Linear Magnetoelectric Effect Research Articles

Spontaneous Magnetization Induced by Antiferromagnetic Toroidal Ordering.

The magnetic toroidal dipole moment, which is induced by a vortex-type spin texture, manifests itself in parity-breaking physical phenomena, such as a linear magnetoelectric effect and nonreciprocal transport. We elucidate that a staggered alignment of the magnetic toroidal dipole can give rise to spontaneous magnetization even under antiferromagnetic structures. We demonstrate the emergence of uniform magnetization by considering the collinear antiferromagnetic structure with the staggered magnetic toroidal dipole moment on a bilayer zigzag chain. Based on the model calculations, we show that the interplay between the collinear antiferromagnetic mean field and relativistic spin-orbit coupling plays an important role in inducing the magnetization.

Rotational magnetoelectric switching in orthorhombic multiferroics

Controlling the direction of ferromagnetism and antiferromagnetism by an electric field in single-phase multiferroics will open the door to the next generation of devices for spintronics and electronics. The typical magnetoelectric coupling such as the linear magnetoelectric effect is very weak in type-I multiferroics and therefore the magnetoelectric switching is rarely achieved. Here, using first-principles simulations, we propose a magnetoelectric switching mechanism to achieve such highly desired control in orthorhombic multiferroics. One class of two-dimensional proper multiferroics (CrX2Se3 and MnX2Te3, X = Sn, Ge) and perovskite multiferroics (EuTiO3 and BiFeO3/LaFeO3 superlattice) are taken as examples to show the mechanism. In the ferroelectric switching process, the proper polarization rotates its direction by 180° and keeps its magnitude almost unchanged, the ferromagnetic or antiferromagnetic vector is rotationally switched by 180° following the rotation of ferroelectric polarization. This rotational magnetoelectric switching results from in-plane structural anisotropy and magnetic anisotropy, and the process of switching is governed by cosine functions from the phenomenological Landau-type models. This study addresses the challenge of magnetoelectric switching in type-I multiferroics by proposing a general magnetoelectric switching mechanism.

Spin-Reorientation-Driven Linear Magnetoelectric Effect in Topological Antiferromagnet Cu_{3}TeO_{6}.

The search for new materials for energy-efficient electronic devices has gained unprecedented importance. Among the various classes of magnetic materials driving this search are antiferromagnets, magnetoelectrics, and systems with topological spin excitations. Cu_{3}TeO_{6} is a material that belongs to all three of these classes. Combining static electric polarization and magnetic torque measurements with phenomenological simulations we demonstrate that magnetic-field-induced spin reorientation needs to be taken into account to understand the linear magnetoelectric effect in Cu_{3}TeO_{6}. Our calculations reveal that the magnetic field pushes the system from the nonpolar ground state to the polar magnetic structures. However, nonpolar structures only weakly differing from the obtained polar ones exist due to the weak effect that the field-induced breaking of some symmetries has on the calculated structures. Among those symmetries is the PT (1[over ¯]^{'}) symmetry, preserved for Dirac points found in Cu_{3}TeO_{6}. Our findings establish Cu_{3}TeO_{6} as a promising playground to study the interplay of spintronics-related phenomena.

Probing magnetoelectric effect in the spin-modulated magnet Fe2GeO4

The distinct spin amplitude wave was reported in a highly frustrated magnetic compound Fe2GeO4, which is very different from observations on other members of the M2GeO4 (M = Fe, Co, and Ni) family, raising interest in this compound for some additional emergent phenomena. In particular, this non-uniform spin order allows the intrinsic connection between ferroelectric polarization and magnetically gradient structure to probe the potential linear magnetoelectric (ME) effect. In this work, we address this issue and investigate the magnetism of Fe2GeO4 single crystal that hosts two successive anomalies at antiferromagnetic (AFM) Néel temperatures T N1 ∼ 7.5 K and T N2 ∼ 6.7 K, respectively. Our results reveal a remarkable metamagnetic transition in the magnetization as a function of the magnetic field, occurring at a critical magnetic field H c ∼ 4.1 T when applied along the [110] and [1–10] directions, while such transition along the [001] direction is pointedly absent. Further exploration uncovers two predominant off-diagonal ME coefficients αyz and αzy in the incommensurate AFM phase between T N1 and T N2. Additionally, all components of the linear ME tensor remain non-vanishing in the canting AFM phase below T N2. This indicates the ME mechanisms for the two phases that may be driven by different magnetic structures. All these presented results are sufficient for us to draw a non-trivial ME phase diagram, which is beneficial to understanding the ME behavior of Fe2GeO4. Therefore, our study implies that Fe2GeO4, an unusual frustrated magnet, provides a platform for manipulating the fascinating ME effect in the spinel structure.

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.

Colossal Linear Magnetoelectricity in Polar Magnet Fe_{2}Mo_{3}O_{8}.

The linear magnetoelectric effect is an attractive phenomenon in condensed matters and provides indispensable technological functionalities. Here a colossal linear magnetoelectric effect with diagonal component α_{33} reaching up to ∼480 ps/m is reported in a polar magnet Fe_{2}Mo_{3}O_{8}. This effect can persist in a broad range of magnetic field (∼20 T) and is orders of magnitude larger than reported values in literature. Such an exceptional experimental observation can be well reproduced by a theoretical model affirmatively unveiling the vital contributions from the exchange striction, while the sign difference of magnetocrystalline anisotropy can also be reasonably figured out.

Electric‐Field‐Tunable Bipolar Linear Magnetoelectric Effect in Zigzag Graphene Nanoribbon‐Based Antiferromagnet

Modern electronic devices are moving toward miniaturization and integration. Therefore, achieving electrical control of magnetization effectively in 1D materials represents a promising field for the practical applications in memory elements. Herein, it is discovered, from first‐principles calculations, that an electric‐field‐tunable bipolar linear magnetoelectric effect can be realized in 1D antiferromagnets based on double‐Gd‐adsorbed graphene nanoribbon with four zigzag carbon chains (2Gd‐4ZGNR). It is found that, compared with the bare 4ZGNR, the adsorption of two Gd atoms on the 4ZGNR reduces the bandgap. As a result, 2Gd‐4ZGNR transits from antiferromagnetic semiconductor to ferrimagnetic metal at a relatively low critical external transverse (perpendicular) electric field, where the net magnetic moment can be induced. The antiferromagnetism and inversion‐symmetrical crystal structure further allow to realize a bipolar linear magnetoelectric effect, where the 2Gd‐4ZGNR forms two groups of independent linear magnetic response states, acting as a magnetoelectric memory element.

Observation of linear magnetoelectric effect in a Dirac magnon antiferromagnet Cu3TeO6

Cu3TeO6, a three-dimensional antiferromagnet forming a unique spin-web lattice of spin-1/2 Cu2+ ions below the Néel temperature TN ≈ 62 K, has recently been found to exhibit topological Dirac or nodal magnon dispersion. In this study, we report the discovery of the linear magnetoelectric (ME) effects in Cu3TeO6 below TN. Our pyroelectric current measurements at a constant magnetic field (H) reveal a linear increase of electric polarization (P) with H for both P//H and P⊥ H configurations; a maximum P//[110] = 20 µC/m2 is obtained at µ0H//11¯0 = 14 T, corresponding to a linear ME coefficient 1.8 ps/m. Magnetic point group analysis and Monte-Carlo simulations confirm that finite linear ME coefficients are allowed in the off-diagonal and diagonal ME tensor components, consistent with the magnetic point group of 3¯′. As the parity-time symmetry can be broken in the presence of H or electric field E in the linear ME materials, we envisage that Cu3TeO6 should exhibit a H- or E-induced transformation in the topological magnon dispersion from a Dirac point/nodal line type into two Weyl point types.

Mg doping enhanced magnetoelectric effect in the polar magnet Fe2Mo3O8

Magnetoelectric (ME) effect has given rise to a new design principle for novel low-power electronic devices. The polar magnet ${\mathrm{Fe}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ with linear ME effect is one of the promising candidates. Unfortunately, for this material, a large ME response only appears in the ferrimagnetic state, which needs a high magnetic field to be activated. In this work, we successfully synthesize single-crystal ${({\mathrm{Fe}}_{0.95}{\mathrm{Mg}}_{0.05})}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ (FMMO), which achieves a linear ME effect in the antiferromagnetic ground state and shows a significantly improved ME coefficient in the ferrimagnetic state. Compared with the parent phase, six times linear ME coefficient and more than ten orders of magnitude second-order ME coefficient are accomplished in the FMMO. The spin-lattice coupling and the exchange-striction mechanism are believed to play a crucial role in creating the giant ME effect. The present study provides an idea for designing materials with strong ME coupling.

The size effect of BiFeO3 nanocrystals on the spatial spin modulated structure.

The spatial spin modulated structure (SSMS) of the cycloid type present in bulk BiFeO3 prevents the linear magnetoelectric effect. One way to influence this structure is to reduce the crystal size to the nanoscale. Various opinions are circulating in the literature about the effect of nanocrystal size on SSMS, and to investigate this issue, we used a number of methods, with zero-field NMR (ZF NMR) spectroscopy at the forefront. ZF NMR spectroscopy enables the direct observation of the distribution profile of local fields on iron atoms and defines the SSMS presence and its properties. We also examined the synthesized samples using XRD, TEM, and magnetometry. We conclude that SSMS persists as the nanocrystal size decreases to the cycloid period and less, becoming more harmonic. This is accompanied by the change of the anisotropy type from an "easy axis" to an "easy plane". Magnetic measurements show a significant increase in the saturation magnetization, remanent magnetization, coercivity, and exchange bias of nanocrystals with sizes close to the cycloid period, which is probably associated with incomplete spin compensation in the case of an incomplete cycloid period. Despite the fact that SSMS is retained in the samples with decreased size, the magnetic properties experience a sharp increase up to applicable values.

Magnetic Toroidal Moment under Partial Magnetic Order in Hexagonal Zigzag-Chain Compound Ce3TiBi5

We theoretically investigate an antiferromagnetic structure in a hexagonal zigzag-chain compound Ce$_3$TiBi$_5$, which shows a linear magnetoelectric effect in metals and an unfamiliar temperature dependence of magnetic susceptibility. We find a partial magnetic order as a coexistence of a nonmagnetic zigzag chain and staggered antiferromagnetic zigzag chains. The latter accompany in-plane magnetic toroidal dipole moments which are responsible for the observed behaviors. We show that magnetic frustration arising from competing exchange interactions plays an important role to realize such a partial magnetic order. Furthermore, we present the important spin-orbit coupling parameters to induce the physical phenomena driven by the magnetic toroidal dipole moment, such as the linear magnetoelectric effect and nonlinear transport.

Magnetoelectric effects in a composite ferromagnet–piezoelectric heterostructure under pulsed excitation

Magnetoelectric (ME) effects in multiferroic ferromagnet–piezoelectric (PE) composite heterostructures result in a change in the electric polarization under the action of magnetic field or a change in the magnetization under the action of electric field and, therefore, are interesting from scientific point of view and for applications. In this work, the direct and converse ME effects are experimentally studied when a planar amorphous ferromagnet–PE lead zirconate–titanate structure is excited by magnetic and electrical field pulses with duration from microseconds to tens of milliseconds. Under the action of magnetic field pulses, the structure generates damped voltage oscillations with a frequency equal to the acoustic resonance frequency of the structure, as well as an exponentially decreasing dc voltage. By choosing the duration of magnetic pulses, it is possible selectively excite the linear ME effect in the structure or generate the second voltage harmonic at the resonance frequency. Electrical field pulses result in the excitation of damped magnetization oscillations at the resonance frequency of the heterostructure. The pulsed excitation method allows to estimate the ME conversion coefficients for both the direct and converse ME effects.

Magnetoelectric and Magnetostrictive Effects in Scheelite-Type HoCrO4.

Scheelite-type HoCrO4 was prepared by treating the ambient-pressure zircon-type precursor phase under 8 GPa and 700 K. A long-range antiferromagnetic phase transition is found to occur at TN ≈ 23 K due to the spin order of Ho3+ and Cr5+ magnetic ions. However, the antiferromagnetic ground state is sensitive to an external magnetic field and a moderate field of about 1.1 T can induce a metamagnetic transition, giving rise to the presence of a large magnetization up to 8.5 μB/f.u. at 2 K and 7 T. Considerable linear magnetoelectric effect is observed in the antiferromagnetic state, while the induced electric polarization experiences a sharp increase near the critical field of the metamagnetic transition. Ferromagnetism and ferroelectricity thus rarely coexist under higher magnetic fields in scheelite-type HoCrO4. Moreover, a magnetic field also plays an important role in the longitudinal constriction of HoCrO4, and a significant magnetostrictive effect with a value of up to 300 ppm is observed at 2 K and 9 T, which can be attributed to the strong anisotropy of the rare-earth Ho3+ ion. Possible coupling between magnetoelectric and magnetoelastic effects is discussed.

Physics of Composites for Low-Frequency Magnetoelectric Devices.

The article discusses the physical foundations of the application of the linear magnetoelectric (ME) effect in composites for devices in the low-frequency range, including the electromechanical resonance (EMR) region. The main theoretical expressions for the ME voltage coefficients in the case of a symmetric and asymmetric composite structure in the quasi-static and resonant modes are given. The area of EMR considered here includes longitudinal, bending, longitudinal shear, and torsional modes. Explanations are given for finding the main resonant frequencies of the modes under study. Comparison of theory and experimental results for some composites is given.

Anisotropic magnetoelectric effect in lead zirconate titanate and magnetostrictive fiber composite structures

Objectives. The development of composite structures in which a strongly anisotropic magnetoelectric (ME) effect is observed is relevant for the creation of sensors that are sensitive to the direction of the magnetic field. Such an ME effect can arise due to the anisotropy of both the magnetic and the piezoelectric layers. In this work, a new anisotropic material named as a magnetostrictive fiber composite (MFC), comprising a set of nickel wires placed closely parallel to each other in one layer and immersed in a polymer matrix, is manufactured and studied. The study aimed to investigate the linear ME effect in a structure comprising of a new magnetic material, MFC, and lead zirconate titanate (PZT-19).Methods. The magnetostriction for the MFC structure was measured using the strain-gauge method; the ME effect was determined by low-frequency magnetic field modulation.Results. Structures with nickel wire diameters of 100, 150, and 200 μm were fabricated. The MFC magnetostriction field dependences were determined along with the frequency-, field-, and amplitude dependences of the ME voltage in the case of linear ME effect. Measurements were carried out at various values of the angle between the direction of the magnetic field and the wires. All samples demonstrated strong anisotropy with respect to the direction of the magnetic field. When the magnetic field orientation changes from parallel to perpendicular with respect to the nickel wire axes, the ME voltage decreases from its maximum value to zero.Conclusions. The largest ME coefficient 1.71 V/(Oe · cm) was obtained for a structure made of MFC with a wire diameter of 150 μm. With increasing wire diameter, the resonance frequency increases from 3.5 to 6.5 kHz. The magnetostriction of the MFC is comparable in magnitude to that of a nickel plate having the same thickness.

Origin of multiferroism in Sm[formula omitted]BaCuO[formula omitted

Proposing a microscopic model we have investigated the multiferroic properties of Sm2BaCuO5. The heat capacity shows two peaks at the antiferromagnetic transitions temperatures TN1∼ 5 K and TN2∼ 23 K. For the appearing of the extraordinary polarization ΔP in Sm2BaCuO5 we have considered the single-ion magnetostriction mechanism. ΔP is zero without magnetic field. An external magnetic field h induces an electric polarization ΔP below TN2 which varies linearly with h showing a linear magnetoelectric effect. Below TN1ΔP decreases due to ordering of the Sm-sublattice. There are some discrepancies in the experimental data for ΔP(T,h) which we will try to clarify. In addition, the temperature and magnetic field dependence of the dielectric constant is discussed. The observed maximum value of the peak at TN2 shifts to smaller temperature values and increases with increasing external magnetic field.

Enhancement of the Magnetoelectric Effect Using the Dynamic Jahn-Teller Effect in a Transition-Metal Complex.

In this Letter, a novel mechanism to enhance the magnetoelectric (ME) coupling between electric polarization and magnetism using the dynamic Jahn-Teller (JT) effect is demonstrated. Electric polarization of over 100 μC/m^{2} is induced by the magnetic field owing to the second-order ME effect in the noncentrosymmetric transition metal complex [Mn^{III}(taa)]. This appearance of electric polarization does not require magnetic order in contrast to the linear ME effect in ME multiferroic materials. The value of the electric polarization is 1 order larger than that induced by the second-order ME effect, which originates from the p-d hybridization. Our calculation, taking into account the single-ion-type magnetic anisotropy originating from the spin-orbit interaction and ferrodistortive intermolecular interaction, verifies that the alignment of the JT distortion by the magnetic field results in the large electric polarization observed. Thus, our results provide a new method to gain strong ME coupling by tuning the atomic displacement using a magnetic field.

Absence of induced magnetic monopoles in Maxwellian magnetoelectrics

The electromagnetic response of topological insulators is governed by axion electrodynamics, which features a topological magnetoelectric term in the Maxwell equations. As a consequence magnetic fields become the source of electric fields and vice versa, a phenomenon that is general for any material exhibiting a linear magnetoelectric effect. Axion electrodynamics has been associated with the possibility to create magnetic monopoles, in particular, by an electrical charge that is screened above the surface of a magnetoelectric material. Here we explicitly solve for the electromagnetic fields in this geometry and show that while vortexlike magnetic screening fields are generated by the electrical charge their divergence is identically zero at every point in space, which implies an absence of induced magnetic monopoles. Nevertheless magnetic image charges can be made explicit in the problem, and even if no bound state with electric charges yielding a dyon arises, a dyonlike angular momentum follows from our analysis. Because of its dependence on the dielectric constant this angular momentum is not quantized, which is consistent with a general argument that precludes magnetic monopoles to be generated in Maxwell magnetoelectrics. We also solve for topologically protected zero modes in the Dirac equation induced by the point charge. Since the induced topological defect on the topological insulator's surface carries an electric charge as a result of the axion term, these zero modes are not self-conjugated.

Microscopic origin of the spin-induced linear and quadratic magnetoelectric effects

Understanding of the intimate cross-coupling between electric and magnetic degrees of freedom in solids usually requires sophisticated models and time-consuming calculation methods. Instead of macroscopic symmetry analysis, we present a simple but general approach to explore the microscopic mechanism of magnetoelectric (ME) effects in magnetic ordered materials based on local spin and lattice symmetry analysis. Our methods are successfully applied to Cr$_2$O$_3$ and orthorhombic RMnO$_3$ with linear and quadratic ME effects, respectively. We revealed all the possible microscopic origins of every non-zero ME coefficients that cannot be easily fulfilled by other theoretical methods. Moreover, the contribution from each mechanism can be located down to specific spins or spin pairs. Our theoretical approach is capable of providing a detailed guide to explore rich spin-induced magnetoelectrics with strong ME effects.

Symmetry Analysis of Magnetoelectric Effects in Perovskite-Based Multiferroics.

In this article, we performed symmetry analysis of perovskite-based multiferroics: bismuth ferrite (BiFeO3)-like, orthochromites (RCrO3), and Ruddlesden–Popper perovskites (Ca3Mn2O7-like), being the typical representatives of multiferroics of the trigonal, orthorhombic, and tetragonal crystal families, and we explored the effect of crystallographic distortions on magnetoelectric properties. We determined the principal order parameters for each of the considered structures and obtained their invariant combinations consistent with the particular symmetry. This approach allowed us to analyze the features of the magnetoelectric effect observed during structural phase transitions in BixR1−xFeO3 compounds and to show that the rare-earth sublattice has an impact on the linear magnetoelectric effect allowed by the symmetry of the new structure. It was shown that the magnetoelectric properties of orthochromites are attributed to the couplings between the magnetic and electric dipole moments arising near Cr3+ ions due to distortions linked with rotations and deformations of the CrO6 octahedra. For the first time, such a symmetry consideration was implemented in the analysis of the Ruddlesden–Popper structures, which demonstrates the possibility of realizing the magnetoelectric effect in the Ruddlesden–Popper phases containing magnetically active cations, and allows the estimation of the conditions required for its optimization.