The current surge of interest in multiferroic materials demands specialized measurement techniques to support multiferroics research. In this review article we detail well-established measurement techniques of the magneto-electric coupling coefficient in multiferroic materials, together with newly proposed ones. This work is intended to serve as a reference document for anyone willing to develop experimental measurement techniques of multiferroic materials.

Recently, highly sensitive magnetic field sensors using the magnetoelectric effect in composite ferromagnetic-piezoelectric layered structures have been demonstrated. However, most of the proposed concepts are not useful for measuring dc magnetic fields, because the conductivity of piezoelectric layers results in a strong decline of the sensor’s sensitivity at low frequencies. In this paper, a novel functional principle of magnetoelectric sensors for dc magnetic field measurements is described. The sensor employs the nonlinear effect of voltage harmonic generation in a composite magnetoelectric structure under the simultaneous influence of a strong imposed ac magnetic field and a weak dc magnetic field to be measured. This physical effect arises due to the nonlinear dependence of the magnetostriction in the ferromagnetic layer on the magnetic field. A sensor prototype comprising of a piezoelectric fibre transducer sandwiched between two layers of the amorphous ferromagnetic Metglas ^® alloy was fabricated. The specifications regarding the magnetic field range, frequency characteristics, and noise level were studied experimentally. The prototype showed the responsivity of 2.5 V mT ⁻¹ and permitted the measurement of dc magnetic fields in the range of ~10 nT to about 0.4 mT. Although sensor operation is based on the nonlinear effect, the sensor response can be made linear with respect to the measured magnetic field in a broad dynamic range extending over 5 orders of magnitude. The underlying physics is explained through a simplified theory for the proposed sensor. The functionality, differences and advantages of the magnetoelectric sensor compare well with fluxgate magnetometers. The ways to enhance the sensor performance are considered.

Magnetoelectric (ME) effects in a ferromagnetic and piezoelectric composite are the changes in the polarization caused by a magnetic field or the changes in the magnetization caused by an electric field. These effects are aided by the mechanical deformation in the ferroic phases caused by the combination of magnetostriction and piezoelectricity. Interest in ME effects is due to a variety of physical phenomena they exhibit, as well as their potential applications in the creation of highly sensitive magnetic field sensors and other electronic devices. Linear ME effects in structures with layers of different ferroic materials have been studied extensively. However, nonlinear ME effects, which are caused by the nonlinearity of the magnetic, dielectric, and acoustic properties of ferromagnets and piezoelectrics, are less well understood. The purpose of this review is to summarize the current state of knowledge on nonlinear ME (NLME) effects in composite heterostructures and to discuss their potential applications. The review begins by discussing the characteristics of materials that are conductive to the occurrence of NLME effects and ferromagnetic-piezoelectric materials that are most commonly used to study such effects. The review then provides details on theoretical approaches to the description of NLME effects in heterostructures and experimental methods for studying these effects. Finally, the review presents a chronological overview of the experimentally observed NLME effects in composite structures excited by low-frequency and pulsed magnetic or electric fields. The review concludes with a discussion on the potential applications of NLME effects for highly sensitive magnetic field sensors.

Bistable characteristics of a nonlinear multiferroic composite resonator containing ferromagnetic and piezoelectric layers are investigated. The resonator was a borosilicate glass substrate of 25 mm × 2 mm dimensions and 150 μm thickness with a 2 μm thick amorphous ferromagnetic FeCoSiB layer and a 2 μm thick piezoelectric AlN layer deposited on its sides by magnetron sputtering. The resonator was excited by ac voltage at a frequency of 156 kHz, matching its longitudinal acoustic resonance frequency. The bistability loops were observed with increasing and decreasing frequency at constant excitation voltage and with increasing and decreasing voltage at constant frequency. With increasing excitation voltage, the resonator frequency first decreases by ∼0.7 kHz and then increases again to the initial value. A bistability model is suggested that uses Lorentzian shape resonance line and measured dependences of the resonance frequency and transmission coefficient on the output signal, which quantitatively describes experimental data. It is shown that bistability in a multiferroic resonator arises due to the nonlinearity of the ferromagnetic layer.

The strain mediated nonlinear converse magnetoelectric effect (CME) is investigated in a bilayer of an amorphous ferromagnet FeBSiC and piezoelectric lead zirconate titanate (PZT). The magnetic response of the sample to an AC electric field (e) applied to PZT at an acoustic resonance frequency of 76 kHz was measured with a coil wound around the bilayer. With an increase in the amplitude of e over the range 0–250 V/cm, the variation in amplitude of the first and the second harmonics of the induced voltage due to the variation in the magnetic induction B was measured for DC bias magnetic field H = 0–80 Oe. The coefficients of the linear and nonlinear converse ME effects were 5.5 G cm/V and 1.9 × 10⁻² G cm²/V², respectively. The nonlinearity of the CME arises due to the nonlinear dependence of the magnetic induction on the stress. A theoretical model for the nonlinear CME is discussed.

The forward and inverse magnetoelectric (ME) effects are experimentally studied in a two-layer planar structure containing mechanically coupled Galfenol and PZT plates. The process of production of polycrystalline Galfenol plates and their magnetic and magnetostriction characteristics are described. For the forward ME conversion, the dependences of the amplitude of the voltage generated by the structure on the magnitude and orientation of a dc magnetic field and the frequency and amplitude of a modulating magnetic field are measured. For the inverse ME conversion, the dependences of the amplitude of the change in the magnetic induction of the structure on the dc magnetic field and the frequency of an ac electric field applied to the structure are measured. The efficiencies of the forward and inverse ME conversion are estimated for the case of low-frequency field modulation and under conditions of the resonance excitation of bending and longitudinal mechanical vibrations in the structure.