Low-frequency Magnetoelectric Research Articles

Low-Frequency Resonant Magnetoelectric Effects in Layered Heterostructures Antiferromagnet-Piezoelectric

Magnetic field sensors using magnetoelectric (ME) effects in planar ferromagnetic-piezoelectric heterostructures convert a magnetic field into an output voltage. The parameters of ME sensors are determined by characteristics of the magnetic constituent. In this work, the low-frequency ME effects in heterostructures comprising a layer of antiferromagnetic hematite α-Fe2O3 crystal with easy-plane anisotropy and a piezoelectric layer are studied. The effects arise due to a combination of magnetostriction and piezoelectricity because of mechanical coupling of the layers. The field dependences of magnetization and magnetostriction of the hematite crystal are measured. The resonant ME effects in the hematite-piezopolymer and hematite-piezoceramic structures are studied. The strong coupling between magnetic and acoustic subsystems of hematite results in a tuning of the acoustic resonance frequency by the magnetic field. For the hematite layer, the frequency tuning was found to be ~37% with an increase in the bias field up to 600 Oe. For the hematite-PVDF heterostructure, the frequency tuning reached ~24% and the ME coefficient was 58 mV/(Oe∙cm). For the hematite-piezoceramic heterostructure, the frequency tuning was ~4.4% and the ME coefficient 4.8 V/(Oe∙cm). Efficient generation of the second voltage harmonic in the hematite-piezoceramic heterostructure was observed.

A self-biased, low-frequency, miniaturized magnetoelectric antenna for implantable medical device applications

Low-frequency (LF) magnetoelectric (ME) antennas are of great importance in implantable medical device (IMD) applications compared to their electromagnetic (EM) counterparts as they can potentially offer appropriate size miniaturization and lower path loss and higher efficiency. In this work, a self-biased, miniaturized LF ME antenna is proposed, which operates at its electromechanical resonant frequency of 49.9 kHz, with the size scaled down to only 1.75 mm3, which is significantly smaller than that of a comparable EM antenna. The proposed antenna that constitutes of a piezoelectric layer sandwiched between two magnetostrictive layers is characterized in both air and an optimized three-layered human tissue-mimicking phantom media to demonstrate the potential applications in deep-body communications. The near field radiation pattern of the ME antenna is measured experimentally. The maximum received power obtained at a distance of 1.2 m in air and phantom media is 20 and 8 nW, respectively. The proposed antenna has significantly lower path loss of 0.57 dB/m as compared to its higher frequency counterparts. Due to the lower path loss and smaller size, the proposed ME antenna can be suitable in several miniaturized IMD applications.

A miniaturized low frequency (LF) magnetoelectric receiving antenna with an integrated DC magnetic bias

Due to the applications in meteorological broadcasts, radio navigation, and underwater communications, low-frequency (LF) receiving antennas have been actively studied. However, because the frequency range of LF antenna is 30 to 300 kHz, its electromagnetic wavelength is 1 to 10 km, which makes LF electromagnetic antennas difficult to be implemented in miniaturized or portable devices. This article presents a miniaturized LF magnetoelectric (ME) receiving antenna with an integrated DC magnetic bias. The antenna is based on the magnetoelectric effect and operates by resonance at its mechanical resonant frequency. Thus, compared with traditional LF wire antennas, the dimension of ME antenna is reduced significantly. Compared with prior art of ME antennas which do not have DC magnetic bias, higher performance can be achieved by integrating the miniaturized DC magnetic bias. Magnetostrictive TbDyFe2 (Terfenol-D) and piezoelectric lead zirconate titanate thin films are bonded together to form the 38 × 12 × 5.8 mm3 ME receiving antenna. Four 10 × 10 × 10 mm3 Rb magnets are implemented to provide an optimal DC bias for the antenna. A maximum operation distance of 2.5 m is demonstrated with the DC magnetic field bias, 2.27 times of the maximum operation distance of the antenna without DC magnet field bias. The efficiency, gain, and quality factor of the ME receiving antenna are also characterized. The miniaturized LF ME antenna could have potential applications in portable electronics, Internet of things, and underwater communications.

Magnetoelectric laminate composites: an overview of methods for improving the DC and low-frequency response

Magnetoelectric (ME) composite materials have a stronger ME coupling effect in resonant states than in non-resonant states. Typically, these resonant states appear at frequencies of several tens of kHz or even MHz. However, for DC and low-frequency applications of ME composites, obtaining a high ME response is critical. In recent years, many studies have attempted to improve the DC and low-frequency ME performance of ME composite materials at frequencies below 1 kHz. This article reviews the research and major progress in this field and investigates the application of other methods.

Multiferroic Core-Shell Nanofibers, Assembly in a Magnetic Field, and Studies on Magneto-Electric Interactions.

Ferromagnetic–ferroelectric nanocomposites are of interest for realizing strong strain-mediated coupling between electric and magnetic subsystems due to a high surface area-to-volume ratio. This report is on the synthesis of nickel ferrite (NFO)–barium titanate (BTO) core–shell nanofibers, magnetic field assisted assembly into superstructures, and studies on magneto-electric (ME) interactions. Electrospinning techniques were used to prepare coaxial fibers of 0.5–1.5 micron in diameter. The core–shell structure of annealed fibers was confirmed by electron microscopy and scanning probe microscopy. The fibers were assembled into discs and films in a uniform magnetic field or in a field gradient. Studies on ME coupling in the assembled films and discs were done by magnetic field (H)-induced polarization, magneto–dielectric effects at low frequencies and at 16–24 GHz, and low-frequency ME voltage coefficients (MEVC). We measured ~2–7% change in remnant polarization and in the permittivity for H = 7 kOe, and a MEVC of 0.4 mV/cm Oe at 30 Hz. A model has been developed for low-frequency ME effects in an assembly of fibers and takes into account dipole–dipole interactions between the fibers and fiber discontinuity. Theoretical estimates for the low-frequency MEVC have been compared with the data. These results indicate strong ME coupling in superstructures of the core–shell fibers.

Predicting Magnetoelectric Coupling in Layered and Graded Composites.

Magnetoelectric (ME) interaction in magnetostrictive-piezoelectric multiferroic structures consists in inducing the electric field across the structure in an applied magnetic field and is a product property of magnetostriction and piezoelectricity in components. ME voltage coefficient that is the ratio of induced electric field to applied magnetic field is the key parameter of ME coupling strength. It has been known that the ME coupling strength is dictated by the product of the piezoelectric and piezomagnetic coefficients of initial phases. As a result, using the laminates with graded piezoelectric and piezomagnetic parameters are a new pathway to the increase in the ME coupling strength. Recently developed models predict stronger ME interactions in composites based on graded components compared to homogeneous ones. We discuss predicting the ME coupling strength for layered structures of homogeneous and compositionally graded magnetostrictive and piezoelectric components based on the graphs of ME voltage coefficients against composite parameters. For obtaining the graphs, we developed equations for ME output in applied magnetic field for possible modes of operation and layered structure configurations. In particular, our studies have been performed on low-frequency ME coupling, enhanced ME effect in electromechanical resonance (EMR) region for longitudinal and bending modes. Additionally, ME coupling at magnetic resonance in magnetostrictive component and at overlapping the EMR and magnetic resonance is investigated. We considered symmetric trilayers and asymmetric bilayers of magnetostrictive and piezoelectric components and multilayered structures based on compositionally stepped initial components.

Self-assembly of multiferroic core-shell particulate nanocomposites through DNA-DNA hybridization and magnetic field directed assembly of superstructures

Multiferroic composites of ferromagnetic and ferroelectric phases are of importance for studies on mechanical strain mediated coupling between the magnetic and electric subsystems. This work is on DNA-assisted self-assembly of superstructures of such composites with nanometer periodicity. The synthesis involved oligomeric DNA-functionalized ferroelectric and ferromagnetic nanoparticles, 600 nm BaTiO3 (BTO) and 200 nm NiFe2O4 (NFO), respectively. Mixing BTO and NFO particles, possessing complementary DNA sequences, resulted in the formation of ordered core-shell heteronanocomposites held together by DNA hybridization. The composites were imaged by scanning electron microscopy and scanning microwave microscopy. The presence of heteroassemblies along with core-shell architecture is clearly observed. The reversible nature of the DNA hybridization allows for restructuring the composites into mm-long linear chains and 2D-arrays in the presence of a static magnetic field and ring-like structures in a rotating-magnetic field. Strong magneto-electric (ME) coupling in as-assembled composites is evident from static magnetic field H induced polarization and low-frequency magnetoelectric voltage coefficient measurements. Upon annealing the nanocomposites at high temperatures, evidence for the formation of bulk composites with excellent cross-coupling between the electric and magnetic subsystems is obtained by H-induced polarization and low-frequency ME voltage coefficient. The ME coupling strength in the self-assembled composites is measured to be much stronger than in bulk composites with randomly distributed NFO and BTO prepared by direct mixing and sintering.

Magnetoelectric coupling in lead-free piezoelectric Lix(K0.5Na0.5)1 − xNb1 − yTayO3 and magnetostrictive CoFe2O4 laminated composites

To replace lead zirconium titanate in magnetoelectric (ME) composites owing to concerns regarding its toxicity, we investigate the ME coupling in bilayer composites comprising lead-free Lix(K0.5Na0.5)1−xNb1−yTayO3 (LKNNT) (piezoelectric) and CoFe2O4 (magnetostrictive) phases. We prepare the LKNNT ceramics and measure its piezoelectric coefficient d31, a crucial ingredient determining ME couplings, for several Li (x=0.03,0.035,0.04) and Ta (y=0.15,0.2,0.25) concentrations, and find that the highest d31 occurs at y=0.2 for all the values of x studied here. We then evaluate both the transverse (αE,31) and the longitudinal (αE,33) low-frequency ME coupling coefficients of our composites, for each the above composition of (x,y). At x=0.03, we find the usual scenario of αE,31 and αE,33, i.e., the strongest ME coupling occurs when d31 is maximal, namely at y=0.2. On the other hand, interestingly, we also obtain the strongest ME coupling when the LKNNT layer has a relatively weaker d31, e.g., at y=0.25 for x=0.035 and y=0.15 for x=0.04, following from the interplay of d31 and other ingredients (e.g., dielectric constant). Our calculated ME couplings, with αE,31 in magnitude around twice of αE,33, are comparable to those in lead-based composites. The effect of the volume fraction and interface parameter on the ME coupling is also discussed.

Optimization design for magnetoelectric coupling property of the magnet/bimorph composite

Magnetoelectric (ME) composite as one kind of ME material that can yield a strong coupling effect between magnetic and electric fields at room temperature, has drawn widespread attention for decades due to its rich physics contents and significant technological prospect. Except for traditional magnetostrictive/piezoelectric based ME composites, other ME composites have been reported, among which the magnet/piezo-cantilever composites show super strong ME coupling effect. The magnet/piezo-cantilever composite is generally composed of a piezoelectric cantilever and magnets attached at the free end of the cantilever, which realizes ME coupling by force moment-mediated magnetic torque effect and piezoelectric effect. Recently, various configurations of the magnet/piezo-cantilever composites for obtaining higher ME coupling coefficients have been proposed and demonstrated experimentally. However, few theoretical researches of these magnet/piezo-cantilever composites of different configurations have been carried out, which is of great importance for optimizing the design of ME coupling property of the magnet/piezo-cantilever composites. Here in this paper, a theoretical expression for the low-frequency ME coupling coefficient in the magnet/piezo-cantilever composite is deduced based on piezoelectric constitutive equations by using the theory of elastic mechanics. The typical magnet/bimorph composite is chosen as the theoretical model. Based on the deduced theoretical expression, the dependences of the lowfrequency ME coupling coefficients in the magnet/bimorph composite on material and structural parameters are numerically calculated. The results show that there are optimal thickness values of the piezoelectric layers in the magnet/bimorph composite with different metal thickness values and material constituents for achieving maximal lowfrequency ME coupling coefficients. The thicker the metal layer in the magnet/bimorph composite, the less insensitive the low-frequency ME coupling coefficient to the thickness of the piezoelectric layer will be. And the low-frequency ME coupling coefficient of the magnet/bimorph composite decreases when a metal with higher elastic module is selected for bimorph. For the magnet/bimorph composite consisting of hard piezoelectric ceramics (PZT-4), the low-frequency ME coupling coefficient is higher than that of the composite consisting of the soft counterpart ones (PZT-5 H), which is due to the hard piezoelectric ceramics with higher piezoelectric voltage coefficient than the soft counterpart ones. What is more interesting is that when the piezoelectric material in the magnet/bimorph composite is changed into relaxor ferroelectric single crystals Pb(Zn1/3 Nb2/3)O3-PbTiO3 (PZN-PT), an extremely high low-frequency ME coupling coefficient can be obtained, which is 3.8 and 5 times those of the 13 composites with hard and soft piezoelectric ceramics, respectively. This research gives a theoretical guidance for optimal design and practical applications of the magnet/Bimorph composite.

Magnetoelectric Coupling Characteristics of Multiphase Laminate Heterostructures Based on FeCuNbSiB Nanocrystalline Soft Magnetic Alloy

Over the last decade, multiferroic laminate heterostructures, consisting of the piezoelectric layer (such as PZT) and the magnetostrictive layer (such as Terfenol-D), have attracted considerable attention due to their high Curie or Neel temperature and large magnetoelectric (ME) effect at room temperature. The ME laminate materials have demonstrated potential in many applications such as transducers, actuators, magnetic field sensors, energy harvesters, and other devices [1]. ME effect in the multiferroic laminated heterostructures is essentially attributed to the elastic coupling between the piezoelectric and magnetostrictive layers [2]. The effective piezomagnetic coefficient and effective mechanical quality factor play a key role in the performance of the ME materials. However, owing to the small values of the mechanical quality factor and relative permeability, the ME voltage coefficient of the traditional Terfenol-D/PZT (MP) composites is difficult to increase [3, 4]. The nanocrystalline FeCuNbSiB soft magnetic alloy would be a good solution, according to the large interface stress-strain coupling effects. In this paper, a series of FeCuNbSiB/Terfenol-D/PZT (F/M/P) multi-phase laminate heterostructures are presented (Fig. 1), whose ME coupling characteristics have been investigated. Compared to traditional MPM, the ME coupling characteristics of the proposed FMPMF heterostructures were significantly improved. The resonant and low-frequency ME voltage coefficient of the proposed F/M/P heterostructures could be tuned by controlling the layer numbers N. When N is 7 (FMPMPMF), the maximum value of resonant ME voltage coefficient achieves 8.69 V/Oe, which is about 3.65 times higher than that for FMP, 1.81 times higher than that for FMPMF (Fig. 2(a)). Meanwhile, the maximum value of low-frequency ME voltage coefficient for FMPMPMF heterostructures achieves 69.6 mV/Oe at H b =378 Oe (Fig. 2(b)). Remarkably, it indicates that the F/M/P heterostructures have great potential as far as its application in highly sensitive dc magnetic field sensing and vibration energy harvesting.

Zero-Biased Magnetoelectric Effects in Five-Phase Laminate Composites With FeCoV Soft Magnetic Alloy

Magnetoelectric (ME) response has attracted continuously increasing interest in the past decades due to its potential applications in many new multifunctional devices, including magnetic storage, magnetic sensors, current sensors, and energy harvesters.[1] In general, single-phase ME materials are difficult to be utilized in such devices because the ME responses are weak and mostly appear at low temperature. Compared to single-phase ME materials, Magnetoelectric composites consisting of piezoelectric materials (e.g., PZT and PMN-PT) and magnetostrictive materials (e.g., Terfenol-D and Metglas) exhibit strong ME responses at room temperature, and meet the demands of practical application. However, in order to obtain high piezomagnetic coefficient and ME response, most of the reported ME composites require an external bias magnetic field (H bias ) that increases their sizes and costs.[2] To overcome these limitations, more and more researchers have focused on zero-biased ME effects in the composites. Recently, some studies have attempted to achieve high zero-biasd ME response with different methods. For example, Mandal et al. have reported that ME composite of PZT and graded NZFO show an enhancement in the ME coefficient at zero bias. [3]Yang et al. demonstrated a methodology for achieving zero-biased ME response by changing the electrical connections in a sandwiched ME structure of NKNLS-NZF/Ni/NKNLS-NZF. These methods are difficult to realize and require special synthesis process. In fact, utilizing an internal magnetic bias of the magnetostrictive materials in ME composite is a feasible way to solve thisproblem. In this paper, a new zero-biased five-phase laminate composite consists of FeCoV/Terfenol-D/Pb(Zr 1 - x , Ti x )O 3 (PZT)/Terfenol-D/FeCoV (FMPMF) is presented, whose magnetoelectric (ME) coupling characteristics have been investigated. Due to the different magnetic characteristics between FeCoV and Terfenol-D (such as permeability, saturation magnetization and magnetostriction), an internal magnetic field is formed in the compound magnetostrictive layers. It is found that the resonant ME voltage coefficient of five-phase laminate composite is much larger than that of traditional Terfe-nol-D/PZT/Terfenol-D (MPM) laminate composite at zero bias. The experimental results show that the zero-biased resonant ME voltage coefficient strongly depends on the thickness of FeCoV layers as shown in Fig.1. When the thickness of FeCoV layers is 90μm, we obtain the optimum resonant ME voltage cofficient of 1.96 V/Oe at the zero magnetic bias field, which is 1.75 times as great as that of MPM laminate composite. Furthermore, a low-frequency ME voltage coefficient of 50.4 mV/Oe is achieved, which is 2.1 times higher than that of the MPM laminate composite. Meanwhile, the induced zero-bias ME voltage of FMPMF laminate composite shows an excellent linear relationship to ac magnetic field both at the low frequency (1kHz) and the resonant frequency (115.14kHz) as shown in Fig.2. It indicates that the proposed zero-biased five-phase laminate composite shows promising applications for high sensitive dc magnetic field sensors, zero-biased ME transducers and small-size energy harvesters.

Magnetoelectric effect in radially polarized disk–ring composites

A theoretical model is presented for the frequency response of magnetoelectric (ME) effect in the magnetostrictive-piezoelectric (MS-PE) disk–ring composite structures with the PE ring polarized radially. Based on the governing equations of materials and elastodynamic equations of continuum media, the expressions of the ME voltage coefficients for the axial and vertical mode are derived in terms of materials parameters and geometry dimensions. Estimated ME voltage coefficient versus frequency profiles predict a giant ME effect at the electromechanical resonance (EMR) with strong interfacial mechanical coupling. It is shown that increased effective length due to radial polarization instead of thickness polarization of PE-ring is responsible for the improved ME effect in the radially polarized disk–ring structure. The dependences of low-frequency ME effect, resonance frequency and resonance ME effect on geometry dimensions are predicted by our model. Some of the theoretical results are compared with the experimental results, showing good coincidence. It is suggested that proper resonance frequency and better ME effect in the disk–ring structure can be obtained by selecting appropriate materials, optimizing polarization direction and varying its geometry dimensions, which is of interest for the potential application of ME composites in novel multifunctional devices, such as sensors, transducers and memories.

Magnetoelectric coupling characteristics of five-phase laminate composite transducers based on nanocrystalline soft magnetic alloy

A five-phase laminate composite transducer based on nanocrystalline soft magnetic FeCuNbSiB alloy is presented, whose magnetoelectric (ME) coupling characteristics have been investigated. It is found that the resonant ME voltage coefficient of FeCuNbSiB/Terfenol-D/Pb(Zr1-x,Tix)O3 (PZT)/Terfenol-D/FeCuNbSiB (FMPMF) five-phase transducer is much larger than that of traditional Terfenol-D/PZT/Terfenol-D (MPM) transducer, resulting from the enhancement of the effective mechanical quality factor and effective piezomagnetic coefficient of the transducers. Appropriate FeCuNbSiB layer thickness is propitious to the resonant and low-frequency ME coupling characteristics. The maximum resonant ME voltage coefficient achieves 4.81 V/Oe with FeCuNbSiB layer thickness is 60 μm under the DC bias magnetic field Hb = 77 Oe, which is 1.48 times as great as that of traditional MPM transducer. In addition, the maximum ME voltage coefficient at low frequency is 51.2 mV/Oe under the DC bias magnetic field Hb = 442 Oe, which is 1.26 times as great as that of traditional MPM transducer. It indicates that the mentioned five-phase laminate composite transducers have great potential for the application of highly sensitive dc magnetic field sensing and vibration energy harvesting.

A magneto-mechano-electric coupling equivalent circuit of piezoelectric bimorph/magnets composite cantilever

In this study, a magneto-mechano-electric (MME) composite cantilever made of a piezoelectric bimorph and magnets for low-frequency magnetoelectric (ME) coupling was analyzed theoretically and its MME coupling equivalent circuit was developed. Based on equivalent circuit analyses, the dependences of the ME performances, i.e., the ME voltage and charge coefficients, upon the material constants and geometrical parameters of the MME composite cantilever are numerically evaluated. The obtained ME equivalent circuit model provides a theoretical basis to understand and improve the performance of the MME composite cantilever for low-frequency ME coupling.

Multi-parameter magnetoelectric response modeling of magnetostrictive/piezoelectric laminate composites considering shear strain

A low-frequency magnetoelectric (ME) response model of magnetostrictive/piezoelectric laminate composites based on multi-parameter analysis is presented. This model, taken the shear effect as the basis, analyzes the stress and strain of the magnetostrictive and piezoelectric layers by the stress function. The interlayer shear stress and the low-frequency ME response characteristics of ME laminate composites are obtained by using Hamilton principle of minimum energy and in consideration of the influence of stored magnetic field energy of magnetostrictive layer. The theoretical results show that the ME voltage coefficient is related with the magnetic permeability, Poisson ratio, magnetomechanical coupling coefficient, thickness ratio of magnetostrictive material and the Poisson ratio and electromechanical coupling coefficient of piezoelectric material. The influence of these parameters is analyzed. The experimental results show that analytical results are also compared to experimental test data with excellent correlation and their errors are less than 6%.

Low frequency magnetoelectric response analysis of magnetoelectric laminate material based on energy conversion principle

A low frequency magnetoelectric (ME) response model of magnetostrictive/piezoelectric laminate composite is presented based on energy conversion principle, and ME response characteristics of different laminate structures are compared in this paper. In this model it is assumed that the energy transfer between the layers of the composite laminates is achieved by the interlayer shear force. The stresses and strains of the magnetostrictive and piezoelectric layers are analyzed by the stress function method. While the strain and stored magnetic energy of magnetostrictive layers and the strain and electric field energy of piezoelectric layers are solved. Under open-circuit conditions, the interlayer shear force and the low frequency ME response model of laminate composites are obtained by using Hamilton principle of minimum energy. The theoretical results show that the ME voltage coefficient is related to the Poisson ratio, magnetic permeability, magnetomechanical coupling coefficient of magnetostrictive material, Poisson ratio, and electromechanical coupling coefficient of piezoelectric material. The influences of these parameters are analyzed. The magnetoelectric characteristics of two- and three-tier laminated structures are compared in this paper, showing that different laminated structures have different formulas for ME coefficient and calculation errors will be smaller when the corresponding ME coefficient formula is used. The experimental results show that the analytical error is smaller than 6% and the model can better describe the low frequency ME response characteristics of laminated magnetoelectric materials.

Note: High sensitivity self-bias magnetoelectric sensor with two different magnetostrictive materials

The self-bias magnetoelectric (ME) sensor is designed, fabricated, and characterized for detecting weak ac magnetic-field. The two different magnetostrictive materials produce the gradient of magnetization, resulting in an internal magnetic field and a strong ME response. At zero-biased dc magnetic field, a low-frequency ME voltage coefficient (dVME∕dHac) of 22.11 mV∕Oe is achieved, which is 17.69 times higher than that of the previous magnets∕0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 (PMN-PT) sensor. Furthermore, the ME voltage coefficient reaches 2.73 V∕Oe at resonance. The induced ME voltage shows an excellent linear relationship to ac magnetic field when field amplitude varies from ~10(-7) Oe to 1 Oe.

Observation of strong magnetoelectric effects in Ba0.7Sr0.3TiO3/La0.7Sr0.3MnO3 thin film heterostructures

A robust magnetoelectric (ME) response is essential in multiferroic thin films for potential nonvolatile ME memory elements. We report strong ME effects in bilayers and superlattices of Ba0.7Sr0.3TiO3/La0.7Sr0.3MnO3 composite multiferroics. The low-frequency ME coefficient ranges from 35 to 300 mV/cm Oe, depending on thickness, superlattice periodicity, and bias magnetic field and ac magnetic field orientations. Data on ME coupling are fitted well with a modified free-body model to obtain information on magneto-mechanical coupling in the composites. The strong ME coupling in spite of anticipated substrate clamping is a step forward towards the realization of multistate memories and read-write elements.

Hysteresis and remanence in magnetoelectric effects in functionally graded magnetostrictive-piezoelectric layered composites

The observation and theory of a large remanent magnetoelectric (ME) coefficient and coercivity in the static field $H$ dependence of the low-frequency ME effects are reported for bilayers of lead zirconate titanate (PZT) and a functionally graded ferromagnetic layer. The grading involves magnetization with the use of nickel zinc ferrite of composition Ni${}_{0.7}$Zn${}_{0.3}$Fe${}_{2}$O${}_{4}$ (NZFO) and pure Ni. In homogeneous bilayers of PZT-Ni or PZT-NZFO, the ME voltage coefficient (MEVC) vs $H$ data do not show any hysteresis or remanence. Upon grading the ferromagnetic layer, significant changes including hysteresis and remanece are observed. In PZT-Ni-NZFO, MEVC vs $H$ data show a positive remnant MEVC and a negative coercive field. When the grading is reversed, in samples of PZT-NZFO-Ni, the remnant MEVC is negative and the coercive field is positive. A theory is proposed for the low-frequency ME effects in the graded composites. According to the model, the grading in the magnetization leads to a built-in magnetic field in the ferromagnetic layer, and this field depends on the sequence of grading and the thickness of the NZFO and Ni layers. As a result, the total torque moment and flexural deformations in the composite and the bias field dependence of ME voltage coefficient becomes strongly hysteretic. Calculated MEVC vs $H$, remnant MEVC, and coercive field are in good agreement with the data.

Enhancing magnetoelectric effect via the curvature of composite cylinder

We solved analytically the magnetoelectric (ME) effect in a bilayered piezoelectric/piezomagnetic cylinder under harmonic excitation. We revealed that at a fixed thickness ratio of the layers, the static or low-frequency ME effect can be substantially enhanced by increasing the curvature of the cylinder. In the megahertz frequency domain, on the other hand, we observed that the peak ME effect can be considerably increased by decreasing the curvature. We further showed that at a fixed curvature, the ME effect can be tuned to be around the resonant frequency for giant output by varying the boundary condition and thickness ratio.