Magnetoelectric effect in bilayer magnetostrictive-piezoelectric structure. Theory and experiment

Bilayer magnetostrictive-piezoelectric structures have certain advantages compared to bulk composites and this allows us to consider them as perspective materials for the development of devices based on the magnetoelectric effect. The theory of magnetoelectric effect in bilayer magnetostrictive-piezoelectric structure is presented taking into account the thickness dependence amplitude of the mechanical oscillations for the structures in form of rectangular plate. The equation for frequency dependence of the ME effect in the region on the electromechanical resonance was obtained, using motion equation, elastodynamics and electrostatic equations for the magnetostrictive, piezoelectric phases and taking into account the boundary conditions on the interface. The cases of longitudinal and transverse orientations of the electric and magnetic fields were considered. It is shown that the thickness dependence of the ME voltage coefficient has the maximum. The dependence between frequency and the thickness ratio of the layers is presented for both the theory and experiment.     

Influence of an interlayer bonding on the magnetoelectric effect in the layered magnetostrictive-piezoelectric structure

The theory of the magnetoelectric effect in magnetostrictive-piezoelectric bilayer structure is presented considering the interlayer bonding material. The expressions for the dispersion relation and the frequency dependence of the magnetoelectric voltage coefficient in the electromechanical resonance region are obtained, using the simultaneous solution of the motion equation and material equations taking into account the interlayer bonding phase. The theoretical and experimental dependence of the magnetoelectric effect on the thickness of the bonding material layer are presented. Results are in good agreement with the theory and experiment.     

Direct and inverse magnetoelectric effect in layered composites in electromechanical resonance range: A review

A model is presented for the increase in magnetoelectric (ME) coupling in magnetostrictive-piezoelectric bilayers in the electromechanical resonance region. The ME voltage coefficients α_E have been estimated for transverse field orientations corresponding to minimum demagnetizing fields and maximum α_E. We solved the equation of medium motion taking into account the magnetostatic and elastostatic equations, constitutive equations, Hooke's law, and boundary conditions. The resonance enhancement of ME voltage coefficient for the bilayer is obtained at antiresonance frequency. To obtain the inverse ME effect, a pick up coil wound around the sample is used to measure the ME voltage due to the change in the magnetic induction in magnetostrictive phase. The measured static magnetic field dependence of ME voltage has been attributed to the variation in the piezomagnetic coefficient for magnetic layer. The frequency dependence of the ME voltage shows a resonance character due to the longitudinal acoustic modes in piezoelectric layer. The model is applied to specific cases of cobalt ferrite–lead zirconate titanate and nickel–lead zirconate titanate bilayers. Theoretical ME voltage coefficients versus frequency profiles are in agreement with data.     

磁电异质结及器件应用

磁电异质结是由铁磁和铁电材料通过连接层耦合而成,其磁电效应来源于铁电相的压电效应和铁磁相的磁致伸缩效应.相对于颗粒混相磁电复合材料,层状磁电异质结材料具有更高的磁电耦合系数和更低的介电损耗,使得其在磁场传感器、能量收集器、天线以及存储器等领域都有着巨大的应用前景.本综述重点总结了磁电异质结材料的发展历程以及相关应用领域的最新进展,最后评述了磁电异质结材料发展的挑战和前景展望.     

Magnetoelectric effect in a magnetostrictive-piezoelectric bilayer structure

The results of theoretical and experimental investigations of the magnetoelectric effect in a magnetostrictive-piezoelectric bilayer structure have been presented. The expression for the magnetoelectric voltage coefficient in the region of electromechanical resonance has been derived based on the joint solution of the equations of motion for the magnetostrictive and piezoelectric media and the constitutive relations. The dependence of the magnitude of the effect on the thickness of the ferrite and piezoelectric layers has been analyzed. The experimental results for nickel-lead zirconate-titanate bilayer structures have been reported. The theoretical results agree perfectly with the experimental data.     

考虑损耗的磁致/压电层合材料谐振磁电响应分析

运用等效电路法，对磁致/压电层合材料谐振状态下的磁电响应进行分析，得到了材料在谐振状态下的磁电电压转换系数理论计算公式. 详细地分析了磁致/压电层合材料在谐振点附近的磁损耗、机械损耗、电损耗，并给出了各种损耗相应的计算方法和大小，发现谐振状态下，材料的主要损耗来源于机械损耗. 分析结论较好地解释了磁电层合材料在不同偏置磁场下磁电响应的实验结果. 关键词： 磁致/压电层合材料 磁电效应 谐振 损耗分析     

Ni/Pb(Zr,Ti)O3/TbFe2层状复合材料的谐振磁电特性研究

采用化学镀和黏接法制备层状磁电复合材料Ni/PZT/TbFe₂,研究其磁电性能及谐振频率随Ni层厚度的变化情况. 结果表明:Ni/PZT/TbFe₂层状磁电复合材料与其他结构的磁电性能不同,其一阶弯曲谐振峰值和纵向谐振峰值都很大. 随着Ni层厚度的增加,Ni/PZT/TbFe₂层状磁电复合材料的一阶纵向谐振峰值逐渐增大. 结合实验数据和理论计算值得出了材料的一阶弯曲谐振频率fr1和一阶纵向谐振频率f 关键词： 磁电效应 正磁致伸缩 负磁致伸缩 谐振频率     

磁致伸缩/压电层叠复合材料磁电效应分析

采用有限元分析软件COMSOL5.0建立了三维悬臂梁模型,分析了磁致伸缩/压电/磁致伸缩叠层复合材料的磁电系数α_(ME),并就几何参数对复合结构磁电系数的影响进行了优化分析.首先,利用稳态求解器研究了磁电层状复合结构内部的应力、应变、位移以及电势分布情况,利用瞬态求解分析了磁电复合结构各变量动态分布规律;其次,应用小信号频域分析研究了该结构的谐振频率以及在不同偏置磁场对输出电压的影响,结果表明,随着直流偏置磁场的增加,输出电压逐渐减小.改变复合材料不同层的厚度,分析了磁电层与压电层厚度比t_m/t_p对磁电系数的影响,结果表明,随着厚度比增加,α_(ME)逐渐增大,其增加速率逐渐减小;最后,分析了磁电系数α_(ME)随复合结构面积、长宽比的变化情况.分析表明,α_(ME)随磁电复合结构面积的增加逐渐增加,其增加速率逐渐减小;当磁电复合结构面积恒定时,其磁电系数随长宽比L/W增加表现出先增加后减小的趋势,存在最优值.     

Frequency response of magnetoelectric effect in piezoelectric-magnetostrictive disk-ring composite structures

A theoretical model is presented for frequency dependence of magnetoelectric (ME) effect in piezoelectric-magnetostrictive disk-ring composite structures. Expressions for ME voltage coefficients in piezoelectric-magnetostrictive (PE-MS) disk-ring and MS-PE disk-ring are obtained by solving elastodynamic equations. The calculated resonance frequency and frequency dependence of ME voltage coefficients are in good agreement with the experimental results. This model indicates better mechanical coupling in disk-ring structure than that in traditional layered structure, and this may be responsible for the enhancing ME effect. The analysis suggests the disk-ring composites structures are promising for magnetoelectric applications.     

磁致伸缩/压电叠层复合材料磁-机-电耦合系数分析

分析和推导了磁致伸缩/压电叠层复合材料的机-电耦合系数、磁-机耦合系数及磁-电耦合系数与磁致伸缩层和压电层性能参数及几何参数之间的关系.进一步分析表明,叠层复合材料低频时的磁电电压系数正比于磁-电耦合系数,谐振时的磁电电压系数正比于磁-电耦合系数与机械品质因素的乘积;磁电电压系数还与复合结构的本征阻抗有关,本征阻抗越大磁电电压系数越大.通过性能差异较大的Terfenol-D和FeNi基弹性合金分别与压电材料PZT5-H和PZT8相互组合构成复合材料的比较分析,进一步阐明了磁电复合材料磁-电耦合系数和机械品 关键词： 磁电效应 磁-机-电耦合系数 磁致伸缩材料 压电材料     

基于能量转换原理的磁电层合材料低频磁电响应分析

提出了一种基于能量转换原理的磁致伸缩/压电层合材料低频磁电响应模型,并对不同层合结构的磁电响应特性进行了对比研究.该模型假定层合材料层间能量传递通过层间剪切力来实现,利用应力函数法分析了磁致伸缩层和压电层的应力与应变,求出了磁致伸缩层的应变能和存储磁场能以及压电层的应变能和电场能;利用Hamilton最小能量原理求出了层间剪切力的大小,获得了开路状态下层合材料的低频磁电响应模型.发现磁电电压系数与磁致伸缩材料的磁导率、泊松比、磁机耦合系数以及压电材料的泊松比、机电耦合系数等有关,并对这些参数的影响进行了分析.同时对两层和三层结构的层合材料磁电特性进行了对比研究,发现层合结构不同则获得的磁电系数公式不同,用相应的公式计算得到的误差才会最小.研究结果表明,本文的理论误差小于6.5%,与其他方法相比,本文的理论模型能更好地描述磁电层合材料的低频磁电响应特性.     

Origin of Negative Imaginary Part of Effective Permittivity of Passive Materials

The anti-resonant phenomenon of effective electromagnetic parameters of metamaterials has aroused controversy due to negative imaginary permittivity or permeability. It is experimentally found that the negative imaginary permittivity can occur for the natural passive materials near the Fabry-Perot resonances. We reveal the nature of negative imaginary permittivity, which is correlated with the magnetoelectric coupling. The anti-resonance of permittivity is a non-inherent feature for passive materials, while it can be inherent for devices or metamaterials.Our finding validates that the negative imaginary part of effective permittivity does not contradict the second law of thermodynamics for metamaterials owing to the magnetoelectric coupling.     

Insights into the regulation mechanism of ring-shaped magnetoelectric energy harvesters via mechanical and magnetic conditions

This paper presents a theoretical model for predicting and tuning magnetoelectric(ME) effect of ring-shaped composites, in which stress boundary conditions are empoyed and the multi-field coupling property of giant magnetostrictive materials are taken into account. A linear analytical solutions for the closed-and open-circuit ME voltages are derived simultaneously using mechanical differential equations, interface and boundary conditions, and electrical equations. For nonlinear ME coupling effect, the nonlinear multi-field coupling constitutive equation is reduced to an equivalent form by expanding the strains as a Taylor series in the vicinity of bias magnetic field. Sequentially, the linear model is generalized to a nonlinear one involving the field-dependent material parameters. The results show that setting a stress-free condition is beneficial for reducing resonance frequency while applying clamped conditions on the inner and outer boundaries may improve the maximum output power density. In addition, performing stress conditions on one of the boundaries may enhance ME coupling significantly, without changing the corresponding resonance frequency and optimal resistance. When external stimuli like bias magnetic field and pre-stress are applied to the ring-shaped composites, a novel dual peak phenomenon in the ME voltage curve around resonance frequencies is revealed theoretically, indicating that strong ME coupling may be achieved within a wider bias field region. Eventually, the mutual coordination of the bias field and pre-stress may enhance ME coupling as well as tuning the resonance frequency, and thus is pivotal for tunable control of ME energy harvesters. The proposed model can be applied to design high-performance energy harvesters by manipulating the mechanical conditions and external stimuli.     

Inverse magnetoelectric effect in disk-shaped samples of ferrite piezoelectric composites

A theory of the inverse magnetoelectric effect in the vicinity of electromechanical resonance in disk-shaped samples is presented. An expression for the coefficient of the inverse magnetoelectric transformation has been obtained using the effective parameter method. It has been shown that a sharp increase in the magnitude of the effect occurs at a frequency of electromechanical resonance, and the resonance frequencies for the direct and inverse magnetoelectric effects are different. The dependences of the resonance frequencies on the ferrite percentage in ferrite-nickel spinel samples and lead zirconate titanate samples have been studied experimentally.     

Large tunable FMR frequency shift by magnetoelectric coupling in oblique-sputtered Fe_(52.5)Co_(22.5)B_(25.0)/PZN-PT multiferroic heterostructure

In this study, we observe a strong inverse magnetoelectric coupling in Fe_(52.5)Co_(22.5)B_(25.0)/PZN-PT multiferroic heterostructure, which produces large electric field(E-field) tunability of microwave magnetic properties. With the increase of the E-field from 0 to 8 kV/cm, the magnetic anisotropy field Heffis dramatically enhanced from 169 to 600 Oe, which further leads to a significant enhancement of ferromagnetic resonance frequency from 4.57 to 8.73 GHz under zero bias magnetic field, and a simultaneous decrease of the damping constant α from 0.021 to 0.0186. These features demonstrate that this multiferroic composite is a promising candidate for fabricating E-field tunable microwave components.     

Polarity of magnetic field related magnetoelectric effects in heterotypic composite system of lead zirconate titanate and Terfenol-D

Using the idea of “stress-field-controlled graded ferroelectrics”, a ring-shaped composite system of Pb(Zr,Ti)O₃/Terfenol-D was fabricated. The magnetoelectric coupling of the composite was investigated. A resonant peak was observed at frequency of 69.6 kHz. The magnetoelectric frequency spectrum was found to relate to the polarity of the applied magnetic field, resulting in positive and negative magnetoelectric effects around the resonant point. Analysis shows that elastic resonance of the composite decides the resonant frequency and the magnetostrictive state of the Terfenol-D was responsible for the magnetoelectric coupling at different frequencies.     

Optimal magnetoelectric coupling performance of Terfenol-D/PZT composites in resonance state under bias magnetic field

Laminated magnetoelectric (ME) composites with various thickness ratios were optimized, fabricated and experimentally investigated in this work. The Terfenal-D/PZT specimens with optimal thickness ratio between the magnetostrictive phase and piezoelectric phase, and two other values were tested for their ME coupling performance. The coupling voltage output increases linearly with the increase of DC bias magnetic field. The ME voltage coefficient increases more than 100 times in the resonance state for the optimal laminate. The DC bias magnetic field affects the ME voltage coefficient significantly, and also has little effect on the resonant frequency. The strength of AC magnetic field also slightly affects the ME voltage coefficient in resonance state, but does not affect the resonant state under which the same DC magnetic field is required. The experimental results can help understand the coupling performance of ME composite under bias magnetic field and prompt the application of ME devices.     

Investigations on ferroelectric PMN-PT and PZN-PT single crystals ability for power or resonant actuators

Ferroelectric single crystals of PZN-PT and PMN-PT exhibit outstanding properties: high charge coefficient (dij), high coupling factor (kij) and high strain levels under DC fields. Besides, their mechanical quality factor is believed to be low. Their usefulness for non-resonant or large bandwidth transducers has therefore been previously investigated. However, few studies have been devoted to the dielectric and mechanical losses of single crystals and to their stability under high levels of excitations (electric fields, temperature and mechanical stress). A knowledge and understanding of such performances is needed to determine whether single crystals are suitable materials for power or resonant transducers. In this work, losses and non-linearity versus external excitations are investigated. Dielectric losses and mechanical losses are measured versus electric field for different compositions, orientations. The evolution of d33 and epsilonT33 are obtained versus electric field and temperature for the longitudinal mode. Strain and hysteresis versus sweep mode (up and down) are measured near the resonance frequency using a laser Doppler vibrometer.     

磁电薄膜与微波作用研究

建立了双层磁电复合薄膜模型,当磁电材料尺寸可以与微波波长相比拟时,微波在传播方向上的偏导不为零,得到了微波与磁电材料作用的非齐次偏微分方程,并在谐振条件下对该方程进行了解析求解.推导出磁电系数和材料等效电学参数的解析表达式,结果表明磁电材料的磁电系数多出相关的耦合项,其大小不但与材料本身参数有关,还与微波在材料中的波速有关;等效导纳多出的耦合项与微波的频率有关.     

Current-voltage characteristics of lead zirconate titanate/nickel bilayered hollow cylindrical magnetoelectric composites

Current--voltage measurements obtained from lead zirconate titanate/nickel bilayered hollow cylindrical magnetoelectric composite showed that a sinusoidal current applied to the copper coil wrapped around the hollow cylinder circumference induces voltage across the lead zirconate titanate layer thickness. The current--voltage coefficient and the maximum induced voltage in lead zirconate titanate at 1~kHz and resonance (60.1~kHz) frequencies increased linearly with the number of the coil turns and the applied current. The resonance frequency corresponds to the electromechanical resonance frequency. The current--voltage coefficient can be significantly improved by optimizing the magnetoelectric structure geometry and/or increasing the number of coil turns. Hollow cylindrical lead zirconate titanate/nickel structures can be potentially used as current sensors.