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 $\delta H_E$ in the resonance field for the ferromagnet. The strength of ME coupling is obtained from data on $\delta H_E$ vs $E$. Studies were performed at $9.3\mathrm{GHz}$ on bilayers of (111) yttrium iron garnet (YIG) films and (001) lead magnesium niobate-lead titanate (PMN-PT). The samples were positioned outside a ${\mathrm{TE}}_{102}$-reflection type cavity. Resonance profiles were obtained for $E=0–8\mathrm{kV}∕\mathrm{cm}$ 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 $1–5.4\mathrm{Oe}\mathrm{cm}∕\mathrm{kOe}$, 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.

A phenomenological theory of magnetic and magnetoelectric (ME) susceptibilities of ferroelectric/ferromagnetic composites is presented and applied to the special case of layered structures. Expressions have been obtained relating the magnetic and ME susceptibility tensor components of the composite (symmetry point group $3m$ and $4mm)$ to ME coupling constants. The theory predicts a unique resonance in the electric-field dependence of the magnetic susceptibility. It is shown that the ME susceptibility is the product of magnetic susceptibility, composite magnetization, and ME coupling constants. The model is used to obtain the magnetic and ME susceptibilities versus electric-field profiles for three bilayer composites of importance: lithium ferrite (LFO)–lead zirconate titanate (PZT), nickel ferrite (NFO)-PZT, and yttrium iron garnet (YIG)-PZT. Our calculations reveal the largest electric-field effects for NFO-PZT and the weakest effect for YIG-PZT. Three measurement methods for ME susceptibility, resonant ME coupling, electrical dipole transitions, and ME effect at ferromagnetic resonance (FMR) are proposed. As an example, we consider multilayers of LFO-PZT and determine the ME constants from data on electric-field influence on FMR. The ME parameters are then used to calculate the susceptibilities. The results indicate strong high-frequency ME effects in the composite. The theory is useful for measurements of ME susceptibility and for the design and analysis of electrically controlled high-frequency magnetic devices.

A phenomenological theory is proposed to treat the magnetoelectric (ME) coupling at frequencies corresponding to ferromagnetic resonance in a multilayer composite consisting of alternate layers of piezoelectric and magnetostrictive phases. We discuss two models: (i) a simple two-layer (bimorph) structure and (ii) a generalized approach in which the multilayer structure is considered to be a homogeneous medium. Expressions for the stress induced shift $\delta H$ in the ferromagnetic resonance field due to an applied electric field E have been obtained for both cases. For a bimorph, $\delta H$ is directly proportional to the product of the applied electric field and the ME coupling constant. For a nickel ferrite–lead zirconate titanate (PZT) two layer structure, the theory predicts a factor of 5 stronger effect than in yttrium iron garnet-PZT. When the composite is considered to be a homogeneous medium, the corresponding shift $\delta H$ is given by $2M_0$ ${(B}_{33}-B_{31})$ E, where $M_0$ is the composite magnetization and B’s are the ME coefficients. For this model, a method for the calculation of magnetoelectric coefficients from experimental data is presented.

We present the first data and theory for the bias magnetic field dependence of magnetoelectric coupling in the electromechanical resonance (EMR) region for ferromagnetic-piezoelectric heterostructures. Trilayers of Permendur, a $\mathrm{Co}-\mathrm{Fe}-\mathrm{V}$ alloy, and lead zirconate titanate were studied. Measurements of the magnetoelectric (ME) voltage coefficient ${\alpha }_E$ indicate a strong ME coupling in the low-frequency range and a giant ME effect due to EMR at $200–300\mathrm{kHz}$ for radial modes and at $\sim 2.7\mathrm{MHz}$ for thickness modes. Data were obtained for the bias field $H$ dependence of two key parameters, the EMR frequency $f_r$ and the ME coefficient ${\alpha }_{E,R}$ at resonance. With increasing $H$, an increase in $f_r$ and a rapid rise and fall in ${\alpha }_{E,R}$ are measured. In our model we consider two mechanisms for the magnetic field influence on ME interactions: (i) a shift in the EMR frequency due to changes in compliance coefficients ($\Delta E$ effect) and (ii) variation in the piezomagnetic coefficient that manifests as a change in ${\alpha }_{E,R}$. Theoretical profiles of ${\alpha }_E$ vs frequency and estimates of frequency shift based on the $\Delta E$ effect are in excellent agreement with the data.

The nature of strain mediated magnetoelectric (ME) coupling is investigated in laminates of lead zirconate titanate (PZT) and compositionally stepped ferrite with grading of piezomagnetic coefficient. ME effects that could only be attributed to grading related bending strain are observed in a trilayer of ferrite and oppositely poled PZT. It is shown that in a bilayer, grading induced flexural strain counteracts bending moment due to structural asymmetry and enhances ME coupling by a factor of 2. A zero-bias field ME effect is observed in such laminates. The graded composites are of interest for self-biased magnetic field sensors.