Multiferroic magnetoelectric materials, which simultaneously exhibit ferroelectricity and ferromagnetism, have recently stimulated a sharply increasing number of research activities for their scientific interest and significant technological promise in the novel multifunctional devices. Natural multiferroic single-phase compounds are rare, and their magnetoelectric responses are either relatively weak or occurs at temperatures too low for practical applications. In contrast, multiferroic composites, which incorporate both ferroelectric and ferri-/ferromagnetic phases, typically yield giant magnetoelectric coupling response above room temperature, which makes them ready for technological applications. This review of mostly recent activities begins with a brief summary of the historical perspective of the multiferroic magnetoelectric composites since its appearance in 1972. In such composites the magnetoelectric effect is generated as a product property of a magnetostrictive and a piezoelectric substance. An electric polarization is induced by a weak ac magnetic field oscillating in the presence of a dc bias field, and/or a magnetization polarization appears upon applying an electric field. So far, three kinds of bulk magnetoelectric composites have been investigated in experimental and theoretical, i.e., composites of (a) ferrite and piezoelectric ceramics (e.g., lead zirconate titanate), (b) magnetic metals/alloys (e.g., Terfenol-D and Metglas) and piezoelectric ceramics, and (c) Terfenol-D and piezoelectric ceramics and polymer. The elastic coupling interaction between the magnetostrictive phase and piezoelectric phase leads to giant magnetoelectric response of these magnetoelectric composites. For example, a Metglas/lead zirconate titanate fiber laminate has been found to exhibit the highest magnetoelectric coefficient, and in the vicinity of resonance, its magnetoelectric voltage coefficient as high as ${10}^2\mathrm{V}∕\mathrm{cm}\mathrm{Oe}$ orders has been achieved, which exceeds the magnetoelectric response of single-phase compounds by many orders of magnitude. Of interest, motivated by on-chip integration in microelectronic devices, nanostructured composites of ferroelectric and magnetic oxides have recently been deposited in a film-on substrate geometry. The coupling interaction between nanosized ferroelectric and magnetic oxides is also responsible for the magnetoelectric effect in the nanostructures as was the case in those bulk composites. The availability of high-quality nanostructured composites makes it easier to tailor their properties through epitaxial strain, atomic-level engineering of chemistry, and interfacial coupling. In this review, we discuss these bulk and nanostructured magnetoelectric composites both in experimental and theoretical. From application viewpoint, microwave devices, sensors, transducers, and heterogeneous read/write devices are among the suggested technical implementations of the magnetoelectric composites. The review concludes with an outlook on the exciting future possibilities and scientific challenges in the field of multiferroic magnetoelectric composites.

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 ${\alpha }_E^{\prime }=\delta E/\delta H,$ where $\delta E$ is the induced electric field for an applied ac magnetic field $\delta H,$ 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 $\left({\alpha }_{E,L}^{\prime }\right)$ in which the poling field E, bias field H, and ac fields $\delta E$ and $\delta H$ are all parallel to each other and perpendicular to the sample plane, (ii) transverse fields $\left({\alpha }_{E,T}^{\prime }\right)$ for in-plane H and $\delta H$ parallel to each other and perpendicular to out-of-plane E and $\delta E,$ and (iii) in-plane longitudinal fields $\left({\alpha }_{E,IL}^{\prime }\right)$ 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 ${\alpha }_E^{\prime }$ are carried out as a function of the interface coupling k and volume fraction ν for the piezoelectric phase. In unclamped samples, ${\alpha }_E^{\prime }$ 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 $\nu =0.1\mathrm{}$ 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 in-plane longitudinal fields and the weakest coupling for the (out-of-plane) longitudinal case. (ii) In ferrite-based composites, ${\alpha }_{E,T}^{\prime }$ and ${\alpha }_{E,IL}^{\prime }$ are a factor of 2–10 higher than ${\alpha }_{E,L}.$ (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 the volume and static magnetic field dependence of ${\alpha }_E^{\prime }.$ 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. This work is concerned with the theory and companion data for magnetoelectric (ME) coupling at electromechanical resonance (EMR) in the layered samples. Estimated ME voltage coefficient versus frequency profiles for nickel, cobalt, or lithium ferrite and lead zirconate titanate (PZT) predict a giant ME effect at EMR with the highest coupling expected for cobalt ferrite-PZT. There is excellent agreement between the theory and data for layered nickel ferrite-PZT; the ME voltage coefficient at resonance increases by a factor of 40 compared to low frequency values. Similar measurements on layered ferromagnetic alloy-PZT and bulk ferrite-PZT reveal even a stronger EMR assisted enhancement in ME coupling.

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.

In strong magnetic fields up to 20 T quasistatic measurements of the magnetic-field-induced electric polarization have been performed in ${\mathrm{LiNiPO}}_4$ single crystals between 4.2 and $\sim 25$ K. The magnetoelectric (ME) effect has been studied in detail near the Néel temperature. The temperature hysteresis of the polarization induced by a magnetic field was found. An anomalous temperature dependence of the magnetoelectric susceptibility during the phase transition and the ME “butterfly loop” were observed. The phenomenological theory of the magnetoelectric effect in ${\mathrm{LiCoPO}}_4$ and ${\mathrm{LiNiPO}}_4$ has been developed. A tentative explanation of the existence of the magnetoelectric “butterfly loop” is given. It is shown that there is a non-Lifshitz invariant in the free energy expansion which is linear in the spatial derivatives. Hence the phase transition to a space-modulated spin structure is possible. The influence of such a structure on the linear magnetoelectric effect is examined.