Magnetoelectric Laminate Research Articles

Optimal configuration of magnetoelectric composites under various mechanical boundary conditions

The magnetoelectric (ME) coupling effect of magneto-electro-elastic composites is generated by the product property of magnetostriction and piezoelectricity via elastic deformation. Since mechanical deformation and interlayer stress interaction directly influence the extrinsic ME effect, composite configurations between magnetostrictive and piezoelectric materials critically influence the energy conversion efficiency of ME composites, as also do the imposed mechanical boundary conditions (BCs). Here, we aim to identify the material configurations in the composites under different BCs, in order to maximize their ME effects. The problem is set up as optimization problems solved by a genetic algorithm while the required multiphysics simulation is performed by finite element analysis. For five major mechanical BCs, we determined optimal ME laminate layer configurations and compared their magneto-electric conversion efficiency with that by typical sandwiched laminate composites. We also investigated how much the efficiency can be increased if arbitrary-arranged material distributions are allowed. The present study is expected to provide useful guidelines for the design of ME composites, and offers the possibility of finding new ME composite structures.

A coupling finite element model for analysis the nonlinear dynamic magnetoelectric response of tri-layer laminate composites

In this study, we investigate the nonlinear magnetoelectric (ME) response of a tri-layer ME laminate structure in a harmonic magnetic field. A coupling three dimensional (3D) finite element model of ME composite is built. Based on the Maxwell equations and a nonlinear magnetization relation proposed by Liu and Zheng, the inhomogeneous magnetic field distribution inside the layered ME composite are investigated by using the finite element method (FEM), moreover, the width of structure on magnetic field distribution and ME response are discussed in detail. Subsequently, the non-uniform distributions of stress, displacement, magnetic flux density and voltage are studied, and edge effect appears. Besides, the dynamic ME coefficient is also calculated and discussed. The results indicate that it’s necessary to consider the real distribution of the magnetic field in the calculating the nonlinear ME response. The geometric size affect the ME coefficient obviously, the ME coefficient considered the width effect is smaller than analytical result and more close to the experimental data. Through analysis the stress state of the structure, the result shows that both the normal stress and shear stress in the interface are large when the laminate structure under resonance, which may lead to the interfacial debonding.

Deformation and Fracture of Electromagnetic Thin Films and Laminates under Multi-field Loading

The deformation and fracture behaviors of magnetoelectric materials under mechanical loading are affected considerably by an external electric or magnetic field. To provide a deep understanding of the intrinsic coupling properties, several macro/micro-nano multi-field instruments have been designed and constructed, including an electro-magneto-mechanical nanoindentation apparatus and a multi-field bulge-test instrument. With these instruments, several new experimental results have been observed, such as multi-field indentation scaling relationship and magnetic field control of 180° ferroelectric domain switching for magnetoelectric laminates. Furthermore, an electro-magneto-mechanical coupling model considering the effects of surface stress and a finite element based real-space phase field model are developed, which provide reference for structure design of magnetoelectric intelligent device at small scale.

Nonlinear resonance converse magnetoelectric effect modulated by voltage for the symmetrical magnetoelectric laminates under magnetic and thermal loadings

Based on the tri-layer symmetrical magnetoelectric laminates, a equivalent circuit for the nonlinear resonance converse magnetoelectric coupling effect is established. Because the nonlinear thermo-magneto-mechanical constitutive equations of magnetostrictive material were introduced, a converse magnetoelectric coefficient model was derived from the equivalent circuit, which can describe the influence of bias electric field, bias magnetic field and ambient temperature on the resonance converse magnetoelectric coupling effect. Especially, the model can well predict the modulation effect of bias electric field/voltage on the magnetism of magnetoelectric composite or the converse magnetoelectric coefficient, which is absolutely vital in applications. Both of the converse magnetoelectric coefficient and the resonance frequency predicted by the model have good agreements with the existing experimental results in qualitatively and quantitatively, and the validity of the model is confirmed. On this basis, according to the model, the nonlinear trends of the resonance converse magnetoelectric effect under different bias voltages, bias magnetic fields and ambient temperatures are predicted. From the results, it can be found that the bias voltage can effectively modulate the curve of the resonance converse magnetoelectric coefficient versus bias magnetic field, and then change the corresponding optimal bias magnetic field of the maximum converse magnetoelectric coefficient; with the increasing volume ratio of piezoelectric layers, the modulation effect of bias voltage becomes more obvious; under different bias magnetic fields, the modulation effect of bias voltage on the converse magnetoelectric effect has nonvolatility in a wide temperature region.

Origin of Large Phase Shift and Magnetoelectric Resonance in Magnetoelectric Laminate Composite

Magnetoelectric composites enjoy large magnetoelectric transfer efficiency at resonance frequency, accompanying a large phase shift. We prepared two magnetoelectric laminate composites to research the origin of large phase shift and magnetoelectric characteristics by electric-field-induced strain and magnetic-field-induced strain. The piezoelectric part plays a dominant role in both the direct and converse magnetoelectric resonances. The electromechanical resonance inspires direct and converse magnetoelectric resonant peaks, and results in the magnetoelectric phase shift of near $\pi $ around the resonance frequency. However, the magnetostrictive part is difficult to inspire the magnetoelectric resonance and phase shift.

Power conversion efficiency and resistance tunability in coil-magnetoelectric gyrators

The power efficiency and resistance tunability of magnetoelectric (ME) gyrators consisting of two-phase magnetostrictive-piezoelectric ME longitudinal-transverse (L-T) mode sandwich laminates and coils, have been studied. The copper wire coil provided an inductance-based coil port (CoilP) and the piezoelectric layer of the ME laminate provided a capacitance-based ME port (MEP). The device behaved as a 2-port 4-wire ME gyrator. The current-to-voltage and voltage-to-current (I-V and V-I, respectively) conversion ratios, resistance-inductance/capacitance tunabilities (TR-L and TR-C, respectively) and direct/converse power efficiencies (PED and PEC, respectively) were measured. Maximum values of 1454 V/A and 0.468 mA/V for the I-V and V-I conversion ratios, 76 μH/Ω and 0.17 pF/Ω for TR-L and TR-C coefficients, and ∼35% for both PED and PEC were found by measuring the performance characteristics. Compared with the electromagnetic and piezoelectric transformers, ME gyrators have good input and output characteristics that change the capacitance and inductance features of the input and output ports. Our findings open a promising direction for developing a generation of converters for power electronics.

Theoretical prediction of resonant and off-resonant magnetoelectric coupling in layered composites with anisotropic piezoelectric properties

In order to explain unique magnetoelectric (ME) coupling behaviors found in a trilayer ME laminate having a piezoelectric crystal particularly with anisotropic planar piezoelectric properties, a theoretical model based on the average field method is developed. New analytical expressions could be derived to predict the transverse ME voltage coefficients at off- and in-resonance frequencies respectively. It is predicted that transverse ME voltage coefficients should be anisotropic under in-plane magnetic fields at both off- and in-resonance frequencies. Furthermore, numerical simulations based on material parameters of a representative 2-2 trilayer, composed of Metglas/[011] Pb(Mg1/3Nb2/3)O3–PbTiO3 crystal/Metglas, prove the emergence of multiple resonance frequencies and characteristic phase difference in the complex ME voltages at each resonant frequency. All these theoretical predictions are in good agreement with the experimental results both at off- and in-resonant frequencies. The theoretical expressions developed here could be broadly applicable to the various types of layered ME laminates with a piezoelectric material with or without anisotropic piezoelectric coefficients.

Equivalent magnetic noise reduction at high frequency range due to polarized direction optimization in Terfenol-D/Pb(Mg1/3Nb2/3)O3-PbTiO3 magnetoelectric laminate sensors

In this paper, we investigate the responsivities and output voltage noise power spectral densities of magnetoelectric (ME) laminate sensors, consisting of length magnetized Terfenol-D alloys and transverse/width poled Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMNT) crystals (i.e. L-T mode and L-W mode respectively), which are directly integrated with custom-build low noise charge amplifier circuits. Both the theoretical analyses and experimental results prove that the L-W mode sensor with the optimized polarized direction of the PMNT plate possesses lower magnetic detection limit at the interested high frequency range of 10kHz≤f≤50kHz. The equivalent magnetic noise (EMN) of the L-W mode sensor is 0.78pT/Hz1/2 at 30kHz, which is about 1.7 times lower than the 1.35pT/Hz1/2 for conventional L-T mode sensor. Furthermore, an effective method of using operational amplifiers with low equivalent input noise voltage and employing ME laminate composites with high voltage coefficient to reduce the EMNs of the ME laminate sensors at high frequency range has been established.

A cost-effective self-biased magnetoelectric effect in SrFe12O19/Metglas/Pb(Zr,Ti)O3 laminates

By introducing the hard magnetic SrFe12O19 ribbon, a self-biased magnetoelectric laminate—SrFe12O19/Metgals/Pb(Zr,Ti)O3 was successfully designed. Without any external magnetic field, the laminates exhibit giant self-biased ME responses of 1 V (cm Oe)−1 at quasi-static condition, and up to 29 V (cm Oe)−1 at high-frequency resonance. The induced ME voltage shows a good linear relationship to the applied ac magnetic field with amplitude as low as 10−8 T at 1 kHz, and the self-biased ME property presents an outstanding stability in a time span of 12 months.

Strong self-biased magnetoelectric charge coupling in a homogenous laminate stack for magnetic sensor

In this study, we report a strong self-biased magnetoelectric (ME) charge coupling in homogenous two-phase magnetostrictive/piezoelectric laminate stack. The proposed ME stack Ni/PZT-stack is made up of hard-processing Nickel foils (Ni) and a tape-casting multilayer Pb(Zr, Ti)O3 (PZT) plate with high capacitance. Resonant ME couplings of Ni/PZT-stack with different thickness ratio (n) of Ni foil are investigated in detail. The experimental results show that the Ni/PZT-stack with n = 0.4 has maximum zero-biased resonant ME charge coefficient (αQ,r) of 47.52 nC/Oe, which is far larger higher than that previously reported for other ME laminates. The proposed self-biased miniature ME structure may be useful for multifunctional devices such as electromagnetic energy harvesting, magnetic-to-electric generators or magnet field sensing based on a charge-detection method.

Multiphysics Modeling of Thin-Layer Magnetoelectric Laminate Composites Using Shell Element

This paper proposes to use the nodal shell element in a finite-element multiphysics formulation to simulate the magnetoelectric (ME) laminate composites constituted of the thin magnetostrictive layers. The multiphysics model considers the nonlinearity of the thin-layer magnetostrictive material as well as the electrical load effects of the ME laminate composites. A trilayer ME Metglas/PZT/Metglas problem is solved in order to prove the efficiency of the proposed method. This paper provides the basis to study the ME devices composed of laminated thin layers.

Self-biased magnetoelectric effect in (Pb, Zr)TiO3/metglas laminates by annealing method

FeBSiC metglas was annealed at an optimized condition (350°C, 5min) to achieve the mixed phases with pristine amorphous phase and crystallization phase. With such annealed metglas, a self-biased magnetoelectric (ME) laminate of metglas/Pb(Zr, Ti)O3/metglas was fabricated. Without any external magnetic field, the composite exhibits the ME coefficient αE31 of 103mV/(cm Oe) at 1kHz and 15.5V/(cm Oe) at electromechanical resonance frequency. The induced ME voltage shows a good linear relation to the applied AC magnetic field with amplitude as low as 10−7T at 1kHz. It is expected that such self-biased ME composites provide a practical application of economical and compact magnetic sensors.

Nonlinear resonant magnetoelectric coupling model for dual-peak phenomenon in magnetoelectric laminates

We investigated the dual-peak phenomenon in the response curve of the magnetoelectric (ME) coupling coefficient versus magnetic field for Terfenol-D/PZT/Terfenol-D tri-layer magnetoelectric laminated composites. Using nonlinear constitutive relations for the magnetostrictive material, an expression for the resonance ME coefficient that considers nonlinear resonance mechanical loss is established with the aid of the equivalent circuit method. The established model effectively predicts the complex behavior related to dual-peak phenomenon in regard to pre-stress, bias magnetic field, frequency of the alternating magnetic field, and nonlinear mechanical loss, and explains the origin of the dual peaks. The response curves obtained are consistent with experimental results. It can be found from the further predictions that in a given resonance frequency band, selecting an appropriate pre-stress can regulate two peaks in dual-peak curve, so that a giant ME coupling effect is obtained on the first peak, or a stronger resonance peak is achieved by adjusting stress to merge two peaks. With our resonance ME dual-peak model, we also demonstrate a giant ME coupling by regulating the dual-peak resonances by pre-stress engineering.

Magnetoelectric Coupling in Metglas/BaTiO<sub>3</sub>/Metglas Lead-Free Magnetoelectric Composites

We report the magnetoelectric (ME) coupling in ME composites composed of NiFe2O4 (NFO) or metglas as magnetostrictive phases and BaTiO3 (BTO) as piezoelectric phase, targeting lead free magetnic field sensors. NFO and BTO phases were synthesized by solid state sintering method and further characterized by using XRD and FESEM techniques. The P-E hysteresis curve shows good ferroelectric behavior with saturation polarization of Ps = 15.87 C/cm2 and coercive electric field of 130 kV/cm. The ME response was characterized as a function of dc magnetic field at a fixed frequency. The transverse ME voltage coefficient, αME31 shows 2 times larger magnitude than that of longitudinal ME voltage coefficient, αME31. The maximum αME31 of 37 mV/cm•Oe (@Hdc = 250 Oe) is observed for NFO/BTO/NFO ME composites with thickness ratio of tm/tp = 1.0. The ME coupling is further enhanced by replacing NFO layers by highly magnetostrictive metglas layers. Metglas/BTO/metglas laminates show large αME31 value of 81 mV/cm•Oe at relatively lower Hdc of 145 Oe. The present laminates can offer promising opportunities of engineering environmental friendly ME laminate for applications in ME devices such as energy harvester and magnetic field sensors.

Theoretical investigation of magnetoelectric surface acoustic wave characteristics of ZnO/Metglas layered composite

The surface acoustic wave properties of piezoelectric/magnetostrictive layered structures consisting of insulating ZnO and metallic Metglas with giant Δ E effect were studied based on a stable scattering matrix method. Only the first Rayleigh mode was found with phase velocity between 2200 m/s and 2650 m/s, and the maximum electro-mechanical coupling coefficient about 1%. It was found that the center frequency of ZnO/Metglas is highly sensitive on the change of magnetic field, up to 440 MHz/Oe. However, there is a cutoff Young’s modulus of Metglas for different designs of SAW, below which the Rayleigh mode will disappear. For a magnetoelectric SAW design with the center frequency of 335 MHz and covering a full magnetic field range from -1.4 to +1.4 Oe, the frequency sensitivity is 212 MHz/Oe, equivalent to a magnetic field sensitivity of 5 × 10−12 Tesla. Unlike conventional magnetoelectric bulk laminates or film stacks, the detection of frequency shift instead of electrical charge allows not only shrinkage of device volume but also a broad frequency band detection of weak magnetic field.

Equivalent circuit model of converse magnetoelectric effect for the tri-layer magnetoelectric laminates with thermal and stress loadings

For the converse magnetoelectric coupling effect of the piezoelectric/magnetostrictive/piezoelectric tri-layer symmetric magnetoelectric laminates, based on the nonlinear thermo-magneto-mechanical constitutive equations of the giant magnetostrictive materials and the thermo-electro-mechanical constitutive equations of the piezoelectric materials, according to Newton’s second law and the magnetic circuit theorem, an equivalent circuit is established. Then an expression of the converse magnetoelectric coefficient describing nonlinear thermo-magneto-electro-mechanical coupling is established. The curve of the nonlinear converse magnetoelectric coefficient versus the bias magnetic field, is predicted effectively by the expression, and the predictions are in good agreement with the experimental result both qualitatively and quantitatively. Furthermore, the model can predict the complex influences of the bias magnetic field, the stress and the ambient temperature on the converse magnetoelectric coefficient. It can be found from these predictions that the converse magnetoelectric coefficient decreases with the increasing temperature and increases with the increasing tensile stress. Under the common effect of the ambient temperature and the stress, it is also found that the converse magnetoelectric coefficient changes sharply with the ambient temperature when the tensile stress is applied on the laminates, but it has a good stability of temperature when a large compressive stress is applied. Therefore, this work contributes to the researches on the giant converse magnetoelectric coefficient and the designs of magnetoelectric devices based on the converse magnetoelectric coupling.

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.

Broadband high-sensitivity current-sensing device utilizing nonlinear magnetoelectric medium and nanocrystalline flux concentrator.

A broadband current-sensing device with frequency-conversion mechanism consisting of Terfenol-D/Pb(Zr.Ti)O3 (PZT)/Terfenol-D magnetoelectric laminate and Fe73.5Cu1Nb3Si13.5B9 nanocrystalline flux concentrator is fabricated and characterized. For the purpose of acquiring resonance-enhanced sensitivity within broad bandwidth, a frequency-modulation mechanism is introduced into the presented device through the nonlinearity of field-dependence giant magnetostrictive materials. The presented configuration provides a solution to monitor the weak currents and achieves resonance-enhanced sensitivity of 178.4 mV/A at power-line frequency, which exhibits ∼3.86 times higher than that of direct output at power-line frequency of 50 Hz. Experimental results demonstrate that a weak step-change input current of 1 mA can be clearly distinguished by the output amplitude or phase. This miniature current-sensing device provides a promising application in power-line weak current measurement.

Lumped-equivalent circuit model for multi-stage cascaded magnetoelectric dual-tunable bandpass filter**Project supported by the National Natural Science Foundation of China (Grant Nos. 11172285 and 11472259) and the Natural Science Foundation of Zhejiang Province, China (Grant No. LR13A020002).

A lumped-equivalent circuit model of a novel magnetoelectric tunable bandpass filter, which is realized in the form of multi-stage cascading between a plurality of magnetoelectric laminates, is established in this paper for convenient analysis. The multi-stage cascaded filter is degraded to the coupling microstrip filter with only one magnetoelectric laminate and then compared with the existing experiment results. The comparison reveals that the insertion loss curves predicted by the degraded circuit model are in good agreement with the experiment results and the predicted results of the electromagnetic field simulation, thus the validity of the model is verified. The model is then degraded to the two-stage cascaded magnetoelectric filter with two magnetoelectric laminates. It is revealed that if the applied external bias magnetic or electric fields on the two magnetoelectric laminates are identical, then the passband of the filter will drift under the changed external field; that is to say, the filter has the characteristics of external magnetic field tunability and electric field tunability. If the applied external bias magnetic or electric fields on two magnetoelectric laminates are different, then the passband will disappear so that the switching characteristic is achieved. When the same magnetic fields are applied to the laminates, the passband bandwidth of the two-stage cascaded magnetoelectric filter with two magnetoelectric laminates becomes nearly doubled in comparison with the passband filter which contains only one magnetoelectric laminate. The bandpass effect is also improved obviously. This research will provide a theoretical basis for the design, preparation, and application of a new high performance magnetoelectric tunable microwave device.

A passive current sensor employing self-biased magnetoelectric transducer and high-permeability nanocrystalline flux concentrator

A passive current sensor, consisting of SmFe2/PZT/SmFe2 self-biased magnetoelectric (ME) composite and Fe73.5Cu1Nb3Si13.5B9 nanocrystalline flux concentrator for weak current detection at power-line frequency, was fabricated and characterized. Giant magnetostrictive material of SmFe2 plate with large anisotropic constant provides a huge internal anisotropic field to bias the ME transducer in closed magnetic loop. Consequently, the additional magnetomotive force induced by the internal field and the corresponding increased effective permeability contribute to the improvement of the sensitivity. Experimental results demonstrate that the presented sensor has a higher sensitivity of 152 mV·A−1 at 50 Hz with a slight nonlinearity of ~0.01 % full scale (FS) and matches well with the predicted value. This presented current-sensing device exhibits approximately 2.3 times higher sensitivity than that of conventional ME composite with [Pb(Zr0.48,Ti0.52)O3] (PZT) and Terfenol-D plates serving as a key sensitive component. In addition, time stabilities of the presented sensor were evaluated for a long period of 72 h and analyzed through mathematical statistics method, and favorable stabilities with an uncertainty of 0.5 μV are obtained in continuous 1 h testing. These results provide a significant advancement toward promising application of the tri-layer self-biased ME laminate for power-line electric cords monitoring.