First principles studies of multiferroic materials

Multipiezo Effect in Altermagnetic V2SeTeO Monolayer

Strain engineering has been used as an efficient method to modulate various properties of quantum materials and electronic devices. One may establish piezo effects based on a disciplined response to the strain in multifunctional nanosystems. Inspired by a recent theoretical proposal on the interesting piezomagnetism and C-paired valley polarization in the V2Se2O monolayer, we predict a stable altermagnetic Janus monolayer V2SeTeO using density functional theory calculations. It exhibits a novel "multipiezo" effect combining piezoelectricity, piezovalley, and piezomagnetism. Most interestingly, the valley polarization and the net magnetization under strain in V2SeTeO exceed these in V2Se2O, along with the additional large piezoelectric coefficient. The "multipiezo" effect makes Janus monolayer V2SeTeO as a tantalizing material for potential applications in nanoelectronics, optoelectronics, spintronics, and valleytronics.

Theoretical Justification of Structural, Magnetoelectronic and Optical Properties in QFeO3 (Q = Bi, P, Sb): A First-Principles Study

One of the primary objectives of scientific research is to create state-of-the-art multiferroic (MF) materials that exhibit interconnected properties, such as piezoelectricity, magnetoelectricity, and magnetostriction, and remain functional under normal ambient temperature conditions. In this study, we employed first-principles calculations to investigate how changing pnictogen elements affect the structural, electronic, magnetic, and optical characteristics of QFeO3 (Q = Bi, P, SB). Electronic band structures reveal that BiFeO3 is a semiconductor compound; however, PFeO3 and SbFeO3 are metallic. The studied compounds are promising for spintronics, as they exhibit excellent magnetic properties. The calculated magnetic moments decreased as we replaced Bi with SB and P in BiFeO3. A red shift in the values of ε2(ω) was evident from the presented spectra as we substituted Bi with Sb and P in BiFeO3. QFeO3 (Q = Bi, P, SB) showed the maximum absorption of incident photons in the visible region. The results obtained from calculating the optical parameters suggest that these materials have a strong potential to be used in photovoltaic applications.

Flux Method Growth and Structure and Properties Characterization of Rare-Earth Iron Oxides Lu1−xScxFeO3 Single Crystals

Perovskite rare-earth ferrites (REFeO3) have attracted great attention for their high ferroelectric and magnetic transition temperatures, strong magnetoelectric coupling, and electric polarization. We report on the flux method growth of rare-earth iron oxide Lu1−xScxFeO3 single crystals through a K2CO3-B2O3-Bi2O3 mixture as a flux solution, and give a detailed characterization of the microstructure, magnetism, and ferroelectric properties. X-ray diffraction (XRD) and energy dispersive X-ray spectroscopy (EDX) measurements revealed that the obtained single crystals can be designated to three different crystal structures of different chemical compositions, that is, Lu0.96Sc0.04FeO3 (perovskite phase), Lu0.67Sc0.33FeO3 (hexagonal phase), and Lu0.2Sc0.8FeO3 (bixbyite phase), respectively. Magnetic measurements indicate that the perovskite Lu0.96Sc0.04FeO3 is an anisotropic hard ferromagnetic material with a high Curie transition temperature, the bixbyite Lu0.2Sc0.8FeO3 is a low temperature soft ferromagnetic material, and the hexagonal Lu0.67Sc0.33FeO3 exhibits multiferroic properties. Lu0.67Sc0.33FeO3 possesses a weak ferromagnetic transition at about 162 K. We further investigate the ferroelectric domain structures in hexagonal sample by scanning electron microscope and the characteristic atomic structures in ferroelectric domain walls by atomically resolved scanning transmission electron microscope. Our successful growth of perovskite Lu1−xScxFeO3 single crystals with distinct crystal structures and stochiometric Lu-Sc substitutions is anticipated to provide a useful ferrites system for furthering exploitation of their multiferroic properties and functionalities.

Neutron powder-diffraction study of phase transitions in strontium-doped bismuth ferrite: 1. Variation with chemical composition

We report results from a study of the crystal and magnetic structures of strontium-doped BiFeO₃using neutron powder diffraction and the Rietveld method. Measurements were obtained over a wide range of temperatures from 300-800 K for compositions between 10%-16% replacement of bismuth by strontium. The results show a clear variation of the two main structural deformations-symmetry-breaking rotations of the FeO₆octahedra and polar ionic displacements that give ferroelectricity-with chemical composition, but relatively little variation with temperature. On the other hand, the antiferromagnetic order shows a variation with temperature and a second-order phase transition consistent with the classical Heisenberg model. There is, however, very little variation in the behaviour of the antiferromagnetism with chemical composition, and hence with the degree of the structural symmetry-breaking distortions. We therefore conclude that there is no significant coupling between antiferromagnetism and ferroelectricity in Sr-doped BiFeO₃and, by extension, in pure BiFeO₃.

van der Waals force layered multiferroic hybrid perovskite (CH3NH3)2CuCl4 single crystals

In inorganic-organic perovskites, the three-dimensional arrangement of the organic group results in more subtle balance of charge, spin and space, thereby providing an attractive route toward new multiferroics. Here we report the existing of multiple ferroic orderings in inorganic-organic layered perovskites with relative strong hydrogen bond ordering of the organic chains intra plane. In addition, the inter plane in perovskite is stacking via van der Waals force. However, such magnetoelectric coupling properties for this compound have not been reported since it is difficult to characterize the properties in single crystals since most of the hybrid perovskites are usually deliquescent and unstable when exposed to air. To deal with these problems, we synthesized a (CH₃NH₃)₂CuCl₄ single crystal by using a simple evaporation technique, and demonstrated ferroelectric, magnetic and magneto-electric properties of (CH₃NH₃)₂CuCl₄. The internal hydrogen bonding of easily tunable organic unit combined with 3d transition-metal layers in such hybrid perovskites make (CH₃NH₃)₂CuCl₄ a multiferroic crystal with magnetoelectrical coupling and offer an new way to engineer multifunctional multiferroic.

Uncovering ferroelectric polarization in tetragonal (Bi1/2K1/2)TiO3-(Bi1/2Na1/2)TiO3 single crystals

We report the robust ferroelectric properties of (1 − x)(Bi_1/2Na_1/2)TiO₃–x(Bi_1/2K_1/2)TiO₃ (x = 33%) single crystals grown by a top-seeded solution growth process under a high oxygen-pressure (0.9 MPa) atmosphere. The sample exhibit a large remanent polarization of 48 μC/cm² and a sizeable piezoelectric strain constant of 460 pm/V. Neutron powder diffraction structural analysis combined with first-principles calculations reveals that the large ferroelectric polarization comparable to PbTiO₃ stems from the hybridization between Bi-6p and O-2p orbitals at a moderately negative chemical pressure.

Realizing Magnetoelectric Coupling with Hydrogen Intercalation

Materials with a coexistence of magnetic and ferroelectric order (i.e., multiferroics) provide an efficient route for the control of magnetism by electric fields. Unfortunately, a long-sought room temperature multiferroic with strongly coupled ferroelectric and ferromagnetic (or ferrimagnetic) orderings is still lacking. Here, we propose that hydrogen intercalation in antiferromagnetic transition-metal oxides is a promising way to realize multiferroics with strong magnetoelectric coupling. Taking brownmillerite SrCoO_{2.5} as an example, we show that hydrogen intercalated SrCoO_{2.5} displays strong ferrimagnetism and large electric polarization in which the hydroxide acts as a new knob to simultaneously control the magnetization and polarization at room temperature. We expect that ion intercalation will become a general way to design magnetoelectric and spintronic functional materials.

Tunable metal-insulator transition, Rashba effect and Weyl Fermions in a relativistic charge-ordered ferroelectric oxide

Controllable metal-insulator transitions (MIT), Rashba-Dresselhaus (RD) spin splitting, and Weyl semimetals are promising schemes for realizing processing devices. Complex oxides are a desirable materials platform for such devices, as they host delicate and tunable charge, spin, orbital, and lattice degrees of freedoms. Here, using first-principles calculations and symmetry analysis, we identify an electric-field tunable MIT, RD effect, and Weyl semimetal in a known, charge-ordered, and polar relativistic oxide Ag2BiO3 at room temperature. Remarkably, a centrosymmetric BiO6 octahedral-breathing distortion induces a sizable spontaneous ferroelectric polarization through Bi3+/Bi5+ charge disproportionation, which stabilizes simultaneously the insulating phase. The continuous attenuation of the Bi3+/Bi5+ disproportionation obtained by applying an external electric field reduces the band gap and RD spin splitting and drives the phase transition from a ferroelectric RD insulator to a paraelectric Dirac semimetal, through a topological Weyl semimetal intermediate state. These findings suggest that Ag2BiO3 is a promising material for spin-orbitonic applications.

Molecular analogue of the perovskite repeating unit and evidence for direct MnIII-CeIV-MnIII exchange coupling pathway

The perovskite manganites AMnO₃ and their doped analogues A_1–xB_xMnO₃ (A and B = main group and lanthanide metals) are a fascinating family of magnetic oxides exhibiting a rich variety of properties. They are thus under intense investigation along multiple fronts, one of which is how their structural and physical properties are modified at the nanoscale. Here we show that the molecular compound [Ce₃Mn₈O₈(O₂CPh)₁₈(HO₂CPh)₂] (Ce^III₂Ce^IVMn^III₈; hereafter Ce₃Mn₈) bears a striking structural resemblance to the repeating unit seen in the perovskite manganites. Further, magnetic studies have established that Ce₃Mn₈ exhibits both the combination of pairwise Mn^III₂ ferromagnetic and antiferromagnetic exchange interactions, and the resultant spin vector alignments that are found within the 3-D C-type antiferromagnetic perovskites. First-principles theoretical calculations reveal not only the expected nearest-neighbor Mn^III₂ exchange couplings via superexchange pathways through bridging ligands but also an unusual, direct Mn^III–Ce^IV–Mn^III metal-to-metal channel involving the Ce^IVf orbitals.

Perovskite manganites exhibit intriguing but poorly understood properties, including multiferroicity. Here, the authors synthesize a Ce₃Mn₈ cluster that structurally resembles a perovskite repeat unit, and use this molecular analogue to elucidate mechanisms driving bulk perovskite properties.

Impact of Fe on structural modification and room temperature magnetic ordering in BaTiO3

Ba_1-xFe_xTiO₃ (x=0, 0.005, 0.01) polycrystalline ceramics are prepared using solid state reaction method. Structural studies through XRD, Raman and XPS confirm single tetragonal phase for BaTiO₃ whereas a structural disorder tends to intervene with the introduction of smaller Fe ions which reduces the tolerance factor and tetragonality ratio. Grain size of the samples is estimated using SEM micrographs with ImageJ software and chemical composition is confirmed using EDX spectra. Raman spectra measured in the temperature range of 303K to 573K showers light on the structural phase transition exploiting a significant disappearance of the 306cm^-1 mode. Further, structural analyses suggest the entry of Fe into the B-site upon increasing its concentration in BaTiO₃. The dopant sensitive modes lying at around 640cm^-1 and 650cm^-1 are assigned to lattice strain. A reduction in ferroelectric to paraelectric transition temperature is observed with a transformation from diffused type to normal ferroelectric upon the increased Fe content. The oxidation state of Fe in the BaTiO₃ lattice has been decided using EPR Spectra precisely. Room temperature magnetic ordering is observed in Fe substituted BaTiO₃ using PPMS. The coexistence of ferroelectric and magnetic ordering is established in the present study for optimized Fe substituted BaTiO₃.

Modulating Magnetic Properties by Tailoring In-Plane Domain Structures in Hexagonal YMnO3 Films

Periodic structures and the coupling of multiorder parameters in complex oxides heterojunctions can generate exotic properties, of interest both for fundamental researches and for device applications. Here, we report a self-assembling in-plane periodic domain structure, and the resulting rich magnetic states, in a h-YMnO3 thin film fabricated on c-face sapphire substrate. Detailed structural investigations at atomic-level reveal the fashion of alternating domains under tensile or compressive strains separated by a boundary region. Tuned by this in-plane domain structure, the abnormal magnetic properties, such as the ferromagnetic enhancement and the unexpected spin glass state (below ∼38 K), are realized. Moreover, the existence of ferroelectric polarization is confirmed by scanning transmission electron microscopy, which brings in the chances of magnetoelectric coupling effect. These results manifest the close connections between the magnetic properties and such in-plane microstructures, suggesting the possibility of tuning the coupling effects via strain engineering in the hexagonal manganite film.

Multifunctional magnetoelectric materials for device applications

Over the past decade magnetoelectric (ME) mutiferroic (MF) materials and their devices are one of the highest priority research topics that has been investigated by the scientific ferroics community to develop the next generation of novel multifunctional materials. These systems show the simultaneous existence of two or more ferroic orders, and cross-coupling between them, such as magnetic spin, polarisation, ferroelastic ordering, and ferrotoroidicity. Based on the type of ordering and coupling, they have drawn increasing interest for a variety of device applications, such as magnetic field sensors, nonvolatile memory elements, ferroelectric photovoltaics, nano-electronics etc. Since single-phase materials exist rarely in nature with strong cross-coupling properties, intensive research activity is being pursued towards the discovery of new single-phase multiferroic materials and the design of new engineered materials with strong magneto-electric (ME) coupling. This review article summarises the development of different kinds of multiferroic material: single-phase and composite ceramic, laminated composite and nanostructured thin films. Thin-film nanostructures have higher magnitude direct ME coupling values and clear evidence of indirect ME coupling compared with bulk materials. Promising ME coupling coefficients have been reported in laminated composite materials in which the signal to noise ratio is good for device fabrication. We describe the possible applications of these materials.

Predicting a ferrimagnetic phase of Zn(2)FeOsO(6) with strong magnetoelectric coupling

Multiferroic materials, in which ferroelectric and magnetic ordering coexist, are of practical interest for the development of novel memory devices that allow for electrical writing and nondestructive magnetic readout operation. The great challenge is to create room temperature multiferroic materials with strongly coupled ferroelectric and ferromagnetic (or ferrimagnetic) orderings. BiFeO_{3} is the most heavily investigated single-phase multiferroic to date due to the coexistence of its magnetic order and ferroelectric order at room temperature. However, there is no net magnetic moment in the cycloidal (antiferromagneticlike) magnetic state of bulk BiFeO_{3}, which severely limits its realistic applications in electric field controlled memory devices. Here, we predict that LiNbO_{3}-type Zn_{2}FeOsO_{6} is a new multiferroic with properties superior to BiFeO_{3}. First, there are strong ferroelectricity and strong ferrimagnetism at room temperature in Zn_{2}FeOsO_{6}. Second, the easy plane of the spontaneous magnetization can be switched by an external electric field, evidencing the strong magnetoelectric coupling existing in this system. Our results suggest that ferrimagnetic 3d-5d LiNbO_{3}-type material may therefore be used to achieve voltage control of magnetism in future memory devices.

Intrinsic interfacial phenomena in manganite heterostructures

We review recent advances in our understanding of interfacial phenomena that emerge when dissimilar materials are brought together at atomically sharp and coherent interfaces. In particular, we focus on phenomena that are intrinsic to the interface and review recent work carried out on perovskite manganites interfaces, a class of complex oxides whose rich electronic properties have proven to be a useful playground for the discovery and prediction of novel phenomena.

Absence of significant structural changes near the magnetic ordering temperature in small-ion rare earth perovskite RMnO3

Detailed structural measurements on multiple length scales were conducted on a new perovskite phase of ScMnO3, and on orthorhombic LuMnO3 as a benchmark. Complementary density functional theory (DFT) calculations were carried out, and predict that ScMnO3 possesses E-phase magnetic order at low temperature with displacements of the Mn sites (relative to the high temperature state) of ∼0.07 Å, compared to ∼0.04 Å predicted for LuMnO3. However, detailed local, intermediate and long-range structural measurements by x-ray pair distribution function analysis, single crystal x-ray diffraction and x-ray absorption spectroscopy, find no local or long-range distortions on crossing into the low temperature E-phase of the magnetically ordered state. The measurements place upper limits on any structural changes to be at most one order of magnitude lower than DFT predictions and suggest that this theoretical approach does not properly account for the spin-lattice coupling in these oxides and may possibly predict the incorrect magnetic order at low temperatures. The results suggest that the electronic contribution to the electrical polarization dominates and should be more accurately treated in theoretical models.

Structure and spin dynamics of multiferroic BiFeO3

Multiferroic materials have attracted much interest due to the unusual coexistence of ferroelectric and (anti-)ferromagnetic ground states in a single compound. They offer an exciting platform for new physics and potentially novel devices. BiFeO3 is one of the most celebrated multiferroic materials and has highly desirable properties. It is the only known room-temperature multiferroic with TC ≈ 1100 K and TN ≈ 650 K, and exhibits one of the largest spontaneous electric polarisations, P ≈ 80 µC cm(-2). At the same time, it has a magnetic cycloid structure with an extremely long period of 620 Å, which arises from competition between the usual symmetric exchange interaction and the antisymmetric Dzyaloshinskii-Moriya (DM) interaction. There is also an intriguing interplay between the DM interaction and single ion anisotropy K. In this review, we have attempted to paint a complete picture of bulk BiFeO3 by summarising the structural and dynamic properties of both the spin and lattice parts and their magneto-electric coupling.

Beyond standard local density approximation in the study of magnetoelectric effects in Fe/BaTiO3 and Co/BaTiO3 interfaces

First-principles density functional theory (DFT) simulations for Fe/BaTiO(3) and Co/BaTiO(3) junctions have been performed with different treatments of the exchange-correlation potential, ranging from standard semilocal density approximations to a Hubbard-like approach and to hybrid functionals. With the aim of elucidating the role of correlations in the microscopic interplay between ferroelectricity and magnetism in the interfacial region, we find that, compared to standard DFT approximations, Hubbard-like approaches and hybrid functionals do not qualitatively modify the physical origin behind magnetoelectric effects driven by interfacial orbital hybridization. Rather, more accurate treatments of correlations for both Fe/BaTiO(3) and Co/BaTiO(3) interfaces predict a stronger change of the interface magnetization upon switching the direction of polarization in the ferroelectric layer.

Ferromagnetism and orbital order in a topological ferroelectric

We explore via density functional calculations the magnetic doping of a topological ferroelectric as an unconventional route to multiferroicity. Vanadium doping of the layered perovskite La(2)Ti(2)O(7) largely preserves electric polarization and produces robust ferromagnetic order and, hence, proper multiferroicity. The marked tendency of dopants to cluster into chains results in an insulating character at generic doping. Ferromagnetism stems from the symmetry breaking of the multiorbital V system via an unusual "antiferro"-orbital order, and from the host's low-symmetry layered structure.

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.

Electric field control of magnetism in multiferroic heterostructures

We review the recent developments in the electric field control of magnetism in multiferroic heterostructures, which consist of heterogeneous materials systems where a magnetoelectric coupling is engineered between magnetic and ferroelectric components. The magnetoelectric coupling in these composite systems is interfacial in origin, and can arise from elastic strain, charge, and exchange bias interactions, with different characteristic responses and functionalities. Moreover, charge transport phenomena in multiferroic heterostructures, where both magnetic and ferroelectric order parameters are used to control charge transport, suggest new possibilities to control the conduction paths of the electron spin, with potential for device applications.

Giant ferroelectric polarization of CaMn7O12 induced by a combined effect of Dzyaloshinskii-Moriya interaction and exchange striction

By extending our general spin-current model to noncentrosymmetric spin dimers and performing density functional calculations, we investigate the causes for the helical magnetic order and the origin of the giant ferroelectric polarization of CaMn7O12. The giant ferroelectric polarization is proposed to be caused by the symmetric exchange striction due to the canting of the Mn4+ spin arising from its strong Dzyaloshinskii-Moriya interaction. Our study suggests that CaMn7O12 may exhibit a novel magnetoelectric coupling mechanism in which the magnitude of the polarization is governed by the exchange striction, but the direction of the polarization by the chirality of the helical magnetic order.

Substrate clamping effects on irreversible domain wall dynamics in lead zirconate titanate thin films

The role of long-range strain interactions on domain wall dynamics is explored through macroscopic and local measurements of nonlinear behavior in mechanically clamped and released polycrystalline lead zirconate-titanate (PZT) films. Released films show a dramatic change in the global dielectric nonlinearity and its frequency dependence as a function of mechanical clamping. Furthermore, we observe a transition from strong clustering of the nonlinear response for the clamped case to almost uniform nonlinearity for the released film. This behavior is ascribed to increased mobility of domain walls. These results suggest the dominant role of collective strain interactions mediated by the local and global mechanical boundary conditions on the domain wall dynamics. The work presented in this Letter demonstrates that measurements on clamped films may considerably underestimate the piezoelectric coefficients and coupling constants of released structures used in microelectromechanical systems, energy harvesting systems, and microrobots.

Pseudo Jahn-Teller origin of perovskite multiferroics, magnetic-ferroelectric crossover, and magnetoelectric effects: the d0-d10 problem

The conditions of multiferroicity in d(n) perovskites are derived from the pseudo Jahn-Teller effect, due to which ferroelectric displacements are triggered by vibronic coupling between ground and excited electronic states of opposite parity but same spin multiplicity; it takes place for some specific d(n) configurations and spin states only. In combination with the high-spin-low-spin crossover effect this leads to a novel phenomenon, the magnetic-ferroelectric (multiferroics) crossover which predicts magnetoelectric effects with exciting functionalities including electric magnetization and demagnetization.

Ab initio study of magnetoelectricity in Fe/BaTiO3: the effects of n-doped perovskite interfaces

On the basis of ab initio calculations we study the interfacial magnetoelectric effect in a prototypical biferroic Fe(L)/XO2/BaO/BaTiO3(001) (X = Ti, V, Co), with an Fe thickness L ≤ 2 monolayers. We anticipate that the use of the n-type perovskite termination instead of nominally neutral TiO2 may enhance magnetoelectricity in the system when its magnetization is robustly changed by substrate-polarization reversal.

General theory for the ferroelectric polarization induced by spin-spiral order

The ferroelectric polarization of triangular-lattice antiferromagnets induced by helical spin-spiral order is not explained by any existing model of magnetic-order-driven ferroelectricity. We resolve this problem by developing a general theory for the ferroelectric polarization induced by spin-spiral order and then by evaluating the coefficients needed to specify the general theory on the basis of density functional calculations. Our theory correctly describes the ferroelectricity of triangular-lattice antiferromagnets driven by helical spin-spiral order and incorporates known models of magnetic-order-driven ferroelectricity as special cases.

Fe, Mn, and Cr doped BiCoO₃ for magnetoelectric application: a first-principles study

The tetragonal compound BiCoO(3) may play a significant role in magnetoelectric devices if its magnetism can be tuned and its strong ferroelectricity maintained. Here we have studied Fe, Mn, and Cr doped BiCoO(3) with a concentration of 12.5% by density functional theory (DFT) and DFT + U calculations. It is found that all the doped magnetic ions favor ferromagnetic coupling in the C-type antiferromagnetic BiCoO(3) lattice, leading to net magnetic moments of 1, 1, 0 μ(B) for Bi(8)Co(7)XO(24), where X = Fe, Cr, and Mn, respectively. Meanwhile, the Berry phase calculations indicate that the strong ferroelectricity is almost preserved for Fe, Cr, and Mn doped BiCoO(3), with values of 172.7, 152.1, and 169.8 µC cm(-2), respectively, close to the original polarization value of 174.9 µC cm(-2). As a result, Cr or Fe doping may be useful to make the BiCoO(3) system ferrimagnetic while maintaining its excellent ferroelectric performance.

Multi-ferroic and magnetoelectric materials and interfaces

The existence of multiple ferroic orders in the same material and the coupling between them have been known for decades. However, these phenomena have mostly remained the theoretical domain owing to the fact that in single-phase materials such couplings are rare and weak. This situation has changed dramatically recently for at least two reasons: first, advances in materials fabrication have made it possible to manufacture these materials in structures of lower dimensionality, such as thin films or wires, or in compound structures such as laminates and epitaxial-layered heterostructures. In these designed materials, new degrees of freedom are accessible in which the coupling between ferroic orders can be greatly enhanced. Second, the miniaturization trend in conventional electronics is approaching the limits beyond which the reduction of the electronic element is becoming more and more difficult. One way to continue the current trends in computer power and storage increase, without further size reduction, is to use multi-functional materials that would enable new device capabilities. Here, we review the field of multi-ferroic (MF) and magnetoelectric (ME) materials, putting the emphasis on electronic effects at ME interfaces and MF tunnel junctions.

Structure and properties of functional oxide thin films: insights from electronic-structure calculations

The confluence of state-of-the-art electronic-structure computations and modern synthetic materials growth techniques is proving indispensable in the search for and discovery of new functionalities in oxide thin films and heterostructures. Here, we review the recent contributions of electronic-structure calculations to predicting, understanding, and discovering new materials physics in thin-film perovskite oxides. We show that such calculations can accurately predict both structure and properties in advance of film synthesis, thereby guiding the search for materials combinations with specific targeted functionalities. In addition, because they can isolate and decouple the effects of various parameters which unavoidably occur simultaneously in an experiment-such as epitaxial strain, interfacial chemistry and defect profiles-they are able to provide new fundamental knowledge about the underlying physics. We conclude by outlining the limitations of current computational techniques, as well as some important open questions that we hope will motivate further methodological developments in the field.

Ferroelectricity due to orbital ordering in E-type undoped rare-earth manganites

Aiming at understanding the origin of the electronic contribution to ferroelectric polarization in undoped manganites, we evaluate the Berry phase of orbital-polarizable Bloch electrons as an orbital ordering (OO) establishes in the background of an antiferromagnetic E-type configuration. The onset of OO is tuned by the Jahn-Teller (JT) interaction in a tight-binding model for interacting electrons moving along zigzag chains. A finite polarization is found as soon as the JT coupling is strong enough to induce OO, supporting the large electronic contribution predicted from first principles.

Interplay between charge order, ferroelectricity, and ferroelasticity: tungsten bronze structures as a playground for multiferroicity

Charge order is proposed as a driving force behind ferroelectricity in iron fluoride K(0.6)Fe(0.6)(II)Fe(0.4)(III)F(3). By means of density functional theory, we propose several noncentrosymmetric d(5)/d(6) charge-ordering patterns, each giving rise to polarization with different direction and magnitude. Accordingly, we introduce the concept of "ferroelectric anisotropy" (peculiar to improper ferroelectrics with polarization induced by electronic degrees of freedom), denoting the small energy difference between competing charge-ordered states. Moreover, we suggest a novel type of charge-order-induced ferroelasticity: a monoclinic distortion is induced by a specific charge-ordering pattern, which, in turn, determines the direction of polarization. K(0.6)Fe(0.6)(II)Fe(0.4)(III)F(3) therefore emerges as a prototypical compound, in which the intimately coupled electronic and structural degrees of freedom result in a peculiar multiferroicity.

Electrical polarization and orbital magnetization: the modern theories

Macroscopic polarization P and magnetization M are the most fundamental concepts in any phenomenological description of condensed media. They are intensive vector quantities that intuitively carry the meaning of dipole per unit volume. But for many years both P and the orbital term in M evaded even a precise microscopic definition, and severely challenged quantum-mechanical calculations. If one reasons in terms of a finite sample, the electric (magnetic) dipole is affected in an extensive way by charges (currents) at the sample boundary, due to the presence of the unbounded position operator in the dipole definitions. Therefore P and the orbital term in M--phenomenologically known as bulk properties--apparently behave as surface properties; only spin magnetization is problemless. The field has undergone a genuine revolution since the early 1990s. Contrary to a widespread incorrect belief, P has nothing to do with the periodic charge distribution of the polarized crystal: the former is essentially a property of the phase of the electronic wavefunction, while the latter is a property of its modulus. Analogously, the orbital term in M has nothing to do with the periodic current distribution in the magnetized crystal. The modern theory of polarization, based on a Berry phase, started in the early 1990s and is now implemented in most first-principle electronic structure codes. The analogous theory for orbital magnetization started in 2005 and is partly work in progress. In the electrical case, calculations have concerned various phenomena (ferroelectricity, piezoelectricity, and lattice dynamics) in several materials, and are in spectacular agreement with experiments; they have provided thorough understanding of the behaviour of ferroelectric and piezoelectric materials. In the magnetic case the very first calculations are appearing at the time of writing (2010). Here I review both theories on a uniform ground in a density functional theory (DFT) framework, pointing out analogies and differences. Both theories are deeply rooted in geometrical concepts, elucidated in this work. The main formulae for crystalline systems express P and M in terms of Brillouin-zone integrals, discretized for numerical implementation. I also provide the corresponding formulae for disordered systems in a single k-point supercell framework. In the case of P the single-point formula has been widely used in the Car-Parrinello community to evaluate IR spectra.