Nonlinear Magnetoelectric Research Articles

Electric field tuning of a nickel zinc ferrite resonator by non-linear magnetoelectric effects

The nature of nonlinear magnetoelectric (NLME) effect has been investigated at room-temperature in a single-crystal Zn substituted nickel ferrite. Tuning of the frequency of magnetostatic surface wave (MSSW) modes under an applied pulsed DC electric field/current has been utilized to probe the effect. The frequencies of the modes at 8–20 GHz were found to decrease by ~ 400 MHz for an applied DC power P of ~ 100 mW and the frequency shift was the same for all of the MSSW modes and linearly proportional to P. A model is proposed for the effect and the NLME phenomenon was interpreted in terms of a reduction in the saturation magnetization due to the DC current. The decrease of magnetization with applied electric power, estimated from data on mode frequency versus P, was − 2.50 G/mW. The frequency tuning efficiency of the MSSW modes due to NLME effects in the ferrite resonator was found to be 4.1 MHz/mW which is an order of magnitude higher than the shift reported for M-type strontium and barium hexaferrite resonators investigated earlier. The spinel ferrite resonator discussed here has the potential for miniature, electric field tunable, planar microwave devices for the 8–20 GHz frequency range.

Nonlinear magnetoelectric effect in a ring composite heterostructure

Objectives. The relevance of the study of magnetoelectric (ME) effect in ring ferromagnetic–piezoelectric heterostructures is due to the possibility of creating various ME devices having improved characteristics. A detailed investigation of the nonlinear ME effect in a ring composite heterostructure based on lead zirconate titanate (PZT) piezoceramics and Metglas® amorphous ferromagnetic (FM) alloy under circular magnetization is presented.Methods. The ME effect was measured by the low-frequency magnetic field modulation method. Excitation alternating- and constant magnetic bias fields were created using toroidal coils wound on a ring heterostructure for circular magnetization of the FM layer.Results. When excited with circular magnetic fields in a non-resonant mode, the ME ring heterostructure generates a nonlinear ME voltage of higher harmonics. The field and amplitude dependencies of the first three ME voltage harmonics were investigated. ME coefficients were obtained for the linear ME effect α(1) = 5.2 mV/(Oe·cm), the nonlinear ME effect α(2) = 6 mV/(Oe2·cm), and α(3) = 0.15 mV/(Oe3·cm) at an excitation magnetic field frequency f = 1 kHz. The maximum amplitudes of the 1st and 3rd harmonics were observed at a constant bias magnetic field H ~ 7 Oe, which is almost two times smaller than in planar PZT–Metglas® heterostructures.Conclusions. A nonlinear ME effect was observed and investigated in a ring heterostructure based on PZT piezoceramics and Metglas® amorphous FM alloy. Due to the absence of demagnetization during circular magnetization of the closed FM layer, nonlinear ME effects are detected at significantly lower amplitudes of the exciting alternating and constant bias magnetic fields as compared to planar heterostructures. The investigated ring heterostructures are of potential use in the creation of frequency multipliers.

Magnetoelectric Effect in Amorphous Ferromagnetic FeCoSiB/Langatate Monolithic Heterostructure for Magnetic Field Sensing.

This paper investigates the possibilities of creating magnetic field sensors using the direct magnetoelectric (ME) effect in a monolithic heterostructure of amorphous ferromagnetic material/langatate. Layers of 1.5 μm-thick FeCoSiB amorphous ferromagnetic material were deposited on the surface of the langatate single crystal using magnetron sputtering. At the resonance frequency of the structure, 107 kHz, the ME coefficient of linear conversion of 76.6 V/(Oe∙cm) was obtained. Furthermore, the nonlinear ME effect of voltage harmonic generation was observed with an increasing excitation magnetic field. The efficiency of generating the second and third harmonics was about 6.3 V/(Oe2∙cm) and 1.8 V/(Oe3∙cm), respectively. A hysteresis dependence of ME voltage on a permanent magnetic field was observed due to the presence of α-Fe iron crystalline phases in the magnetic layer. At the resonance frequency, the monolithic heterostructure had a sensitivity to the AC magnetic field of 4.6 V/Oe, a minimum detectable magnetic field of ~70 pT, and a low level of magnetic noise of 0.36 pT/Hz1/2, which allows it to be used in ME magnetic field sensors.

Low-frequency resonant magnetoelectric effects in a planar heterostructure of ferromagnetic yttrium iron garnet film and piezoelectric quartz

Low-frequency resonant magnetoelectric (ME) effects in a planar heterostructure containing a 50 μm thick single-crystal film of yttrium iron garnet (YIG) and a crystalline quartz platelet were studied. The ME effects in the mechanically coupled composite arise due to a combination of magnetostriction of the YIG film and the piezoelectric effect in quartz. The effects manifest as mutual transformation of ac magnetic and electric fields. When the layered composite was excited by an ac magnetic field (direct ME effect) at a planar acoustic resonance frequency of 128 kHz, the ME field conversion coefficient was 8.8 V/(Oe∙cm). When excited by an ac electric field (converse effect), the ME conversion coefficient was 0.32 G/(V/cm). Nonlinear ME effects caused by the nonlinear magnetostriction of the YIG film were observed as frequency doubling upon excitation of the direct ME effect by a magnetic field at a frequency equal to half the resonant frequency, as well as at the converse ME effect upon excitation by an electric field at the frequency of the resonance of the structure. In spite of weak magnetostriction for YIG, the resonant ME effects in the YIG-quartz composite are comparable in magnitude to the effects in composites with high magnetostriction materials, show high quality factor of Q ∼ 2200 and are observed in weak magnetic fields H ∼ 0–60 Oe. These results demonstrate the potential for YIG film-quartz composites application in electronic devices.

Electric polarization reversal and nonlinear magnetoelectric coupling in the honeycomb antiferromagnet Fe4Nb2O9 single crystal

As a new magnetoelectric material, honeycomb-based antiferromagnet ${\mathrm{Fe}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$ has attracted a great deal of attention due to its prominent magnetoelectric (ME) coupling and high N\'eel temperature, while the physics of magnetoelectricity is far from understood. In the present study, we present our systematic investigations of the anisotropic ME effect, electric polarization reversal, and nonlinear ME effect of ${\mathrm{Fe}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$ single crystals, thus highlighting the phase diagram extended down to 10 K. Our results provide clear evidence for electric polarization reversal driven by magnetic field ($H$) along the [110] and [1-10] directions, respectively, while no such polarization reversal occurs as $H$ is applied along the [001] direction. The nonlinear ME effects and electric control of magnetism are unambiguously demonstrated. In addition, the angular-dependent probing reveals a 2\ensuremath{\theta} rotation of the induced electric polarization around the $c$ axis upon the rotation of magnetic field by an angle \ensuremath{\theta}. The electric polarization responses and concomitant ME coupling are well explained by means of the metal-ligand hybridization $p\text{\ensuremath{-}}d$ mechanism. This work represents an essential step forward in the understanding of ME coupling not only in this ${A}_{4}{M}_{2}{\mathrm{O}}_{9}$ honeycomb magnet.

Nonlinear magnetoelectric effect in atomic vapor and its application to precision radio-frequency magnetometry

We demonstrate the nonlinear magnetoelectric (ME) effect in atomic vapor achieved through the parametric interaction of optical electric and radio-frequency (rf) magnetic fields leading to the generation of new optical electric fields. Density matrix calculations are performed to validate the experimental results. Moreover, the predicted dependence of the generated optical electric field amplitudes on the rf magnetic field strength is experimentally verified to confirm the ME effect. The system provides a technique for precision rf magnetometry based on this phenomenon. We could experimentally achieve an rf magnetic field sensitivity of 70 $\mathrm{fT}/\sqrt{\text{Hz}}$ at 1 kHz to 7.5 $\mathrm{pT}/\sqrt{\text{Hz}}$ at 3 MHz for zero bias field in an unshielded environment. The appealing features of the proposed rf magnetometer using our system include a high dynamic range up to ${10}^{12}$, 6 dB bandwidth of 450 kHz, and arbitrary frequency resolution, which are intrinsic to the nonlinear ME effect in the medium.

Anisotropy of magnetoelectric effects in a planar heterostructure comprising a piezoelectric substrate and a ferromagnetic grating

Anisotropic magnetoelectric (ME) effects are investigated in a planar multiferroic heterostructure consisting of a piezoelectric lead zirconate-titanate substrate and a grating of ferromagnetic Ni-strips electrodeposited on its surface. The heterostructure is placed in a tangential dc magnetic field H and excited by an alternating magnetic field h at the frequency of bending acoustic resonance. It is shown that the magnitudes of both the linear and nonlinear ME effects depend on the orientation of the h and H fields with respect to the axis of Ni-strips and the distance between the strips. Strong anisotropy of ME effects arises due to demagnetization in a single Ni-strip and dipole-dipole interaction between the adjacent strips. The calculation technique is proposed that qualitatively well describes the anisotropy of linear and nonlinear ME effects in the heterostructure. The anisotropic ME effect can be used to create magnetic field sensors sensitive to the field orientation.

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.

Resonance magnetoelectric effect in a composite ferromagnet–dielectric–piezoelectric Langevin-type resonator

The direct and converse magnetoelectric (ME) effects in a Langevin-type resonator are observed and investigated for the first time. The resonator comprised a disk made of lead–zirconate titanate ceramic, located between two sapphire cylinders, with layers of amorphous ferromagnet glued to its side surfaces. ME effects were observed at frequencies of bending (∼70 kHz) and longitudinal (∼200 kHz) oscillations of the resonator upon its excitation by ac magnetic and electric fields. The field conversion efficiency for the direct ME effect was α E ≈ 31 V (Oe−1 cm−1). The magnetization modulation efficiency for the converse ME effect reached α B ≈ 0.72 G cm−1 V−1. The nonlinear ME effects such as frequency doubling, frequency mixing, and resonance frequency shift are observed at high field amplitudes. The magnitude of both the direct and converse ME effects in the resonator is controlled by an external dc magnetic field. The Langevin-type ME resonators can be used in highly sensitive magnetic field sensors, controlled resonators and transformers, and other components of electronics and microsystem technology.

Nonlinear magnetoelectric effects in Al-substituted strontium hexaferrite

This report is on the observation and theory of electric field E induced non-linear magnetoelectric (NLME) effects in single crystal platelets of ferrimagnetic M-type strontium aluminum hexagonal ferrite. Using microwave measurement techniques, it was found that a DC electric field along the hexagonal c-axis results in significant changes in the saturation magnetization and uniaxial magneto-crystalline anisotropy field and these changes are proportional to the square of the applied static electric field. The NLME effects were present with or without an external bias magnetic field. The E-induced variation in magnetic order parameters is attributed to weakening of magnetic exchange and spin–orbit interactions since conduction electrons in the ferrite are effectively excluded from both interactions while being in transit from one Fe ion to another. We present a phenomenological theory which considers magneto-bielectric effects characterized by a quadratic term in electric field E in the free energy density. The coefficients for the NLME coupling terms have been calculated from experimental data and they do show variations with the Al substitution level and the largest rates of change of the saturation magnetization and anisotropy constant change with the applied power were observed for x = 0.4. It was also clear from the study that strength of the NLME effect does not depend on the amount Al substitution, but critically depends on the electrical conductivity of the sample with the highest NLME coefficients estimated for the sample with the highest conductivity. Results of this work are of importance for a new family of electric field tunable, miniature, high frequency ferrite devices.

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.

An analytical model for nonlinear magnetoelectric effect in laminated composites

This paper presents an analytical and explicit theoretical model for the nonlinear magnetoelectric (ME) effect in laminated composites, in which the multi-field coupled properties of magnetostrictive materials are taken into account. The adopted explicit nonlinear constitutive equation is equivalent to the one in series form through expanding the magnetostriction as a Taylor series in the vicinity of the applied bias field. Then the field-dependent materials’ parameters are derived as functions of bias field and stress. Analytical solutions of nonlinear ME voltages in various modes are obtained simultaneously using mechanical differential equations, boundary conditions, and electric equations. It is predicted that the frequency-multiplying behavior observed in the composites can be tuned by bias magnetic field. Only even harmonics occur in the absence of bias field, while odd harmonics appear once a bias field is applied. An optimal bias field corresponding to the maximum linear voltage and zero nonlinear voltage is obtained, where the highest piezomagetic effect generates. It is proved that the ME distortions under a fixed ac field is actually caused by the competition results between the linear piezomagnetic effect and high-order magnetostrictive effect. Moreover, pre-stress may enhance ME voltages and reduce the optimal field due to the multi-field coupled character, and control the resonance frequency via ΔE effect. Eventually, the origin of the observed dual-peak phenomenon around resonance frequencies is revealed and explained theoretically, indicating that strong ME effect may be achieved in a wider bias field range. The analytical solutions from this study can be applied to design tunable ME sensors, energy harvesters, and some other nonlinear devices via manipulating the external bias field and pre-stress.

Spin Symmetry Breaking: Superparamagnetic and Spin Glass-Like Behavior Observed in Rod-Like Liquid Crystalline Organic Compounds Contacting Nitroxide Radical Spins

Liquid crystalline (LC) organic radicals were expected to show a novel non-linear magnetic response to external magnetic and electric fields due to their coherent collective molecular motion. We have found that a series of chiral and achiral all-organic LC radicals having one or two five-membered cyclic nitroxide radical (PROXYL) units in the core position and, thereby, with a negative dielectric anisotropy exhibit spin glass (SG)-like superparamagnetic features, such as a magnetic hysteresis (referred to as ‘positive magneto-LC effect’), and thermal and impurity effects during a heating and cooling cycle in weak magnetic fields. Furthermore, for the first time, a nonlinear magneto-electric (ME) effect has been detected with respect to one of the LC radicals showing a ferroelectric (chiral Smectic C) phase. The mechanism of the positive magneto-LC effect is proposed and discussed by comparison of our experimental results with the well-known magnetic properties of SG materials and on the basis of the experimental results of a nonlinear ME effect. A recent theoretical study by means of molecular dynamic simulation and density functional theory calculations suggesting the high possibility of conservation of the memory of spin-spin interactions between magnetic moments owing to the ceaseless molecular contacts in the LC and isotropic states is briefly mentioned as well.

Anisotropy of magnetoelectric effects in an amorphous ferromagnet-piezoelectric heterostructure

In-plane anisotropy of linear and nonlinear magnetoelectric (ME) effects in a heterostructure composed of mechanically coupled layers of amorphous iron-based ferromagnet and piezoelectric lead zirconate-titanate ceramics has been investigated. The measurements were performed on a disk-shaped sample subjected to a low-frequency excitation magnetic field h oriented either parallel or perpendicular to a bias magnetic field H0. The first harmonic of the voltage response was recorded in the case of the linear ME effect, which was excited at frequencies of acoustic resonances of the sample, and the second harmonic in the case of the nonlinear ME effect excited in the non-resonance regime. Strong uniaxial or biaxial anisotropy for different directions of the bias field within the sample plane was observed. The uniaxial anisotropy of the ME effect occurs due to the uniaxial magnetic and magnetostrictive anisotropy of the amorphous ferromagnetic layer that is a result of its fabrication by the ultrafast cooling method. The biaxial anisotropy at resonant frequencies is the manifestation of the spatial structure of the excited acoustic modes. The anisotropy of ME effects should be taken into account when developing magnetoelectric devices based on composite heterostructures.

Unusual magnetoelectric effect in paramagnetic rare-earth langasite

Violation of time reversal and spatial inversion symmetries has profound consequences for elementary particles and cosmology. Spontaneous breaking of these symmetries at phase transitions gives rise to unconventional physical phenomena in condensed matter systems, such as ferroelectricity induced by magnetic spirals, electromagnons, non-reciprocal propagation of light and spin waves, and the linear magnetoelectric (ME) effect—the electric polarization proportional to the applied magnetic field and the magnetization induced by the electric field. Here, we report the experimental study of the holmium-doped langasite, HoxLa3−xGa5SiO14, showing a puzzling combination of linear and highly non-linear ME responses in the disordered paramagnetic state: its electric polarization grows linearly with the magnetic field but oscillates many times upon rotation of the magnetic field vector. We propose a simple phenomenological Hamiltonian describing this unusual behavior and derive it microscopically using the coupling of magnetic multipoles of the rare-earth ions to the electric field.

Differential configuration of 180° anti-phase-modulated nonlinear magnetoelectric effect of parallel-placed dual FeNiMoSiB/Pb(Zr1−xTix)O3 composites for magnetic field sensing

Magnetic sensors based on nonlinear magnetoelectric (ME) effect can be used to measure weak dc and ac magnetic fields at room temperature. The focus of this paper is to present the nonlinear ME effect of parallel-placed dual FeNiMoSiB/PZT/FeNiMoSiB composites with small size which are operated in 180° anti-phase modulated mode and differential output configuration. In this design, the strong ME voltage at even order harmonics due to frequency doubling effect of magnetostriction is greatly attenuated. This is of great benefit to the design of the sensor signal conditioning circuit because strong even order harmonics limit the magnification of the first stage amplifier. Due to the nonlinear ME effect, the induced ME voltage of the odd order harmonics is modulated by a weak dc/ac magnetic field to be measured. The wideband frequency of weak magnetic field from dc-0.9f (f is the frequency of the driving field) can be recovered from the 1 st harmonic response by the lock-in demodulation method. The sensitivity and limit of detection of the anti-phase modulated differential ME dual-unit are 176.1 μV/μT and 2 nT/√Hz at 10 Hz, respectively.

Anisotropic Magnetoelectric Effect in a Planar Heterostructure Comprising Piezoelectric Ceramics and Magnetostrictive Fibrous Composite.

The direct magnetoelectric (ME) effect is investigated in a planar structure comprising mechanically coupled layers of a magnetostrictive fibrous composite (MFC) and a piezoelectric ceramics (lead zirconate titanate, PZT). The MFC is an array of Ni-wires with a diameter of 200 μm that are aligned parallel to each other in a single layer. The wires are separated by a distance of 250 or 500 μm and fixed in a polyamide matrix. The structure was placed in a tangential constant field H and was excited by an alternating magnetic field h parallel to H, while the voltage generated by the PZT layer was measured. The resulting field dependences of the magnetization M(H) and the magnetostriction λ(H) were determined by the orientation of the field H in the plane of the structure and the distance between the Ni-wires. The ME coupling coefficient of the structure decreased from 4.8 to 0.25 V/A when the orientation of H was changed from parallel to perpendicular to Ni-wires. With an increase in the excitation field amplitude h, a nonlinear ME effect in the output voltage, namely frequency doubling, was observed. The frequency and field dependences of the efficiency of the ME transduction in the MFC-piezoelectric heterostructure are well described by the existing theory.

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.

Magnetoelectric effects in a layered ferromagnet-electrostrictor heterostructure

Magnetoelectric (ME) effects in a heterostructure consisting of mechanically coupled layers of amorphous ferromagnet FeBSiC and electrostrictive lead magnesium niobate-lead titanate (PMN-PT) ceramics are observed and investigated. Magnetoelectric characteristics of the structure strongly differ from those of the ferromagnetic-piezoelectric one. The FeBSiC-PMN-PT structure did not show the direct ME effect under excitation with an alternating magnetic field. For the converse ME effect, when the structure was excited with alternating electric fields, the frequency doubling and mixing of electric fields frequencies were observed. Nonlinear ME effects arise due to the nonlinear electrostrictive strain vs electric field dependence. Efficiency of nonlinear ME conversion is proportional to the piezomagnetic coefficient of the ferromagnetic layer, nonlinear electrostriction coefficient of the electrostrictive layer, and amplitudes of the excitation fields. A theory for nonlinear ME effects in the ferromagnet-electrostrictor heterostructures was developed.

Static nonlinear model of both ends clamped magnetoelectric heterostructures with fully magneto-mechanical coupling

A static fully magneto-mechanical coupling nonlinear model of magnetoelectric (ME) effect in both ends clamped magnetostrictive/piezoelectric heterostructures is established. The magnetoelectric effect, which arose from piezoelectric effect driven by magnetostrictive force, is studied. As the both ends of the heterostructures are fixed, the piezoelectric material can be equivalent to the linear spring load of magnetostrictive actuator. The nonlinear theoretical model is built based on a nonlinear magnetostrictive constitutive relation and a linear piezoelectric model. The hysteresis and fully coupled magneto-mechanical effects, including stress-dependent magnetization, stress-dependent magnetostriction and ΔE effect of magnetostrictive material are considered in this model. Using the model, the influence of the pre-stress, magnetic field and the length fraction of the magnetostrictive material on the magnetoelectric response is qualitatively predicted. Furthermore, the model can explain the “self-biased” response caused by the hysteretic characteristics of the ME composites. A ME heterostructures prototype is designed and manufactured based on Terfenol-D/PZT heterostructures. The model is validated by comparing the simulated ME response with experiment at the quasi-static condition. The nonlinear ME model provides a theoretical basis for the optimization design of high-performance ME devices.