Magnetoelectric effect in perovskite quantum paraelectric EuTiO3

On the basis of successful theoretical explanation of the observed large magnetic-field effect (by ∼7% with 1.5 T) on the dielectric constant below the Néel temperature T_N of 5.5 K, we have demonstrated convincingly the magnetoelectric effect in an antiferromagnetic quantum paraelectric EuTiO₃ system. The mutual control of electric and magnetic properties is revealed by the variation of the electric-field-induced polarization with applied magnetic fields as well as the change of the magnetic-field-induced spin moments under the control of electric fields. It is found that the applied electric field (magnetic field) acts like a fictitious magnetic field (electric field) on the EuTiO₃ system. The magnetoelectric susceptibility is deduced to be proportional to the product of the magnetization, electrical polarization, magnetic susceptibility and dielectric susceptibility.     

Magnetoelectric effect and magnetic dynamics in the Gd2CuO4 antiferromagnet

The magnetoelectric effect and the magnetic dynamics in Gd₂CuO₄ have been studied using a phenomenological approach and group-theory methods. Vector order parameters are introduced based on four magnetic sublattices. Invariant products of the order parameters are determined, from which the thermodynamic potential density is constructed. Using the spin-wave representation, the calculations can be significantly simplified and the ground orientation magnetic state can be presumably determined. The magnetic dynamics is described by the Landau-Lifshitz equations, from which the antiferromagnetic resonance frequency and the dynamic susceptibilities, namely, magnetic, antiferromagnetic, magnetoelectric, and antiferroelectric susceptibilities are found. The frequency and the susceptibility are shown to be controlled by applied electric field.     

复合多铁链的磁电耦合行为与外场调控

对含有界面磁电耦合的有限长铁电-铁磁多铁链体系进行了研究,基于矢量离散化思想,构建了描述其磁电性质的微观海森伯模型.利用传递矩阵方法获得了磁化强度、电极化强度、磁电化率等关键热力学量的解析表达式,重点探讨了界面磁电耦合、外场以及单离子各向异性对体系磁电耦合行为的影响和调控.研究结果表明,界面磁电耦合对体系的磁化强度和电极化强度均起促进作用.电场驱动下的电致磁电化率具有更强的磁电关联效应,预示着外电场能够有效地调控体系的磁性行为.而在磁致磁电化率中观察到的低温峰主要源于外磁场的诱导.此外,在高电场作用下体系比热容还呈现出有趣的三峰结构,这种三峰结构是自旋态的热激发以及电偶极矩的电场和温度共同激发导致的.     

Study of magnetoelectric coupling effect in the hexagonal ferroelectromagnet

Soft-mode theory based on Diffour model for ferroelectric subsystem, and mean-field theory as well as Heisenberg model for antiferromagnetic subsystem are utilized to investigate the magnetoelectric coupling effect in a hexagonal ferroelectromagnet, in which the ferroelectric and antiferromagnetic orders spontaneously coexist below a certain temperature. An anomaly of polarization at the magnetic transition temperature is ascribed to the effect of magnetoelectric coupling. The magnetic excitation has also been studied by spin-wave theory over the three-sublattice model. It is demonstrated that role of magnetoelectric coupling effect is not only related with the strength of magnetoelectric coupling but also special spin lattice structure. Our results show the magnetic specific heat induced by magnetic excitation experiences a suppression by the magnetoelectric coupling.     

Magnetoelectric effect in antiferromagnetic crystals

Magnetoelectric experiments provide information on spin configurations, critical indices and microscopic ionic interactions. The basic theory of the magnetoelectric effect in antiferromagnets is rederived in this article and extended to situations in which there is an external magnetic field including the spin-flop phase. It is found that measurements of the magnetoelectric tensor α as a function of field in the antiferromagnetic and spin-flop phases of an antiferromagnet can provide more complete information in all three categories above. Certain higher-order terms are examined and it is found that it is possible to measure the staggered susceptibility directly in magnetoelectric materials. It is shown that a non-zero value of α causes a tetragonal antiferromagnet to be optically biaxial. A pedagogical discussion of the origins of magnetoelectric effects is given in the Appendix.     

Spatially modulated antiferromagnetic structures in an easy-plane multiferroic

Possible types of spatially modulated periodic antiferromagnetic structures in a uniaxial rhombohedral multiferroic with BiFeO₃ crystal symmetry have been studied depending on the ratio of the uniaxial anisotropy and magnetoelectric interaction parameters. It has been shown that, along with symmetric cycloid antiferromagnetic structures with zero transverse component of the antiferromagnetism vector, there are changes in the antiferromagnetism vector direction with both right and left nonzero components of the antiferromagnetic moment, which are branched from the high-symmetry spatially modulated distribution. These solutions degenerate into a homogeneous state at a critical value of the normalized easy-plane anisotropy parameter. The existence of the found spatially inhomogeneous antiferromagnetic states with an incommensurate period can lead to additional features in magnetoelectric properties in multiferroics of the type under consideration near magnetic phase transitions in electric and magnetic fields.     

High-frequency properties of KNiPO<Subscript>4</Subscript> in alternating magnetic and electric fields

The dependences of the antiferromagnetic resonance frequencies on the constant magnetic field H and constant electric field E are calculated for a KNiPO₄ crystal with spontaneous electric polarization and antiferromagnetic order. It is demonstrated that the KNiPO₄ crystal is characterized by an exchange-enhanced effect of the electric field E on the antiferromagnetic resonance frequencies. This effect is not revealed in the magnetoelectric materials studied earlier. It is established that oscillations of both magnetization and electric polarization exhibit resonance response at antiferromagnetic resonance frequencies. The expressions for these responses in alternating magnetic and electric fields are presented.     

Domain-based magnetoelectric studies for single crystals of chromium oxide

As is well known, the sign of parallel magnetoelectric susceptibility for chromium oxide can be positive or negative both depending on prehistory of the sample, but it is always opposite to the perpendicular susceptibility. In order to explain this behaviour, the concept of antiferromagnetic domains depending on the existence of two possibilities spin orientation in a magnetic unit cell was invoked both by Rado and Astrov. The authors have carried out detailed studies of domain-based magnetoelectric effect for Cr₂O₃ and the results are presented in this communication. Investigations were carried out both for static and dynamic effect. For static measurements the dielectric constant method developed earlier has been used. The domain pattern in the sample is altered by cooling in simultaneous presence of different electric (E) and magnetic (B) fields from paramagnetic state to the ordered state, and the magnetoelectric susceptibility evaluated. From the measurements it is concluded that the deciding parameter of magnetoelectric susceptibility if product of fields EB for low fields as reported by Martin and Anderson. For high fields, the electric field seems to play a more significant role, and magnetoelectric susceptibility is a function of E²B used for cooling. Static measurements are also extended to low temperatures for parallel susceptibility for the sample with largest magnetoelectric susceptibility. In the temperature range used (90 K to room temperature) the change in susceptibility observed is not very significant, a fact which is hard to explain. Data about the effect of variation of cooling rate and step function cooling is also presented, and it is concluded, though not in a definite manner, that rectangular step function cooling is as effective as continuous rate cooling in deciding magnetoelectric susceptibility of the sample.For dynamic studies, again the dielectric constant method is used, and measurements are reported at different frequencies for a sample with possibly a large number of domains. Two resonant peaks in the dielectric constant are observed and they are tentatively explained on the basis of domain wall resonance.     

Anisotropy of antiferromagnetic 180° domains in magnetoelectric LiMPO<Subscript>4</Subscript> (M = Fe,Co, Ni)

An unusual variety of magnetic, magnetoelectric and ferrotoroidic properties was observed in the lithium-orthophosphates LiMPO₄ with M = Fe, Co, Ni by optical second harmonic generation. In spite of a largely similar magnetic and crystallographic structure the compounds exhibit pronounced differences in the topology of antiferromagnetic 180° domains. In LiCoPO₄ the antiferromagnetic domains coexist with ferrotoroidic, i.e., magnetic vortex domains. For LiNiPO₄ it was shown that the weak ferrimagnetic moment of the LiMPO₄ compounds along the spin direction is rigidly coupled to the AFM order parameter so that the sign of the magnetoelectric effect is reversed by a magnetic field only. Further effects of a static magnetic field on the system are discussed.     

Effect of electric field on the magnetic characteristics of a ferromagnetic nanosemiconductor

A theory is developed to describe the effect of an electric field on the magnetization of a thin ferromagnetic semiconductor plate. It is shown that the magnetic moment density is nonuniform under these conditions and that the total magnetic moment and its density depend on the electric field and the temperature. An electric field is found to increase the Curie temperature, and an inflection point is detected in the temperature dependence of the derivative of the total magnetic moment with respect to temperature.     

Conventional and rotating magnetoelectric effect of a half-filled spin-electron model on a doubly decorated square lattice

A conventional and rotating magnetoelectric effect of a half-filled spin-electron model on a doubly decorated square lattice is investigated by exact calculations. An importance of the electron hopping and spatial orientation of the electric field upon a magnetoelectric effect is examined in detail. A critical temperature may display one or two consecutive round maxima as a function of the electric field. Although the rotating magnetoelectric effect (RME) does not affect the ground-state ordering, the pronounced RME is found close to a critical temperature of continuous phase transition. It is shown that RME is amplified upon strengthening of the electric field, which additionally supports thermal fluctuations in destroying a spontaneous antiferromagnetic long-range order.     

Ferroelectricity of polycrystalline GdMnO3 and multifold magnetoelectric responses

The multiferroic behaviors of polycrystalline GdMnO₃ are investigated by focusing on the ferroelectric response to the spin ordering sequence and external magnetic field. The polarization current shows sensitive response to both the Mn cycloidal spin order and Gd antiferromagnetic (AFM) order. The complicated magnetoelectric behaviors suggest that the Mn cycloidal spin order can be modulated by the Gd AFM order at low temperature via the Gd–Mn spin interaction. Due to the possible disorder and defects in polycrystalline nature, polycrystalline GdMnO₃ may accommodate the cycloidal spin order in addition to the A-type AFM order at Mn sites, as illustrated by simulation based on the two-orbit double exchange model and measured hysteresis loops of polarization against magnetic field, indicating the switching of the ferroelectric domains coupled with the magnetic domains in response to magnetic field.     

On the interpretation of magnetization data for antiferromagnetic nanoparticles

We have investigated the influence of anisotropy on the magnetization curves of antiferromagnetic nanoparticles. We show that if such curves are analyzed in a conventional way, i.e. using a Langevin function in combination with a linear term, this usually results in good quality fits, but with an apparent temperature dependence of parameters such as the magnetic moment per particle and the antiferromagnetic susceptibility. In order to avoid the problems associated with anisotropy as well as volume/moment distributions we propose that the initial susceptibility is used when analyzing the temperature dependence of the magnetic moment.     

Lumped-equivalent circuit model for multi-stage cascaded magnetoelectric dual-tunable bandpass filter

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

Electric field control of nonvolatile four-state magnetization at room temperature

We find the realization of large converse magnetoelectric (ME) effects at room temperature in a magnetoelectric hexaferrite Ba0.52Sr2.48Co2Fe24O41 single crystal, in which rapid change of electric polarization in low magnetic fields (about 5 mT) is coined to a large ME susceptibility of 3200 ps/m. The modulation of magnetization then reaches up to 0.62μ(B)/f.u. in an electric field of 1.14 MV/m. We find further that four ME states induced by different ME poling exhibit unique, nonvolatile magnetization versus electric field curves, which can be approximately described by an effective free energy with a distinct set of ME coefficients.     

Induced moment antiferromagnet in an external magnetic field—II: Green's function theory

A two level two sublattice antiferromagnetic induced moment system is examined in the Green's function theory in the random phase approximation. Attentions are drawn to the effects of an externally applied magnetic field. It is shown that a “soft mode” behavior occurs at the transition field similar to that observed at the transition temperature in the absence of a field. The transition becomes first order in the RPA. The sublattice magnetizations and the transition field are significantly lowered compared to the molecular field theory results.     

Specificity of magnetoelectric effects in a new GdMnO<Subscript>3</Subscript> magnetic ferroelectric

A complex study of the magnetic, electric, magnetoelectric, and magnetoelastic properties of GdMnO₃ single crystals has been performed in the low-temperature region in strong pulsed magnetic fields up to 200 kOe. An anomaly of the dielectric constant along the a axis of a crystal has been found at 20 K, where a transition from an incommensurate modulated phase to a canted antiferromagnetic phase, as well as electric polarization along the a and b axes of the crystal induced by the magnetic field H‖ b (H_cr ～ 40 kOe), is observed. Upon cooling the crystal in an electric field, the magnetic-field-induced electric polarization changes its sign depending on the sign of the electric field. The occurrence of the electric polarization is accompanied by anisotropic magnetostriction, which points to a correlation between the magnetoelectric and magnetoelastic properties. Based on these results, it has been stated that GdMnO₃ belongs to a new family of magnetoelectric materials with the perovskite structure.     

Correlated giant dielectric peaks and antiferromagnetic transitions near room temperature in pure and alkali-doped BaMnO(3-δ)

We report structural, magnetic, dielectric and thermal properties of single-crystal BaMnO(2.99) and its derivatives BaMn(0.97)Li(0.03)O(3) and Ba(0.97)K(0.03)MnO(3). The hexagonal 15R-BaMnO(2.99) perovskite phase is a known antiferromagnetic insulator that orders at a Néel temperature T(N) = 220 K. We find dilute Li and K doping change the ratio of cubic to hexagonal layers and cause drastic changes in the dielectric and magnetic properties. Unusually large high-temperature magnetoelectric shifts (up to 85%) are observed near temperatures at which pronounced peaks in the dielectric constant are observed for applied electric fields along either the c or a axis, respectively. The temperatures of the dielectric peaks are strongly correlated with anomalies in the c- or a-axis magnetic susceptibility and the specific heat for all compositions studied. All our data suggest that the strongly anisotropic magnetic and dielectric anomalies (which occur near, or above room temperature) originate from the same Mn ion sites, which implies these materials form an exceptional class of magnetoelectrics.     

Magnetic and structural phase transitions in YMn<Subscript>2</Subscript>O<Subscript>5</Subscript> ferromagnetoelectric crystals induced by a strong magnetic field

Magnetic, magnetoelectric, and magnetoelastic properties of YMn₂O₅ ferromagnetoelectric single-crystals are investigated in strong pulsed magnetic fields of up to 250 kOe and in static magnetic fields of up to 12 kOe. It is found that, in YMn₂O₅ at T < T_N=42 K, a transverse weakly ferromagnetic moment of σ ₀=0.8 G cm³/g exists that is oriented along axis a and is attributed to the magnetoelectric interaction. When a magnetic field is directed along axis b, which is likely to be the axis of antiferromagnetism, a spin-flop transition is observed that is accompanied by jumps in magnetostriction and electric polarization. When a magnetic field is directed along axis a, the temperature of ferroelectric transition shifts from 20 to 25 K at H≈200 kOe. A theoretical analysis of the experimental results is given within phenomenological theory with regard to the fact that a YMn₂O₅ compound belongs to noncollinear antiferromagnetic crystals even in the exchange approximation.     

Ferroelectricity Driven by Dzyaloshinskii-Moriya Interaction in an Anisotropic Heisenberg Antiferromagnetic Chain

We have made a theoretical study on the ferroelectricity and ferromagnetism in an antiferromagnetic Heisenberg chain with a Dzyaloshinskii-Moriya interaction which may induce ferroelectricity in some low-dimensional magnetic materials. Based on the transfer-matrix method, we obtain the analytical results of the average magnetization, polarization and magnetic susceptibility. And these physical quantities as functions of temperature and applied field are discussed respectively under various conditions. We find that the temperature dependence of the magnetic susceptibility exhibits different responses for the external field applied along the chain and perpendicular to the chain, demonstrating the important role of anisotropy.