# Review of Magnetoelectric Effects on Coaxial Fibers of Ferrites and Ferroelectrics
###### Abstract
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temperatures in most of the single phase materials, BiFeO\({}_{3}\) and several hexagonal ferrites are reported to exhibit both magnetic and ferroelectric/anti-ferroelectric orderings at room temperature, but the coupling between the two ferroic orderings is rather weak [9; 10]. This review concerns magneto-electric (ME) coupling in multiferroic composites consisting of ferrimagnetic and ferroelectric phases [3; 4; 5]. The ME effects on such composites arise due to the transfer of mechanical strain produced in one of the two phases in a magnetic or an electric field to the other phase. The piezomagnetic strain in the magnetic phase under an applied magnetic field H leads to variations in the order parameters such as polarization, dielectric permittivity, etc., in the ferroelectric phase and is termed the direct ME (DME) effect [4]. The induced polarization P is related to H by P = \(\alpha\)H, where \(\alpha\) is ME susceptibility, and is a measure of the strength of the ME coupling in the material. In experiments, however, one may measure the magneto-electric voltage coefficient (MEVC) \(\alpha_{\rm E}=\delta E/\delta\)H by applying an AC magnetic field \(\delta\)H and measuring the induced AC electric field \(\delta\)E = \(\delta\)V/t, where \(\delta\)V is the induced voltage and t is the composite thickness. The MEVC is related to \(\alpha\) by \(\alpha_{\rm E}=(1/\varepsilon_{0}\varepsilon_{\rm r})\alpha\), where \(\varepsilon_{0}\) is the permittivity of free space, and \(\varepsilon_{\rm r}\) is the relative permittivity of the material. One may also measure the strength of ME coupling by the converse ME (CME) effect, i.e., piezoelectric strain in an applied E-field resulting in variations in the magnetic order parameter such as the magnetization and anisotropy field. In order to achieve a strong DME in a composite, one prefers a ferromagnetic material with a high piezomagnetic coupling coefficient q = d\(\lambda\)/dH, where \(\lambda\) is the magnetostriction and high initial permeability for the confinement of applied magnetic fields [4]. A ferroelectric with a large d/\(\varepsilon_{\rm r}\), where d is the piezoelectric coupling coefficient, is preferred. For a strong CME, a ferromagnetic phase with a large \(\lambda\) and a small saturation magnetization M\({}_{\rm s}\) and a ferroelectric phase with high d-values are preferred [4]. Numerous composite systems with ferromagnetic phases such as 3D transition metals/alloys, rare earth metals/alloys, spinel and hexagonal ferrites, ferroelectric lead zirconate titanate (PZT), barium titanate (BTO), or lead magnesium niobate-lead titanate (PMN-PT) show strong ME coupling [9; 10; 11]. The mechanical connectivity between the ferroic phases in composites is one of the key factors that determine the strength of ME interactions [12]. Composites with a variety of connectivity including 0-3 (particles of one of the two phases with no connectivity to itself dispersed in a matrix of the second phase with connectivity to itself in all three dimensions), 1-3 (pillars of one phase in a 3D matrix of the second phase), 2-2 (bilayer or multilayers of the two phases with connectivity to itself in 2D), 3-3 (a bulk composite with 3D connectivity for both phases), etc., were studied in the past [3; 4; 5; 6; 7; 11; 13; 14; 15; 16]. The most effective connectivity was realized in 2-2 composites, which can be formed as thick laminates, thin films, or co-fired ceramics. In 2-2 composites, the issue of leakage current was eliminated, which was the cause of poor ME coupling in bulk composites synthesized by mixing and co-firing the two phases [4]. Another key factor that determines the ME coupling strength is the surface-to-volume ratio for the composites since the coupling originates essentially from the strain transfer at the interface of the two phases. One therefore expects a strong ME coupling in nano- and micro-composites compared with bulk structures.