Ferroelectricity induced by spin-dependent metal-ligand hybridization in Ba₂CoGe₂O₇

Magnetic structure of the noncentrosymmetric magnet Sr2MnSi2O7 through irreducible representation and magnetic space group analyses

Magnetic structures of the noncentrosymmetric magnet Sr2MnSi2O7 were examined through neutron diffraction for powder and single-crystalline samples, as well as magnetometry measurements. All allowed magnetic structures for space group P421m with the magnetic wavevector qm = (0, 0, ½) were refined via irreducible representation and magnetic space group analyses. The compound was refined to have in-plane magnetic moments within the magnetic space group Cmc21.1'c (No. 36.177) under zero field, which can be altered to P212121.1'c (No. 19.28) above μ0H = 0.067 (5) T to align induced weak-ferromagnetic components within one layer on the ab plane. All refined parameters are provided following the recent framework based upon the magnetic space group, which better conveys when exchanging crystallographic information for commensurate magnetic structures.

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.

Antiferromagnetic to Ferrimagnetic Phase Transition and Possible Phase Coexistence in Polar Magnets (Fe1-xMnx)2Mo3O8 (0 ≤ x ≤ 1)

In the present work, the magnetic properties of a single crystal (Fe_1-xMn_x)₂Mo₃O₈ (0 ≤ x ≤ 1) have been studied by performing extensive measurements. A detailed magnetic phase diagram is built up, in which the antiferromagnetic state dominates for x ≤ 0.25 and the ferrimagnetic phase arises for x ≥ 0.3. Meanwhile, a sizeable electric polarization of spin origin is commonly observed in all samples, no matter what the magnetic state is. For the samples hosting a ferrimagnetic state, square-like magnetic hysteresis loops are revealed, while the remnant magnetization and coercive field can be tuned drastically by simply varying the Mn content or temperature. A possible coexistence of the antiferromagnetic and ferrimagnetic phases is proposed to be responsible for the remarkable modulation of magnetic properties in the samples.

Double dome structure of the Bose-Einstein condensation in diluted S = 3/2 quantum magnets

Bose-Einstein condensation (BEC) in quantum magnets, where bosonic spin excitations condense into ordered ground states, is a realization of BEC in a thermodynamic limit. Although previous magnetic BEC studies have focused on magnets with small spins of S ≤ 1, larger spin systems potentially possess richer physics because of the multiple excitations on a single site level. Here, we show the evolution of the magnetic phase diagram of S = 3/2 quantum magnet Ba₂CoGe₂O₇ when the averaged interaction J is controlled by a dilution of magnetic sites. By partial substitution of Co with nonmagnetic Zn, the magnetic order dome transforms into a double dome structure, which can be explained by three kinds of magnetic BECs with distinct excitations. Furthermore, we show the importance of the randomness effects induced by the quenched disorder: we discuss the relevance of geometrical percolation and Bose/Mott glass physics near the BEC quantum critical point.

Coexistence and Coupling of Spin-Induced Ferroelectricity and Ferromagnetism in Perovskites

Spin-induced ferroelectricity usually does not occur in perovskites with simple collinear magnetic structures. Here, we demonstrate that in even-layer perovskite systems, some common distortion modes involving octahedral rotation and Jahn-Teller distortion can break the inversion symmetry, allowing the emergence of spin-dependent out-of-plane polarization in a simple magnetic structure. Such spin-induced ferroelectricity is very common in double-perovskite systems and can coexist with ferromagnetism or ferrimagnetism above room temperature. We explain its origin by modifying the spin-dependent p-d hybridization mechanism. Our Letter provides a universal design for two-dimensional multiferroics and enables the control of polarization by means of a magnetic field.

Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice

Topology, an important branch of mathematics, is an ideal theoretical tool to describe topological states and phase transitions. Many topological concepts have found their physical entities in real or reciprocal spaces identified by topological invariants, which are usually defined on orientable surfaces, such as torus and sphere. It is natural to investigate the possible physical realization of more intriguing non-orientable surfaces. Herein, we show that the set of spin-induced ferroelectric polarizations in cubic perovskite oxides AMn3Cr4O12 (A = La and Tb) reside on the topological Roman surface-a non-orientable two-dimensional manifold formed by sewing a Möbius strip edge to that of a disc. The induced polarization may travel in a loop along the non-orientable Möbius strip or orientable disc, depending on the spin evolution as controlled by an external magnetic field. Experimentally, the periodicity of polarization can be the same or twice that of the rotating magnetic field, which is consistent with the orientability of the disc and the Möbius strip, respectively. This path-dependent topological magnetoelectric effect presents a way to detect the global geometry of a surface and deepens our understanding of topology in both mathematics and physics.

High-Field Magnetoelectric and Spin-Phonon Coupling in Multiferroic (NH4)2[FeCl5·(H2O)]

We combine high field polarization, magneto-infrared spectroscopy, and lattice dynamics calculations with prior magnetization to explore the properties of (NH₄)₂[FeCl₅·(H₂O)]─a type II molecular multiferroic in which the mixing between charge, structure, and magnetism is controlled by intermolecular hydrogen and halogen bonds. Electric polarization is sensitive to the series of field-induced spin reorientations, increasing linearly with the field and reaching a maximum before collapsing to zero across the quasi-collinear to collinear-sinusoidal reorientation due to the restoration of inversion symmetry. Magnetoelectric coupling is on the order of 1.2 ps/m for the P∥c, H∥c configuration between 5 and 25 T at 1.5 K. In this range, the coupling takes place via an orbital hybridization mechanism. Other forms of mixing are active in (NH₄)₂[FeCl₅·(H₂O)] as well. Magneto-infrared spectroscopy reveals that all of the vibrational modes below 600 cm^-1 are sensitive to the field-induced transition to the fully saturated magnetic state at 30 T. We analyze these local lattice distortions and use frequency shifts to extract spin-phonon coupling constants for the Fe-O stretch, Fe-OH₂ rock, and NH₄⁺ libration. Inspection also reveals subtle symmetry breaking of the ammonium counterions across the ferroelectric transition. The coexistence of such varied mixing processes in a platform with intermolecular hydrogen- and halogen-bonding opens the door to greater understanding of multiferroics and magnetoelectrics governed by through-space interactions.

Direct Evidence for an Intermediate Multiferroic Phase in LiCuFe2(VO4)3

Magnetic susceptibility, specific heat, dielectric, and electric polarization of LiCuFe₂(VO₄)₃ have been investigated. Two sequential antiferromagnetic transitions at T_N1 ∼ 9.95 K and T_N2 ∼ 8.17 K are observed under zero magnetic field. Although a dielectric peak at T_N1 is clearly identified, the measured pyroelectric current also exhibits a sharp peak at T_N1, implying the magnetically relevant ferroelectricity. Interestingly, another pyroelectric peak around T_N2 with an opposite signal is observed, resulting in the disappearance of electric polarization below T_N2. Besides, the electric polarization is significantly suppressed in response to external magnetic field, evidencing a remarkable magnetoelectric effect. These results suggest the essential relevance of the magnetic structure with the ferroelectricity in LiCuFe₂(VO₄)₃, deserving further investigation of the underlying mechanism.

In Situ Electric-Field Control of THz Nonreciprocal Directional Dichroism in the Multiferroic Ba_{2}CoGe_{2}O_{7}

Nonreciprocal directional dichroism, also called the optical-diode effect, is an appealing functional property inherent to the large class of noncentrosymmetric magnets. However, the in situ electric control of this phenomenon is challenging as it requires a set of conditions to be fulfilled: Special symmetries of the magnetic ground state, spin excitations with comparable magnetic- and electric-dipole activity, and switchable electric polarization. We demonstrate the isothermal electric switch between domains of Ba_{2}CoGe_{2}O_{7} possessing opposite magnetoelectric susceptibilities. Combining THz spectroscopy and multiboson spin-wave analysis, we show that unbalancing the population of antiferromagnetic domains generates the nonreciprocal light absorption of spin excitations.

Electrical Switching of the Nonreciprocal Directional Microwave Response in a Triplon Bose-Einstein Condensate

We present a microwave electron spin resonance study of the quantum spin dimer system TlCuCl_{3}, which shows the magnetic-field-induced ordering with both antiferromagnetic spin order and ferroelectricity by the Bose-Einstein condensation (BEC) of triplon quasiparticles. Our main achievement is an electrical switching of the nonreciprocal directional microwave response in the triplon BEC phase. High-speed directional control of microwave absorption by applying an electric field has been accomplished in this Letter. The strength of the observed nonreciprocal microwave response well agrees with the calculation based on Kubo theory with the parameters, evaluated from the static electric polarization in this material.

Controlling of light with electromagnons

Magnetoelectric coupling in multiferroic materials opens new routes to control the propagation of light. The new effects arise due to dynamic magnetoelectric susceptibility that cross-couples the electric and magnetic fields of light and modifies the solutions of Maxwell equations in media. In this paper, two major effects will be considered in detail: optical activity and asymmetric propagation. In case of optical activity the polarization plane of the input radiation rotates by an angle proportional to the magnetoelectric susceptibility. The asymmetric propagation is a counter-intuitive phenomenon and it represents different transmission coefficients for forward and backward directions. Both effects are especially strong close to resonance frequencies of electromagnons, i. e. excitations in multiferroic materials that reveal simultaneous electric and magnetic character.

Spiral spin structures and skyrmions in multiferroics

In this article, we focus on (1) type-II multiferroics driven by spiral spin orderings and (2) magnetoelectric couplings in multiferroic skyrmion-hosting materials. We present both phenomenological understanding and microscopic mechanisms for spiral spin state, which is one of the essential starting points for type-II multiferroics and magnetic skyrmions. Two distinct mechanisms of spiral spin states (frustration and Dzyaloshinskii–Moriya [DM] interaction) are discussed in the context of the lattice symmetry. We also discuss the spin-induced ferroelectricity on the basis of the symmetry and microscopic atomic configurations. We compare two well-known microscopic models: the generalized inverse DM mechanism and the metal-ligand d-p hybridization mechanism. As a test for these models, we summarize the multiferroic properties of a family of triangular-lattice antiferromagnets. We also give a brief review of the magnetic skyrmions. Three types of known skyrmion-hosting materials with multiferroicity are discussed from the view point of crystal structure, magnetism, and origins of the magnetoelectric couplings. For exploration of new skyrmion-hosting materials, we also discuss the theoretical models for stabilizing skyrmions by magnetic frustration in centrosymmetric system. Several basic ideas for material design are given, which are successfully demonstrated by the recent experimental evidences for the skyrmion formation in centrosymmetric frustrated magnets.

Single-phase multiferroics: new materials, phenomena, and physics

Multiferroics, where multiple ferroic orders coexist and are intimately coupled, promise novel applications in conceptually new devices on one hand, and on the other hand provide fascinating physics that is distinctly different from the physics of high-T_C superconductors and colossal magnetoresistance manganites. In this mini-review, we highlight the recent progress of single-phase multiferroics in the exploration of new materials, efficient roadmaps for functionality enhancement, new phenomena beyond magnetoelectric coupling, and underlying novel physics. In the meantime, a slightly more detailed description is given of several multiferroics with ferrimagnetic orders and double-layered perovskite structure and also of recently emerging 2D multiferroics. Some emergent phenomena such as topological vortex domain structure, non-reciprocal response, and hybrid mechanisms for multiferroicity engineering and magnetoelectric coupling in various types of multiferroics will be briefly reviewed.

Magnetoelectricity in multiferroics: a theoretical perspective

The key physical property of multiferroic materials is the existence of coupling between magnetism and polarization, i.e. magnetoelectricity. The origin and manifestations of magnetoelectricity can be very different in the available plethora of multiferroic systems, with multiple possible mechanisms hidden behind the phenomena. In this review, we describe the fundamental physics that causes magnetoelectricity from a theoretical viewpoint. The present review will focus on mainstream physical mechanisms in both single-phase multiferroics and magnetoelectric heterostructures. The most recent tendencies addressing possible new magnetoelectric mechanisms will also be briefly outlined.

Two types of B-site ordered structures of the double perovskite Y2CrMnO6: experimental identification and first-principles study

From the ABF images, first-principles calculations and image simulations, we conclude that Y₂CrMnO₆ has rock-salt ordered and layer ordered structures.

Magnetic structure and properties of centrosymmetric twisted-melilite K2CoP2O7

Twisted-melilite dipotassium cobalt pyrophosphate (K₂CoP₂O₇, P4₂/mnm, #136), originally reported by Gabelica-Robert (1981), was synthesized in powder form by a standard solid-state reaction route. The magnetic properties of the material were studied by magnetometry and its magnetic structure determined using neutron powder diffraction for the first time. Below T_N = 11 K, the material adopts a G-type antiferromagnetic structure with moments aligned in the ab-plane (magnetic space group Pn'nm, #58.3.473). Ab initio calculations were performed to examine the isotropic magnetic spin exchange parameters as well as the preferred direction of magnetic moments due to spin-orbit coupling. The relationship between crystal structure geometry and the strength of the magnetic interactions was examined and compared to those of melilite-type Sr₂CoGe₂O₇.

The crucial role of Mn spiral spin order in stabilizing the Dy–Mn exchange striction in multiferroic DyMnO3

Mn spiral spin ordering can be a prerequisite for the symmetric Dy–Mn exchange striction in DyMnO₃.

Understanding the multiferroicity in TmMn2O5 by a magnetically induced ferrielectric model

The magnetically induced electric polarization behaviors in multiferroic TmMn₂O₅ in response to varying temperature and magnetic field are carefully investigated by means of a series of characterizations including the high precision pyroelectric current technique. Here polycrystalline rather than single crystal samples are used for avoiding the strong electrically self-polarized effect in single crystals, and various parallel experiments on excluding the thermally excited current contributions are performed. The temperature-dependent electric polarization flop as a major character is identified for different measuring paths. The magneto-current measurements indicate that the electric polarization in the low temperature magnetic phase region has different origin from that in the high temperature magnetic phase. It is suggested that the electric polarization does have multiple components which align along different orientations, including the Mn³⁺-Mn⁴⁺-Mn³⁺ exchange striction induced polarization P_MM, the Tm³⁺-Mn⁴⁺-Tm³⁺ exchange striction induced polarization P_TM, and the low temperature polarization P_LT probably associated with the Tm³⁺ commensurate phase. The observed electric polarization flop can be reasonably explained by the ferrielectric model proposed earlier for DyMn₂O₅, where P_MM and P_TM are the two antiparallel components both along the b-axis and P_LT may align along the a-axis. Finally, several issues on the unusual temperature dependence of ferroelectric polarizations are discussed.

MAGNDATA: towards a database of magnetic structures. I. The commensurate case

A free web page under the name MAGNDATA, which provides detailed quantitative information on more than 400 published magnetic structures, has been developed and is available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. This first article is devoted to explaining the information available on commensurate magnetic structures. Each magnetic structure is described using magnetic symmetry, i.e. a magnetic space group (or Shubnikov group). This ensures a robust and unambiguous description of both atomic positions and magnetic moments within a common unique formalism. A non-standard setting of the magnetic space group is often used in order to keep the origin and unit-cell orientation of the paramagnetic phase, but a description in any desired setting is possible. Domain-related equivalent structures can also be downloaded. For each structure its magnetic point group is given, and the resulting constraints on any macroscopic tensor property of interest can be consulted. Any entry can be retrieved as a magCIF file, a file format under development by the International Union of Crystallography. An online visualization tool using Jmol is available, and the latest versions of VESTA and Jmol support the magCIF format, such that these programs can be used locally for visualization and analysis of any of the entries in the collection. The fact that magnetic structures are often reported without identifying their symmetry and/or with ambiguous information has in many cases forced a reinterpretation and transformation of the published data. Most of the structures in the collection possess a maximal magnetic symmetry within the constraints imposed by the magnetic propagation vector(s). When a lower symmetry is realized, it usually corresponds to an epikernel (isotropy subgroup) of one irreducible representation of the space group of the parent phase. Various examples of the structures present in this collection are discussed.

Heuristic Description of Magnetoelectricity of Cu2OSeO3

CuO2SeO3 is an insulating material that hosts topologically nontrivial spin whirls, so-called skyrmions, and exhibits magnetoelectric coupling allowing to manipulate these skyrmions by means of electric fields. We report magnetic force microscopy imaging of the real-space spin structure on the surface of a bulk single crystal of CuO2SeO3. Based on measurements of the electric polarization using Kelvin-probe force microscopy, we develop a heuristic description of the magnetoelectric properties in CuO2SeO3. The model successfully describes the dependency of the electric polarization on the magnetization in all magnetically modulated phases.

Continuous Magnetoelectric Control in Multiferroic DyMnO3 Films with Twin-like Domains

The magnetic control of ferroelectric polarization is currently a central topic in the multiferroic researches, owing to the related gigantic magnetoelectric coupling and fascinating physics. Although a bunch of novel magnetoelectric effect have been discovered in multiferroics of magnetic origin, the manipulation of polarization was found to be fundamentally determined by the microscopic origin in a certain multiferroic phase, hindering the development of unusual magnetoelectric control. Here, we report emergent magnetoelectric control in DyMnO₃/Nb:SrTiO₃ (001) films showing twin-like domain structure. Our results demonstrate interesting magnetically induced partial switch of polarization due to the coexistence of polarizations along both the a-axis and c-axis enabled by the twin-like domain structure in DyMnO₃ films, despite the polarization-switch was conventionally believed to be a one-step event in the bulk counterpart. Moreover, a continuous and periodic control of macroscopic polarization by an in-plane rotating magnetic field is evidenced in the thin films. This distinctive magnetic manipulation of polarization is the consequence of the cooperative action of the twin-like domains and the dual magnetic origin of polarization, which promises additional applications using the magnetic control of ferroelectricity.

Piezomagnetoelectric Effect of Spin Origin in Dysprosium Orthoferrite

The piezomagnetoelectric effect, namely, the simultaneous induction of both the ferromagnetic moment and electric polarization by an application of uniaxial stress, was demonstrated in the nonferroelectric antiferromagnetic ground state of DyFeO(3). The induced electric polarization and ferromagnetic moment are coupled with each other, and monotonically increase with increasing uniaxial stress. The present work provides a new guiding principle for designing multiferroics where its magnetic symmetry is broken by external uniaxial stress.

Uniaxial-stress control of spin-driven ferroelectricity in multiferroic Ba(2)CoGe(2)O(7)

We have demonstrated that spin-driven ferroelectricity in a tetragonal multiferroic Ba(2)CoGe(2)O(7) is controlled by applying uniaxial stress. We found that the application of compressive stress along the [110] direction leads to a 45° or 135° rotation of the sublattice magnetization of the staggered antiferromagnetic order in this system. This allows the spontaneous electric polarization to appear along the c axis. The present study suggests that an application of anisotropic stress, which is the simplest way to control symmetry of matter, can induce a variety of cross-correlated phenomena in spin-driven multiferroics.

Spin and orbital orderings behind multiferroicity in delafossite and related compounds

Coupling between noncollinear magnetic ordering and ferroelectricicty in magnetoelectric multiferroics has been extensively studied in the last decade. Delafossite family compounds with triangular lattice structure provide a great opportunity to study the coupling between spin and electric dipole in multiferroics due to the variety of magnetic phases with different symmetry. This review introduces the magnetic and ferroelectric phase transitions in delafossite ferrites, CuFe(1-x)X(x)O(2) (X = Al, Ga), AgFeO(2) and the related compound α-NaFeO(2). In CuFeO(2), the ferroelectric phase appears under a magnetic field or chemical substitution. The proper screw magnetic ordering with the magnetic point group 21', which has been determined by detailed analysis in neutron diffraction experiments, induces the ferroelectric polarization along the monoclinic b axis in CuFeO2. The cycloidal magnetic orderings are realized in AgFeO(2) and α-NaFeO(2), which are of the point group m1' allowing polarization in the ac plane. The emergence of ferroelectric polarization can be explained by both the extended inverse Dzyaloshinsky-Moriya effect and the d − p hybridization mechanism. These mechanisms are supported by experimental evidence in CuFe(1-x)Ga(x)O2. The polarized neutron diffraction experiment demonstrated one-to-one correspondence between ferroelectric polarization and spin helicity, S(i) × S(j). The incommensurate orbital ordering with 2 Q wave vector, observed by the soft x-ray resonant diffraction experiment, proved that the spin-orbit interaction ties spin and orbital orders to each other, playing a crucial role for the emergence of ferroelectricity in CuFe(1-x)Ga(x)O2.

Novel multiferroicity in GdMnO3 thin films with self-assembled nano-twinned domains

There have been many interests in exploring multiferroic materials with superior ferroelectric and magnetic properties for the purpose of developing multifunctional devices. Fabrication of thin films plays an important role in achieving this purpose, since the multiferroicity can be tuned via strain, dimensionality, and size effect, without varying the chemical composition. Here, we report exotic multiferroic behaviors, including high-T_C (~75 K) ferroelectric state, a large spontaneous polarization (~4900 μC/m²) and relatively strong ferromagnetism emerging at ~105 K, in orthorhombic GdMnO₃/SrTiO₃ (001) thin films with self-assembled nano-scale twin-like domains. We propose a possible ab-plane spiral-spin-order phase to be responsible for the large spontaneous polarization in the films, which can only be stabilized by relatively high magnetic field H > 6 T in the bulk crystals. It is suggested that the nano-scale twin-like domain structure is essential for the high temperature ferroelectricity and ferromagnetism of the thin films.

Spin-orbital driven ferroelectricity

We study the effect of octahedron rotation on the electric polarization with spin-orbit coupling. Employing local coordinates to represent the tilting of the ligands' octahedra, we evaluate the electric polarization in a chain of transition metal ions with non-polar octahedron rotation. We find the orbital ordering produced by the ligands' rotation and the spin order, together, determine the polarization features, manifesting that non-vanishing polarization appears in collinear spin order and the direction of polarization is no more restricted in the plane of spin rotation in cycloidal ordering.

Multiferroics of spin origin

Multiferroics, compounds with both magnetic and ferroelectric orders, are believed to be a key material system to achieve cross-control between magnetism and electricity in a solid with minute energy dissipation. Such a colossal magnetoelectric (ME) effect has been an issue of keen interest for a long time in condensed matter physics as well as a most desired function in the emerging spin-related electronics. Here we begin with the basic mechanisms to realize multiferroicity or spin-driven ferroelectricity in magnetic materials, which have recently been clarified and proved both theoretically and experimentally. According to the proposed mechanisms, many families of multiferroics have been explored, found (re-discovered), and newly developed, realizing a variety of colossal ME controls. We overview versatile multiferroics from the viewpoints of their multiferroicity mechanisms and their fundamental ME characteristics on the basis of the recent advances in exploratory materials. One of the new directions in multiferroic science is the dynamical ME effect, namely the dynamical and/or fast cross-control between electric and magnetic dipoles in a solid. We argue here that the dynamics of multiferroic domain walls significantly contributes to the amplification of ME response, which has been revealed through the dielectric spectroscopy. Another related issue is the electric-dipole-active magnetic resonance, called electromagnons. The electromagnons can provide a new stage of ME optics via resonant coupling with the external electromagnetic wave (light). Finally, we give concluding remarks on multiferroics physics in the light of a broader perspective from the emergent electromagnetism in a solid as well as from the possible application toward future dissipationless electronics.

Spin-nematic interaction in the multiferroic compound Ba2CoGe2O7

We demonstrate the existence of the spin-nematic interactions in an easy-plane type antiferromagnet Ba2CoGe2O7 by exploring the magnetic anisotropy and spin dynamics. The combination of neutron scattering and magnetic susceptibility measurements reveals that the origin of the in-plane anisotropy is an antiferro-type interaction of the spin-nematic operator. The relation between the nematic operator and the electric polarization in the ligand symmetry of this compound is presented. The introduction of the spin-nematic interaction is useful to understand the physics of spin and electric dipole in multiferroic compounds.

Electronic ferroelectricity induced by charge and orbital orderings

After the revival of the magnetoelectric effect which took place in the early 2000s, the interest in multiferroic materials displaying simultaneous presence of spontaneous long-range magnetic and dipolar order has motivated an exponential growth of research activity, from both the experimental and theoretical perspectives. Within this context, and relying also on the rigorous formulation of macroscopic polarization as provided by the Berry-phase approach, it has been possible to identify new microscopic mechanisms responsible for the appearance of ferroelectricity. In particular, it has been realized that electronic spin, charge and orbital degrees of freedom may be responsible for the breaking of the space-inversion symmetry, a necessary condition for the appearance of electric polarization, even in centrosymmetric crystal structures. In view of its immediate potential application in magnetoelectric-based devices, many efforts have been made to understand how magnetic orderings may lead to ferroelectric polarization, and to identify candidate materials. On the other hand, the role of charge and orbital degrees of freedom, which have received much less attention, has been predicted to be non-negligible in several cases. Here, we review recent theoretical advances in the field of so-called electronic ferroelectricity, focusing on the possible mechanisms by which charge- and/or orbital-ordering effects may cause the appearance of macroscopic polarization. Generally, a naive distinction can be drawn between materials displaying almost localized electrons and those characterized by a strong covalent character and delocalized electrons. As for the latter, an intuitive understanding of basic mechanisms is provided in the framework of tight-binding model Hamiltonians, which are used to shed light on unusual charge/orbital effects in half-doped manganites, whereas the case of magnetite will be thoroughly discussed in light of recent progress pointing to an electronic origin of its proposed ferroelectric and magnetoelectric properties.

Strong Dzyaloshinskii-Moriya interaction and origin of ferroelectricity in Cu2OSeO3

By performing density functional calculations, we investigate the origin of the Skyrmion state and ferroelectricity in Cu2OSeO3. We find that the Dzyaloshinskii-Moriya interactions between the two different kinds of Cu ions are extremely strong and induce the helical ground state and the Skyrmion state in the absence and presence of a magnetic field, respectively. On the basis of the general model for the spin-order induced polarization, we propose that the ferroelectric polarization of Cu2OSeO3 in the collinear ferrimagnetic state arises from an unusual mechanism, i.e., the single-spin-site contribution due to the spin-orbit coupling.

The magnetoelectric effect due to local noncentrosymmetry

Magnetoelectrics often possess ions located in noncentrosymmetric surroundings. Based on this fact we suggest a microscopic model of magnetoelectric interaction and show that the spin-orbit coupling leads to spin-dependent electric dipole moments of the electron orbitals of these ions, which results in non-vanishing polarization for certain spin configurations. The approach accounts for the macroscopic symmetry of the unit cell and is valid for both commensurate and complex incommensurate magnetic structures. The model is illustrated by the examples of MnWO(4), MnPS(3) and LiNiPO(4). Application to other magnetoelectrics is discussed.

Spin-stretching modes in anisotropic magnets: spin-wave excitations in the multiferroic Ba2CoGe2O7

We studied spin excitations in the magnetically ordered phase of the noncentrosymmetric Ba(2)CoGe(2)O(7) in high magnetic fields up to 33 T. In the electron spin resonance and far infrared absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two-sublattice antiferromagnet. We show that a multiboson spin-wave theory describes these unconventional modes, including spin-stretching modes, characterized by an oscillating magnetic dipole and quadrupole moment. The lack of inversion symmetry allows each mode to become electric dipole active. We expect that the spin-stretching modes can be generally observed in inelastic neutron scattering and light absorption experiments in a broad class of ordered S > 1/2 spin systems with strong single-ion anisotropy and/or noncentrosymmetric lattice structure.

Enhanced directional dichroism of terahertz light in resonance with magnetic excitations of the multiferroic Ba2CoGe2O7 oxide compound

We propose that concurrently magnetic and ferroelectric, i.e., multiferroic, compounds endowed with electrically active magnetic excitations (electromagnons) provide a key to producing large directional dichroism for long wavelengths of light. By exploiting the control of ferroelectric polarization and magnetization in a multiferroic oxide Ba(2)CoGe(2)O(7), we demonstrate the realization of such a directional light-switch function at terahertz frequencies in resonance with the electromagnon absorption. Our results imply that this hidden potential is present in a broad variety of multiferroics.