Nonlinear Magnetoelectric Coupling Research Articles

A self-consistent magnetoelectric coupling model for GaN-based /Terfenol-D composites

A magnetoelectric composites is designed and investigated, which combines GaN-based semiconductor and magnetostrictive Terfenol-D. In this work, we study the polarization charge and strain of the multilayer composites under an applied magnetic field and prestress. In order to quantitatively describe the response of composites under different loading environments, a nonlinear magneto-electric self-consistent coupling model is established based on nonlinear constitutive equation, Schrodinger equation, and Poisson equation. The validity of this model is well-proven by comparing experimental data and numerical results under different magnetic fields. The results demonstrate that the giant magnetostriction effect of Terfenol-D offered large tensile strain to decrease the polarization charge and strain in GaN-based semiconductor layer. These conclusions will be of great help to the basic research of piezomagnetic composite materials as well as guidance for the future device design.

D 5 off-centering induced ferroelectric and magnetoelectric correlations in trirutile-Fe2TeO6

We present the rare existence of d5 off-centering induced weak ferroelectric polarization and demonstrate its correlation with observed magnetoelectric (ME) properties in the G type (TN ∼ 210 K) antiferromagnet Fe2TeO6 (FTO) compound. The origin of ferroelectricity (FE) is associated with both lattice and asymmetric electron density (ED) distribution around the ion cores. ME coupling is observed in magnetic field-dependent polarization, ME voltage, and magnetostrain measurements. Short-range magnetic ordering due to intrabilayer dimeric exchange coupling via the double oxygen bridged Fe–O1–Fe pathway is proposed to play a dominating role to exhibit the negative nonlinear magnetic field-dependent ME behavior at 300 K. Interbilayer exchange via Fe–O2–Fe pathways dominantly determines the hysteretic nonlinear magnetic field-dependent ME response below TN. The observed nonlinear ME coupling signifies magnetoelasticity as manifested in the temperature and magnetic field-dependent strain measurement. Hence, the rare existence of FE and magnetoelectric coupling by d5 ion is presented in FTO.

Room temperature magnetoelectric coupling in Pb(Fe1/2Nb1/2)O3 by counterbalancing imbalanced spin moments through spin canting

In this study, ferroelectric Pb(Fe1/2Nb1/2)O3 with an antiferromagnetic polymorph at and below 150 K was converted into a room-temperature magnetoelectrically active multiferroic with soft ferromagnetism by disrupting the existing antiparallel spin alignment of Fe ions through the heavy replacement of Fe by Ni. To maximize the induced soft-ferromagnetic properties and the consequent nonlinear magnetoelectric coupling, the substitution level of Ni should be controlled such that the individual Ni ions are separated from one another to avoid mutual spin cancellation. The induced magnetoelectric coupling was found to originate from the collective contribution of oppositely canted pairs of spins in two nearby Fe3+ ions, which counterbalances the relatively smaller spin moment of the in-between Ni ions. The non-material specific nature of this strategy implies that it can be used in the development of new room-temperature multiferroic perovskite oxides.

Nonlinear magnetoelectric coupling in magnetostrictive-piezoelectric composites

Two micromechanical formulations are established for analysis of nonlinear magnetoelectric coupling in composite materials with 1-3, 0-3 and 2-2 connectivities. The studied two-phase composites are constructed by magnetostrictive and piezoelectric phases that exhibit significant material nonlinearity when each or all of them are subjected to large driving magnetic or electric fields. The simplified unit-cell model is first formulated followed by a reformulation of the Mori-Tanaka model so that a comparison can be made between two micromechanics models in terms of their mathematical structures and micromechanical predictions. In order to analyze the nonlinear composites, a secant linearization is employed for each constituent, concentration-factor tensors are introduced for bridging microscopic and macroscopic behaviors, and residual vectors are defined for quantitation of the errors resulted from the linearization process. Micromechanical simulations show that 1) magnetoelectric coupling can be modulated by the composite connectivity and constituent proportion, and 2) the field-dependent magnetoelectric responses leads to significant difference between linear and nonlinear predictions.

Insights into the regulation mechanism of ring-shaped magnetoelectric energy harvesters via mechanical and magnetic conditions* *Project supported by the National Natural Science Foundation of China (Grant No. 11702202), the Fundamental Research Funds for the Central Universities, China (Grant No. JB210410), and the the National Natural Science Foundation of China (Grant No. 51805401).

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.

Magnetoelectric Coupling in Multiferroic Bilayer VS_{2}.

Based on the first-principles prediction, we report the magnetoelectric coupling effect in two-dimensional multiferroic bilayer VS_{2}. The ground-state 3R-type stacking breaks space inversion symmetry, therefore introducing a spontaneous polarization perpendicular to the layer plane. We further reveal that the out-of-plane ferroelectric polarization of bilayer VS_{2} can be reversed upon interlayer sliding of an in-plane translation. Each VS_{2} layer has a ferromagnetic state with an opposite magnetic moment between two antiferromagnetically ordered layers. We found that ferroelectricity and antiferromagnetism can be coupled together by a ferrovalley in bilayer VS_{2} to realize electronic control of magnetism. Remarkably, a net magnetic moment is generated by reducing the interlayer distance, and an electric field is able to achieve linear and second-order nonlinear magnetoelectric coupling in bilayer VS_{2}.

Effects of Flexoelectricity and Surface Elasticity on the Nonlinear Magnetoelectric Coupling in Unsymmetric Composites

Flexoelectricity is the development of an electric field under an applied strain gradient. This effect is highly size-dependent and is significant at nanoscales. Unsymmetric magnetoelectric (ME) composites undergo bending deformations under a magnetic field that results in non-zero strain gradients. Hence, it is important to give due consideration to flexoelectricity, along with direct piezoelectricity in these composites. This article presents a finite-element model that predicts the static and dynamic behavior of ME nanobeams subjected to magnetic fields. The effect of material nonlinearity of the ferromagnetic phase and flexoelectricity in the ferroelectric phase on the ME coupling are determined, and the obtained results show agreement with the literature. It is found that flexoelectricity results in substantially higher static ME coefficients. However, the resonant ME response is weakened by flexoelectricity. The effect of surface elasticity on the ME coupling coefficient is also investigated by making use of the Gurtin–Murdoch theory. The surface effects are found to improve the ME coefficient at bending resonance, while its effect is trivial at static and axial resonant conditions. Furthermore, the effect of load resistance on the ME voltage and charge coefficients is determined. The results indicate clear changes in the trend between short-circuit and open-circuit conditions.

Magneto-mechanical coupling characteristic analysis of a magnetic energy nanoharvester with surface effect

In the current work, a nonlinear magnetoelectric (ME) coupling model is developed to investigate the working performance of a magnetic energy nanoharvester, which is composed of a magneto-electro-elastic (MEE) laminated cylindrical nanoshell array when the circuit is connected either in series or in parallel. The analytical results indicate that the performance of nanoharvester exhibits obvious size-dependent phenomenon, including the resonant frequency, output electrical power density, efficiency and so forth, which is only attributed to the surface effect. Based on this, a critical thickness, distinguishing micro-scale from macro-scale, is proposed, below which the size-dependent effect must be included during mechanical analysis. On the other hand, it is demonstrated that the output electrical power, as an important performance index, can be improved evidently and tuned artificially via the pre-stress and matched magnetic field, which may provide us opportunity to control the harvester in nano-scale. The current work is essential and crucial for the physical phenomenon explanations and experimental design of the MEE nanodevices, especially in the extremely complex magnetic and pre-stress field environments.

Direct and converse nonlinear magnetoelectric coupling in multiferroic composites with ferromagnetic and ferroelectric phases

In this paper, we develop a theoretical principle to calculate the direct and converse magnetoelectric (ME) coupling response of ferromagnetic/ferroelectric composites with 2-2 connectivity. We first present an experimentally based constitutive equation for Terfenol-D, and then build the mechanism of domain switch for the ferroelectric phase. In the latter, the change of Gibbs free energy, thermodynamic driving force and kinetic equations for domain growth are also established. These two sets of constitutive equations are shown to capture the experimental data of Terfenol-D and PZT, respectively, well. For the direct effect under an applied magnetic field, the induced electric field and the overall ME coupling coefficient are determined. For the converse effect under an applied electric field, the induced magnetization and the excited magnetic field are obtained. Both the induced electric filed under direct effect and the excited magnetic field under converse effect are shown to display the hysteretic characteristics, and also in good agreement with experiments. We conclude that the developed theory can both qualitatively and quantitatively reflect the essential features of nonlinear direct and converse ME coupling of the multiferroic composites.

Enhanced directional second harmonic radiation via nonlinear interference in 1D metamaterials

By using a one-dimensional nonlinear metamaterial in the experiment, we achieve a directional second harmonic radiation via nonlinear interference at approximately 2.5 GHz. Each meta-atom has the structure of coupled split-ring resonators and two varactors arranged parallel (symmetric) or antiparallel (antisymmetric) to each other. With an incident power of approximately −2.7 dBm, the power of the emitted directional wave from the sample is at the scale of nanowatt. This relatively high magnitude of directional nonlinear power is the result of the 1D metamaterial abilities in exhibiting nonlinear magnetoelectric coupling, as well as supporting an electric dipole or magnetic dipole resonance within a narrow second harmonic frequency range.

A quasistatic hysteresis model for magnetoelectric effect in multiferroic nanostructured films with surface effect

The investigation of hysteresis induced self-biased magnetoelectric (ME) coupling in multiferroic nanostructured films is significant for self-biased nano-devices. In this paper, we propose a quasistatic hysteresis model for ME effect in multiferroic nanostructured films based on surface stress model and multi-field coupled hysteretic constitutive model. For an asymmetric structure consisting of different magnetostrictive phases, the flexural strain is considered in the theoretical model. It is revealed that ME coupling in ME composites with nano-scale thickness is significantly size-dependent below critical size, which is enhanced by surface effect. Self-biased ME hysteretic behavior can be observed by considering the hysteretic effect of magnetostrictive materials, resulting in a large ME voltage coefficient in absence of bias magnetic field. The self-biased ME voltage coefficient is affected by pre-stress and thermal variation due to the complex magneto-elastic-thermal coupling characteristics of constituent materials. The proposed model provides a method to analyze and evaluate the nonlinear ME coupling characteristics of self-biased nano-devices operating under extreme stress or temperature conditions.

Finite element simulation of nonlinear magnetoelectric coupling and damage behaviour in multiferroic composites

AbstractIn this paper, the constitutive modelling of nonlinear multifield behavior as well as the finite element implementation are presented. Nonlinear material models describing the magneto‐ferroelectric or electro‐ferromagnetic behaviors are presented. Both physically and phenomenologically motivated constitutive models have been developed for the numerical calculation of principally different nonlinear magnetostrictive behaviors. Further, the nonlinear ferroelectric behavior is based on a physically motivated constitutive model. On this basis, the polarization in the ferroelectric and magnetization in the ferromagnetic and magnetostrictive phases, respectively, are simulated and the resulting effects analyzed. Additionally, the ferroelectric model accounts for damage due to microcrack growth. Numerical simulations focus on the calculation of magnetoelectric coupling and on the prediction of local domain orientations as well as damage processes going along with the poling process, thus supplying information on favorable electric‐magnetic loading sequences. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling of nonlinear magnetoelectric coupling in layered magnetoelectric nanocomposites with surface effect

Multiferroic magnetoelectric (ME) composites are widely discussed for new kinds of smart structures. However, studies on nonlinear ME coupling in layered composites with nano-scale thickness which have unique superiorities are rather limited. It is well known that the physical and mechanical properties of nanostructures are size-dependent. Considering surface effect and nonlinear material characteristics, this work proposes a nonlinear theoretical model for ME nanocomposites with different magnetostrictive materials based on the surface stress model. The results show that surface effect can enhance the ME coupling in the composites with nano-scale thickness. The ME voltage coefficient can be suppressed due to the consideration of flexural strain and imperfect interfacial conditions. The weak-bonding interface makes the optimal volume fraction shift to PZT-rich composites. Moreover, when subjected to combined pre-stress and magnetic loadings, ME nanocomposites exhibit complex magneto-mechanical coupling characteristics. The proposed model provides a method to analyze and evaluate the nonlinear ME coupling characteristics of nanostructures-based devices.

Homogenized description and retrieval method of nonlinear metasurfaces

A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry and material composition, across the electromagnetic spectrum.

Unusual Metallic Multiferroic Transitions in Electron‐Doped PbTiO3

The coexistence of some materials which are normally in mutually exclusive states is attracting considerable attention as an intriguing means of obtaining nontrivial physical phenomena and unconventional multifunctional substances. Although single‐phase materials endowed with integrated ferroelectric, magnetic, and optical multifunctions hold promise for new technological paradigms, the mutually exclusive mechanisms within ferroelectricity, conductivity, and magnetism hinder the discovery of conducting multiferroics. Here, a new path toward metallic multiferroics is provided by theoretically demonstrating the possible compatible nature of ferroelectric distortion, free carriers, and magnetism in electron‐doped PbTiO3 using the hybrid Hartree–Fock density functional theories. Doping with electrons is found to induce metallic conductivity that coexists with and even enhances the ferroelectric distortion in PbTiO3, due to the unique lone‐pair ferroelectricity in this material. The injected excess electrons, in spin‐polarized states, interact with one another in the plane perpendicular to the polar direction, resulting in layer‐arranged ferromagnetism and multiferroics with nonlinear magnetoelectric coupling. These results indicate a means of circumventing conventional restrictions, leading to new types of multifunctional materials in which unusual multiferroic and conductive characteristics are simultaneously present.

Nonvolatile transtance change random access memory based on magnetoelectric P(VDF-TrFE)/Metglas heterostructures

Transtance change random access memory (TCRAM) is a type of nonvolatile memory based on the nonlinear magnetoelectric coupling effects of multiferroics. In this work, ferroelectric P(VDF-TrFE) thin films were prepared on Metglas foil substrates by the sol-gel technique to form multiferroic heterostructures. The magnetoelectric voltage coefficient of the heterostructure can be switched reproducibly to different levels between positive and negative values by applying selective electric-field pulses. Compared with bulk multiferroic heterostructures, the polarization switching voltage was reduced to 7 V. Our facile technological approach enables this organic magnetoelectric heterostructure as a promising candidate for the applications in multilevel TCRAM devices.

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.

Landau-Ginzburg description of anomalous properties of novel room temperature multiferroics Pb(Fe1/2Ta1/2)x(Zr0.53Ti0.47)1-xO3 and Pb(Fe1/2Nb1/2)x(Zr0.53Ti0.47)1−xO3

Landau-Ginzburg thermodynamic formalism is used for the description of the anomalous ferroelectric, ferromagnetic, and magnetoelectric properties of Pb(Fe1/2Ta1/2)x(Zr0.53Ti0.47)1−xO3 and Pb(Fe1/2Nb1/2)x(Zr0.53Ti0.47)1−xO3 micro-ceramics. We calculated temperature, composition, and external field dependences of ferroelectric, ferromagnetic, and antiferromagnetic phases transition temperatures, remanent polarization, magnetization, hysteresis loops, dielectric permittivity, and magnetoelectric coupling. Special attention was paid to the comparison of developed theory with experiments. It appeared possible to describe adequately main experimental results including a reasonable agreement between the shape of calculated and measured hysteresis loops and remnant polarization. Since Landau-Ginzburg thermodynamic formalism appertains to single domain properties of a ferroic, we did not aim to describe quantitatively the coercive field under the presence of realistic poly-domain switching. Information about linear and nonlinear magnetoelectric coupling coefficients was extracted from the experimental data. From the fitting of experimental data with theoretical formula, we obtained the composition dependence of Curie-Weiss constant that is known to be inversely proportional to harmonic (linear) dielectric stiffness, as well as the strong nonlinear dependence of anharmonic parameters in free energy. Keeping in mind the essential influence of these parameters on multiferroic properties, the obtained results open the way to govern practically all the material properties with the help of suitable composition choice. A forecast of the strong enough influence of antiferrodistortive order parameter on the transition temperatures and so on the phase diagrams and properties of multiferroics are made on the basis of the developed theory.

Nonlinear resonant magnetoelectric coupling effect with thermal, stress and magnetic loadings in laminated composites

Since the magnetostrictive strain and magnetization of giant magnetostrictive materials exhibit enhanced nonlinear magneto-elasto-thermal coupling characteristics under the influence of bias magnetic field, prestress and temperature, this paper adopted a 1D nonlinear magnetostrictive constitutive and the linear piezoelectric constitutive relations combined with the equivalent circuit method to establish a 1D enhanced nonlinear magneto-elasto-thermal coupling resonant magnetoelectric (ME) model for Terfenol-D/PZT/Terfenol-D laminated composites. Without considering prestress, the comparisons of curves of resonant ME coefficient peak and its corresponding resonant frequency versus temperature between the theoretical results and experimental results are in good agreement both qualitatively and quantitatively. On this basis, this paper predicted variations in resonant ME coefficient and resonant frequency under different bias magnetic fields, prestresses and temperatures. These results show that the exerted compressive stress can be reduced so as to increase the resonant ME coefficient and lower the required bias magnetic field to the maximum of ME coefficient at relatively low and stable ambient temperatures; however, in extreme temperature environment, a larger compressive stress can be exerted to suppress the dramatic attenuation of ME effect caused by extreme temperature increases. Moreover, as temperature is increased, the resonant frequency tends to increase monotonically under different prestresses.

Room temperature nonlinear magnetoelectric effect in lead-free and Nb-doped AlFeO3 compositions

It is still a challenging problem to obtain technologically useful materials displaying strong magnetoelectric coupling at room temperature. In the search for new effects and materials to achieve this kind of coupling, a nonlinear magnetoelectric effect was proposed in the magnetically disordered relaxor ferroelectric materials. In this context, the aluminum iron oxide (AlFeO3), a room temperature ferroelectric relaxor and magnetic spin glass compound, emerges as an attractive lead-free magnetoelectric material along with nonlinear magnetoelectric effects. In this work, static, dynamic, and temperature dependent ferroic and magnetoelectric properties in lead-free AlFeO3 and 2 at. % Nb-doped AlFeO3 multiferroic magnetoelectric compositions are studied. Pyroelectric and magnetic measurements show changes in ferroelectric and magnetic states close to each other (∼200 K). The magnetoelectric coefficient behavior as a function of Hbias suggests a room temperature nonlinear magnetoelectric coupling in both single-phase and Nb-doped AlFeO3-based ceramic compositions.