltage coefficient for transverse field orientation is estimated to be 25–50% higher than for the longitudinal case. Comparison with data for multilayer samples reveals poor interface coupling in cobalt ferrite-PZT and ideal coupling in nickel ferrite-PZT.

The first observation of microwave magnetoelectric (ME) interactions through ferromagnetic resonance (FMR) in bilayers of single crystal ferromagnetic-piezoelectric oxides and a theoretical model for the effect are presented. An electric field E produces a mechanical deformation in the piezoelectric phase, resulting in a shift δH E in the resonance field for the ferromagnet. The strength of ME coupling is obtained from data on δH E vs E. Studies were performed at 9.3 GHz on bilayers of (111) yttrium iron garnet (YIG) films and (001) lead magnesium niobatelead titanate (PMN-PT). The samples were positioned outside a TE 102 -reflection type cavity. Resonance profiles were obtained for E = 0-8 kV/cm for both in-plane and out-of-plane magnetic fields H. Important results are as follows. (i) The ME coupling in the bilayers is an order of magnitude stronger than in polycrystalline composites and is in the range 1-5.4 Oe cm/kOe, depending on the YIG film thickness. (ii) The coupling strength is dependent on the magnetic field orientation and is higher for out-of-plane H than for in-plane H. (iii) Estimated ME constant and its dependence on volume ratio for the two phases are in good agreement with the data.

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