Dual nature of improper ferroelectricity in a magnetoelectric multiferroic

Linear response theories for interatomic exchange interactions

The linear response is a perturbation theory establishing the relationship between given physical variable and the external field inducing this variable. A well-known example of the linear response theory in magnetism is the susceptibility relating the magnetization with the magnetic field. In 1987, Liechtensteinet alcame up with the idea to formulate the problem of interatomic exchange interactions, which would describe the energy change caused by the infinitesimal rotations of spins, in terms of this susceptibility. The formulation appears to be very generic and, for isotropic systems, expresses the energy change in the form of the Heisenberg model, irrespectively on which microscopic mechanism stands behind the interaction parameters. Moreover, this approach establishes the relationship between the exchange interactions and the electronic structure obtained, for instance, in the first-principles calculations based on the density functional theory. The purpose of this review is to elaborate basic ideas of the linear response theories for the exchange interactions as well as more recent developments. The special attention is paid to the approximations underlying the original method of Liechtensteinet alin comparison with its more recent and more rigorous extensions, the roles of the on-site Coulomb interactions and the ligand states, and calculations of antisymmetric Dzyaloshinskii-Moriya interactions, which can be performed alongside with the isotropic exchange, within one computational scheme. The abilities of the linear response theories as well as many theoretical nuances, which may arise in the analysis of interatomic exchange interactions, are illustrated on magnetic van der Walls materials CrX3(X=Cl, I), half-metallic ferromagnet CrO2, ferromagnetic Weyl semimetal Co3Sn2S2, and orthorhombic manganitesAMnO3(A=La, Ho), known for the peculiar interplay of the lattice distortion, spin, and orbital ordering.

Spin-Chirality-Driven Multiferroicity in van der Waals Monolayers

Driven by the expected contribution of two-dimensional multiferroic systems with strong magnetoelectric coupling to the development of multifunctional nanodevices, here we propose, by means of first-principles calculations, vanadium-halide monolayers as a new class of spin-chirality-driven van der Waals multiferroics. The frustrated 120-deg magnetic structure in the triangular lattice induces a ferroelectric polarization perpendicular to the spin-spiral plane, whose sign is switched by a spin-chirality change. It follows that, in the presence of an applied electric field perpendicular to the monolayers, one magnetic chirality can be stabilized over the other, thereby allowing the long-sought electrical control of spin textures. Moreover, we demonstrate the remarkable role of spin-lattice coupling on magnetoelectricity, which adds to the expected contribution of spin-orbit interaction determined by an anion. Indeed, such compounds exhibit sizeable spin-driven structural distortions, thereby promoting the investigation of multifunctional spin-electric-lattice couplings.

Model for Nonrelativistic Topological Multiferroic Matter

We provide a model capable of accounting for the multiferroicity in certain materials. The model's base is on free electrons and spin moments coupled within nonrelativistic quantum mechanics. The synergistic interplay between the magnetic and electric degrees of freedom that turns into the multiferroic phenomena occurs at a profound quantum mechanical level, conjured by Berry's phases and the quantum theory of polarization. Our results highlight the geometrical nature of the multiferroic order parameter that naturally leads to magnetoelectric domain walls, with promising technological potential.

Spin-Driven Ferroelectricity in Two-Dimensional Magnetic Heterostructures

Achieving magnetic control of ferroelectricity or electric control of magnetism is usually challenging in material systems as their magnetism and ferroelectricity have distinct fundamental origins and are subject to different symmetry constraints. However, such control has significant promise for a wide range of device applications. In this work, we employ first-principles density functional theory calculations to demonstrate the emergence of spin-driven ferroelectricity in a vertically stacked two-dimensional (2D) van der Waals magnetic heterostructure, formed by two ferromagnetic (FM) CrBr3 layers separated by an antiferromagnetic (AFM) MnPSe3 layer, delicately designed to be structurally inversion symmetric but magnetically asymmetric. The spin-induced out-of-plane electric polarization of the entire heterostructure can be reversibly controlled by an external magnetic field. We further validate the effectiveness of this design strategy in several other lattice-matched FM/AFM/FM heterostructures, thereby providing a novel family of multiferroic systems based on 2D materials.

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.

Effects of Substitution and Substrate Strain on the Structure and Properties of Orthorhombic Eu1-xYxMnO3 (0 ≤ x ≤ 0.5) Thin Films

The effects on the structure and magnetic properties of Eu_1-xY_xMnO₃ (0.0 ≤ x ≤ 0.5) thin films due to lattice strain were investigated and compared with those obtained in equivalent composition ceramics. The films were deposited by spin-coating chemical solution onto Pt\TiO₂\SiO₂\Si (100) standard substrates. X-ray diffraction and Raman spectroscopy measurements revealed that all films crystallize in orthorhombic structure with space group Pnma, observing an added contraction of the unit cell with increasing Y-substitution ou Eu, corresponding to a broadening of the Mn-O1-Mn angle and a gradual decrease in magnetic order response.

From Quantum Materials to Microsystems

The expression “quantum materials” identifies materials whose properties “cannot be described in terms of semiclassical particles and low-level quantum mechanics”, i.e., where lattice, charge, spin and orbital degrees of freedom are strongly intertwined. Despite their intriguing and exotic properties, overall, they appear far away from the world of microsystems, i.e., micro-nano integrated devices, including electronic, optical, mechanical and biological components. With reference to ferroics, i.e., functional materials with ferromagnetic and/or ferroelectric order, possibly coupled to other degrees of freedom (such as lattice deformations and atomic distortions), here we address a fundamental question: “how can we bridge the gap between fundamental academic research focused on quantum materials and microsystems?”. Starting from the successful story of semiconductors, the aim of this paper is to design a roadmap towards the development of a novel technology platform for unconventional computing based on ferroic quantum materials. By describing the paradigmatic case of GeTe, the father compound of a new class of materials (ferroelectric Rashba semiconductors), we outline how an efficient integration among academic sectors and with industry, through a research pipeline going from microscopic modeling to device applications, can bring curiosity-driven discoveries to the level of CMOS compatible technology.

Elastic and magnetoelastic properties of TbMnO3single crystal by nanosecond time resolved acoustics and first-principles calculations

Time resolved pump and probe acoustics and first-principles calculations were employed to assess elastic properties of the TbMnO₃perovskite manganite having orthorhombic symmetry. Measuring sound velocities of bulk longitudinal and shear acoustic waves propagating along at least two different directions in the high symmetry planes (100), (010) and (001), provided a powerful mean to selectively determine the six diagonal elastic constantsC₁₁= 227 GPa,C₂₂= 349 GPa,C₃₃= 274 GPa,C₄₄= 71 GPa,C₅₅= 57 GPa,C₆₆= 62 GPa. Among the three remaining off-diagonal ones,C₂₃= 103 GPa was determined with a bissectrice direction. Density functional theory calculations with colinear spin-polarized provided complementary insights on their optical, elastic and magnetoelastic properties.

A short history of multiferroics

The realization that materials with coexisting magnetic and ferroelectric order open up efficient ways to control magnetism by electric fields unites scientists from different communities in the effort to explore the phenomenon of multiferroics. Following a tremendous development, the field has now gained some maturity. In this article, we give a succinct review of the history of this exciting class of materials and its evolution from “ferroelectromagnets” to “multiferroics” and beyond.

Strategy for achieving multiferroic E-type magnetic order in orthorhombic manganites RMnO3 (R = La-Lu)

Based on first-principles calculations, multiferroic properties of orthorhombic manganites (RMnO₃, R = La-Lu) with E-type ground state have been achieved by lanthanide contraction (chemical pressure) and/or external strain. Our research demonstrates that a smaller R radius within the octahedral voids in RMnO₃ results in the increase in the tilts of the octahedra but only a gentle change in the Jahn-Teller (JT) distortion. The reduction of the intraplane octahedral rotation angle and the narrowed e_g states and lifting t_2g band edge are mainly responsible for the intraplane magnetic transition from ferromagnetic (La-Gd) to zigzag-like spin arrangement (Ho-Lu). In turn, the center-broken E-type RMnO₃ bulk characterizes the dominated electronic polarization behavior, benefiting from their distortion response to small R substitution, which gives rise to the strong magnetoelectricity. Subsequently, we have figured out the strain strategy for obtaining an E-type transition in light rare-earth manganites (La-Gd) by imposing a series of hypothetical strains, where the small intraplane rotation angle (Θ) and large JT distortion favor the small aspect ratios of a/b and c/b, respectively. The strained LaMnO₃ and GdMnO₃ achieve E-type transitions successfully by imposing a modest compressive strain along the a- and c-axes and remaining free along the b-direction. Simultaneously, their polarization behaviors were comparatively studied. It was found that the size of the A-site rare-earth ions has a great influence on the external strain response, in addition to its effect on the magnetic phase transition.

Magneto-electric multiferroics: designing new materials from first-principles calculations

In parallel with the revival of interest for magneto-electric multiferroic materials in the beginning of the century, first-principles simulations have grown incredibly in efficiency during the last two decades. Density functional theory calculations, in particular, have so become a must-have tool for physicists and chemists in the multiferroic community. While these calculations were originally used to support and explain experimental behaviour, their interest has progressively moved to the design of novel magneto-electric multiferroic materials. In this article, we mainly focus on oxide perovskites, an important class of multifunctional material, and review some significant advances to which contributed first-principles calculations. We also briefly introduce the various theoretical developments that were at the core of all these advances.

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.

Lattice and spin dynamics in multiferroic BiFeO3 and RMnO3

The multiferroic materials BiFeO₃ and RMnO₃ exhibit coexisting magnetic order and ferroelectricity, and provide exciting platforms for new physics and potentially novel devices, where intriguing interplay between phonons and magnons exists. In this review, we paint a complete picture of bulk BiFeO₃ together with orthorhombic and hexagonal RMnO₃ (R includes rare-earth elements and yttrium) by summarizing the dynamics of spin and lattice and their magnetoelectric coupling, as well as the methods of controlling these characteristics under non-equilibrium conditions, from experimental and simulation perspectives.

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.

Coexistence of long-range cycloidal order and spin-cluster glass state in the multiferroic BaYFeO4

We report the presence of spin glass state below the cycloidal spin ordering in the multiferroic BaYFeO₄. This compound is known to crystallize in an orthorhombic structure with a centrosymmetric space group Pnma and exhibits two successive antiferromagnetic phase transitions. Upon cooling, it undergoes a spin density wave (SDW)-like antiferromagnetic ordering at T _N1 ~ 48 K and a cycloidal ordering at T _N2 ~ 35 K. Using dc magnetic memory effect and magnetization relaxation studies, we have shown that this oxide undergoes a reentrant spin glass transition below T ^* ~ 17 K. Our analysis suggests the presence of spin clusters in the glassy state. The coexistence of spin-cluster glass and long-range cycloidal ordered states results in an exchange bias effect at 2 K. The origin of the glassy state has been attributed to freezing of some Fe³⁺ moments, which do not participate in the long-range ordering.

Magnetoelectric Behavior from S=1/2 Asymmetric Square Cupolas

Magnetoelectric properties are studied by a combined experimental and theoretical study of a quasi-two-dimensional material composed of square cupolas, Ba(TiO)Cu_{4}(PO_{4})_{4}. The magnetization is measured up to the field above the saturation, and several anomalies are observed depending on the field directions. We propose a S=1/2 spin model with Dzyaloshinskii-Moriya interactions, which reproduces the full magnetization curves well. Elaborating the phase diagram of the model, we show that the anomalies are explained by magnetoelectric phase transitions. Our theory also accounts for the scaling of the dielectric anomaly observed in the experiments. The results elucidate the crucial role of the in-plane component of Dzyaloshinskii-Moriya interactions, which is induced by the noncoplanar buckling of a square cupola. We also predict a "hidden" phase and another magnetoelectric response, both of which appear in a nonzero magnetic field.

Synthesis of Orthorhombic Perovskite-Type ZnSnO3 Single-Crystal Nanoplates and Their Application in Energy Harvesting

In recent years, lead-free piezoelectric nanogenerators have attracted much attention because of their great potential for harvesting energy from the environment. Here, we report the first synthesis of two-dimensional (2D) single-crystal ZnSnO₃ hexagon nanoplates and the fabrication of ZnSnO₃ nanoplate-based nanogenerators. The orthorhombic perovskite-structured ZnSnO₃ nanoplates with (111) facets of the exposed plate surface are successfully synthesized via a one-step hydrothermal reaction. Piezoelectric nanogenerators are then fabricated using the as-synthesized single-crystal ZnSnO₃ nanoplates and poly(dimethylsiloxane) (PDMS). A d₃₃ value as high as 49 pC/N for the ZnSnO₃@PDMS composite was obtained without any electrical poling process, which demonstrates that the single-crystal ZnSnO₃ nanoplates have a single-domain structure. To the best of our knowledge, this d₃₃ value is also the highest among lead-free piezoelectric composites. A bending strain can induce the piezoelectric nanogenerator (PENG) to generate a large, stable, and sustainable output open circuit voltage of 20 V and a short circuit current of 0.6 μA, which are higher than many other PENGs. The output signals are sufficient to light a single light-emitting diode (LED), which shows the great potential of the material for scavenging mechanical energy from moving entities, such as road vehicles, railway vehicles, and humans.

Canted magnetic ground state of quarter-doped manganites R 0.75Ca0.25MnO3 (R = Y, Tb, Dy, Ho, and Er)

Polycrystalline samples of the quarter-doped manganites R _0.75Ca_0.25MnO₃ (R  =  Y, Tb, Dy, Ho, and Er) were studied by x-ray diffraction and AC/DC susceptibility measurements. All five samples are orthorhombic and exhibit similar magnetic properties: enhanced ferromagnetism below T ₁ (∼80 K) and a spin glass (SG) state below T _SG (∼30 K). With increasing R ³⁺ ionic size, both T ₁ and T _SG generally increase. The single crystal neutron diffraction results on Tb_0.75Ca_0.25MnO₃ revealed that the SG state is mainly composed of a short-range ordered version of a novel canted (i.e. noncollinear) antiferromagnetic spin state. Furthermore, calculations based on the double exchange model for quarter-doped manganites reveal that this new magnetic phase provides a transition state between the ferromagnetic state and the theoretically predicted spin-orthogonal stripe phase.

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.

Rigorous determination of the ground-state phases and thermodynamics in an Ising-type multiferroic chain

To understand the ferroelectricity driven by collinear magnetism in a multiferroic spin-chain system, we have adopted an elastic diatomic Ising spin-chain model with axial next-nearest-neighbor interaction to describe its magnetoelectric properties. By employing magneto-phonon decoupling and the transfer-matrix method, the possible ground-state configurations and thermodynamic behaviors of the system have been determined exactly. The parameter relation for the appearance of electric polarization has been discussed from the perspective of the ground-state configuration. In the case of nearest-neighbor antiferromagnetic coupling, a novel series of zero-temperature transitions induced by magnetic field have been observed, from the ↑↑↓↓ spin configuration associated with ferroelectric order to the ↑↓↑ state with a peculiar 1/3 magnetization plateau, then to the ↑↑↑↓ state, and finally saturation in the ↑↑↑↑ state.

Pressure dependent structural changes and predicted electrical polarization in perovskite RMnO₃

High pressure x-ray diffraction measurements on perovskite RMnO3 (R  =  Dy, Ho and Lu) reveal that varying structural changes occur for different R ions. Large lattice changes (orthorhombic strain) occur in DyMnO3 and HoMnO3 while the Jahn-Teller (JT) distortion remains stable. Conversely, in the small R-ion system LuMnO3, Mn-O bond distortions are observed between 4 and 8 GPa with a broad minimum in the JT distortion. High pressure infrared measurements indicate that a phonon near 390 cm(-1) corresponding to the complex motion of the Mn and O ions changes anomalously for LuMnO3. It softens in the 4-8 GPa region, which is consistent with the structural change in Mn-O bonds and then hardens at higher pressures. By contrast, the phonons continuously harden with increasing pressure for DyMnO3 and HoMnO3. Density functional theory methods show that E-phase LuMnO3 is the most stable phase up to the 10 GPa pressure examined. Simulations indicate that the distinct structural change under pressure in LuMnO3 can possibly be used to optimize the electric polarization by pressure/strain.

Functional domain walls in multiferroics

During the last decade a wide variety of novel and fascinating correlation phenomena has been discovered at domain walls in multiferroic bulk systems, ranging from unusual electronic conductance to inseparably entangled spin and charge degrees of freedom. The domain walls represent quasi-2D functional objects that can be induced, positioned, and erased on demand, bearing considerable technological potential for future nanoelectronics. Most of the challenges that remain to be solved before turning related device paradigms into reality, however, still fall in the field of fundamental condensed matter physics and materials science. In this topical review seminal experimental findings gained on electric and magnetic domain walls in multiferroic bulk materials are addressed. A special focus is put on the physical properties that emerge at so-called charged domain walls and the added functionality that arises from coexisting magnetic order. The research presented in this review highlights that we are just entering a whole new world of intriguing nanoscale physics that is yet to be explored in all its details. The goal is to draw attention to the persistent challenges and identify future key directions for the research on functional domain walls in multiferroics.

Giant Spin-Driven Ferroelectric Polarization in BiFeO₃ at Room Temperature

The spin-driven polarizations of type-I multiferroics are veiled by the preexisting ferroelectric (FE) polarization. Using first-principles calculations combined with a spin model, we uncover two hidden but huge spin-driven polarizations in the room-temperature multiferroic BiFeO(3). One is associated with the global inversion symmetry broken by a FE distortion, and the other is associated with the local inversion symmetry broken by an antiferrodistortive octahedral rotation. Comparison with recent neutron scatterings reveals tha first polarization reaches ∼3.0  μC/cm(2), which is larger than in any other multiferroic material. Our exhaustive study paves a way to uncover the various magnetoelectric couplings that generate hidden spin-driven polarizations in other type-I multiferroics.

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.

The ferroelectric polarization of Y2CoMnO6 aligns along the b-axis: the first-principles calculations

Double-perovskite A2BB'O6 oxides with magnetic B and B' ions and E*-type antiferromagnetic order (E*-AFM, i.e. the ↑↑↓↓ structure) are believed to exhibit promising multiferroic properties, and Y2CoMnO6 (YCMO) is one candidate in this category. However, the microscopic origins for magnetically induced ferroelectricity in YCMO remain unclear. In this study, we perform detailed symmetry analysis on the exchange striction effect and lattice distortion, plus the first-principles calculations on YCMO. The E*-AFM state as the ground state with other competing states such as ferromagnetic and A-antiferromagnetic orders is confirmed. It is observed that the ferroelectricity is generated by the exchange striction associated with the E*-AFM order and chemically ordered Mn/Co occupation. Both the lattice symmetry consideration and first-principles calculations predict that the electric polarization aligns along the b-axis. The calculated polarization reaches up to 0.4682 μC cm(-2), mainly from the ionic displacement contribution. The present study presents a comprehensive understanding of the multiferroic mechanisms in YCMO and is of general significance for predicting emergent multiferroicity in other double-perovskite magnetic oxides.

Spin rotation driven ferroelectric polarization with a 180° flop in double-perovskite Lu2CoMnO6

The exchange strictive effect and spin-charge ordering are both active in double-perovskite Lu₂CoMnO₆, thus inducing a large ferroelectric polarization along the b-axis. This study provides an effective way to research and design high performance magnetoelectric materials.

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.

BaFe(2)Se(3) a high T(C) magnetic multiferroic with large ferrielectric polarization

The iron selenides are important because of their superconducting properties. Here, an unexpected phenomenon is predicted to occur in an iron-selenide compound with a quasi-one-dimensional ladder geometry: BaFe(2)Se(3) should be a magnetic ferrielectric system, driven by its magnetic block order via exchange striction. A robust performance (high T(C) and large polarization) is expected. Different from most multiferroics, BaFe(2)Se(3) is ferrielectric, with a polarization that mostly cancels between ladders. However, its strong magnetostriction still produces a net polarization that is large (∼0.1  μC/cm(2)) as compared with most magnetic multiferroics. Its fully ferroelectric state, with energy only slightly higher than the ferrielectric, has a giant improper polarization ∼2-3  μC/cm(2).

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.

Phase transition and phase separation in multiferroic orthorhombic Dy(1-x)Ho(x)MnO3 (0 ≤ x ≤ 1)

We report on structural, magnetic, ferroelectric, and thermodynamic properties of polycrystalline orthorhombic manganites Dy_1−xHo_xMnO₃ for Ho substitution levels 0 ≤ x ≤ 1. This system offers a possibility to systemically modulate the multiferroicity of RMnO₃ via tuning the A-site ionic radii as well as the A-site magnetism. The successive transition of the multiferroic ground state is traced from the bc-cycloidal (DyMnO₃) to the E-type antiferromagnetic phase (HoMnO₃). In the middle substitution range 0.4 < x < 0.5, the phase separation is prominent, which's residual may survive in an even wider range. Accompanied with the phase transition and phase separation, obvious enhancement of both the polarization and magnetoelectric response is observed. Our experimental study also confirmed that the rare earth (Dy/Ho)-Mn exchange striction is a crucial role in deciding the multiferroicity of manganites.

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.

Polarization enhancement and ferroelectric switching enabled by interacting magnetic structures in DyMnO₃ thin films

The mutual controls of ferroelectricity and magnetism are stepping towards practical applications proposed for quite a few promising devices in which multiferroic thin films are involved. Although ferroelectricity stemming from specific spiral spin ordering has been reported in highly distorted bulk perovskite manganites, the existence of magnetically induced ferroelectricity in the corresponding thin films remains an unresolved issue, which unfortunately halts this step. In this work, we report magnetically induced electric polarization and its remarkable response to magnetic field (an enhancement of ~800% upon a field of 2 Tesla at 2 K) in DyMnO₃ thin films grown on Nb-SrTiO₃ substrates. Accompanying with the large polarization enhancement, the ferroelectric coercivity corresponding to the magnetic chirality switching field is significantly increased. A picture based on coupled multicomponent magnetic structures is proposed to understand these features. Moreover, different magnetic anisotropy related to strain-suppressed GdFeO₃-type distortion and Jahn-Teller effect is identified in the films.

Influence of lone pair doping on the multiferroic property of orthorhombic HoMnO3: ab initio prediction

Using first principles density functional theory, we predict new multiferroic compounds Ho1/2A1/2MnO3 (A = As, Sb, Bi) with enhanced polarization. We find that doping of lone pair cations with different ionic radii, at the A-site of orthorhombic HoMnO3, results in a marked increase of the electronic polarization and its development along the b-axis. This development of electronic polarization along the b-axis is attributed to the breaking of the two-fold rotational symmetry which leads to the emergence of a polar b-axis. Furthermore, this symmetry breaking leads to the emergence of two inequivalent Mn ions (Mn(0) and Mn(1)) and the variance in their octahedral (Mn(0)O6 and Mn(1)O6) distortions. We rationalize the observed trends in the total polarization in terms of disparate eg electron hopping along the two different Mn(0) and Mn(1) chains. We expect large ionic polarization in the doped compounds due to the presence of 4s(2) As, 5s(2) Sb and 6s(2) Bi lone pairs, but surprisingly the effect of the lone pairs seems to be inactive. This is attributed to the strong GdFeO3 distortions exhibited by the MnO6 octahedron which hinders polar displacement of the lone pair cations.

Melting of chiral order in terbium manganate (TbMnO3) observed with resonant x-ray Bragg diffraction

Resonant Bragg diffraction of soft, circularly polarized x-rays has been used to observe directly the temperature dependence of chiral-order melting in a motif of Mn ions in terbium manganate. The underlying mechanism uses the b-axis component of a cycloid, which vanishes outside the polar phase. Melting is witnessed by the first and second harmonics of a cycloid, and we explain why the observed temperature dependence differs in the two harmonics. Conclusions follow from an exact treatment of diffraction by using atomic multipoles in a circular cycloid, since a standard treatment of the diffraction, based on a single material-vector identified with the magnetic dipole, does not reproduce correctly observations at the second harmonic.

Competing exchanges and spin-phonon coupling in Eu(1-x)R(x)MnO3 (R=Y, Lu)

This work is focused on the phase diagrams and physical properties of Y-doped and Lu-doped EuMnO3. The differences in the corresponding phase boundaries in the (x,T) phase diagram could be overcome by considering a scaling of the Y(3+) and Lu(3+) concentrations to the tolerance factor. This outcome evidences that the tolerance factor is in fact a more reliable representative of the lattice deformation induced by doping. The normalization of the phase boundaries using the tolerance factor corroborates previous theoretical outcomes regarding the key role of competitive FM and AFM exchanges in determining the phase diagrams of manganite perovskites. However, significant differences in the nature and number of phases at low temperatures and concentrations could not be explained by just considering the normalization to the tolerance factor. The vertical phase boundary observed just for Lu-doped EuMnO3, close to 10% Lu, is understood by considering a low temperature Peierls-type spin-phonon coupling, which stabilizes the AFM-4 phase in Lu-doped EuMnO3.

Electric field control of the skyrmion lattice in Cu2OSeO3

Small-angle neutron scattering has been employed to study the influence of applied electric (E-)fields on the skyrmion lattice in the chiral lattice magnetoelectric Cu(2)OSeO(3). Using an experimental geometry with the E-field parallel to the [111] axis, and the magnetic field parallel to the [11(-)0] axis, we demonstrate that the effect of applying an E-field is to controllably rotate the skyrmion lattice around the magnetic field axis. Our results are an important first demonstration for a microscopic coupling between applied E-fields and the skyrmions in an insulator, and show that the general emergent properties of skyrmions may be tailored according to the properties of the host system.

Microscopic origin of large negative magnetoelectric coupling in Sr(1/2)Ba(1/2)MnO3

With a combined ab initio density functional and model Hamiltonian approach we establish that in the recently discovered multiferroic phase of the manganite Sr(1/2)Ba(1/2)MnO3 the polar distortion of Mn and O ions is stabilized via enhanced in-plane Mn-O hybridizations. The magnetic superexchange interaction is very sensitive to the polar bond-bending distortion, and we find that this dependence directly causes a strong magnetoelectric coupling. This novel mechanism for multiferroicity is consistent with the experimentally observed reduced ferroelectric polarization upon the onset of magnetic ordering.

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.

Dielectric properties of charge-ordered LuFe(2)O(4) revisited: the apparent influence of contacts

We show results of broadband dielectric measurements on the charge ordered, proposed to be multiferroic material LuFe(2)O(4). The temperature and frequency dependence of the complex permittivity as investigated for temperatures above and below the charge-order transition near T(CO)≈320  K and for frequencies up to 1 GHz can be well described by a standard equivalent-circuit model considering Maxwell-Wagner-type contacts and hopping induced ac conductivity. No pronounced contribution of intrinsic dipolar polarization could be found, and thus the ferroelectric character of the charge order in LuFe(2)O(4) has to be questioned.