Dual nature of improper ferroelectricity in a magnetoelectric multiferroic

Unexpectedly large electronic contribution to linear magnetoelectricity

We show that the electronic part of the linear magnetoelectric response, usually omitted in first-principles studies, can be comparable in magnitude to that mediated by polar lattice distortions, even in strong magnetoelectrics. Using a self-consistent response to a Zeeman field for noncollinear spins, we show how polarization emerges in magnetoelectrics through both electronic and lattice contributions--analogous to the high- and low-frequency responses of dielectrics. The approach we use is computationally simple, and can be used to study linear and nonlinear responses to magnetic fields.

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.

Multiferroic and magnetoelectric materials--novel developments and perspectives

Magnetoelectric (ME) materials are of utmost interest in view of both fundamental understanding and novel desirable applications. Despite its smallness, the linear ME effect has been shown to control spintronic devices very efficiently, e.g., by using the classic ME antiferromagnet Cr₂O₃. Similar nano-engineering concepts exist also for type-I multiferroic single phase materials like BiFeO₃ and BiMnO₃. Record high ME response has been realized in stress-strain coupled multiphase magnetoelectrics like PZT/FeBSiC composites, enabling applications in sensors. In type-II multiferroics, whose ferroelectricity is due to modulated magnetic ordering, the ME coupling is of fundamental interest. Higher-order ME response characterizes disordered systems, which extend the conventional multiferroic scenario toward ME multiglass (e.g., Sr(1-x)MnxTiO₃).

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.

Temperature-dependent magnetoelectric effect from first principles

We show that nonrelativistic exchange interactions and spin fluctuations can give rise to a linear magnetoelectric effect in collinear antiferromagnets at elevated temperatures that can exceed relativistic magnetoelectric responses by more than 1 order of magnitude. We show how symmetry arguments, ab initio methods, and Monte Carlo simulations can be combined to calculate temperature-dependent magnetoelectric susceptibilities entirely from first principles. The application of our method to Cr2O3 gives quantitative agreement with experiment.

Spin model of magnetostrictions in multiferroic Mn perovskites

We theoretically study origins of the ferroelectricity in the multiferroic phases of the rare-earth (R) Mn perovskites, RMnO(3), by constructing a realistic spin model including the spin-phonon coupling, which reproduces the entire experimental phase diagram in the plane of temperature and Mn-O-Mn bond angle for the first time. Surprisingly we reveal a significant contribution of the symmetric (S·S)-type magnetostriction to the ferroelectricity even in a spin-spiral-based multiferroic phase, which can be larger than the usually expected antisymmetric (S×S)-type contribution. This explains well the nontrivial behavior of the electric polarization. We also predict the noncollinear deformation of the E-type spin structure and a wide coexisting regime of the E and spiral states, which resolve several experimental puzzles.

A phenomenological Landau theory for electromagnons in cubic spinel multiferroic CoCr₂O₄

Non-anisotropic free energy is considered which under minimization yields two magnetic phases: a conical spin density wave and a low temperature conical cycloid. Using equations of motion, the excitation spectrum is studied. Knowing the nature of these excitations, the dielectric function as well as the fluctuation specific heat is computed and compared with the experimental spectrum. Due to the electromagnon going soft, the dielectric function (imaginary part) as well as the specific heat capacity show peaks at the temperature where ferroelectricity appears in the system.

Directional magnetoelectric effects in MnWO4: magnetic sources of the electric polarization

The ferroelectric order and magnetic field induced effects observed in the spiral phase of MnWO4 are described theoretically. It is demonstrated explicitly that the Dzyaloshinskii-Moriya antisymmetric interactions contribute to the correlation between spins and electric dipoles in the incommensurate and commensurate ferroelectric phases of magnetic multiferroics. However, other single-site symmetric interactions are shown to be involved in the magnetoelectric process, suggesting the possible existence of an electric polarization originating from purely symmetric effects.

Spin-spiral states in undoped manganites: role of finite Hund's rule coupling

The experimental observation of multiferroic behavior in perovskite manganites with a spiral spin structure requires a clarification of the origin of these magnetic states and their relation to ferroelectricity. We show that spin-spiral phases with a diagonal wave vector and also an E-type phase exist for intermediate value of Hund's rule and the Jahn-Teller coupling in the orbitally ordered and insulating state of the standard two-band model Hamiltonian for manganites. Our results support the spin-current mechanism for ferroelectricity and present an alternative view to earlier conclusions where frustrating superexchange couplings were crucial to obtaining spin-spiral states.

Magnetoelectric response of multiferroic BiFeO3 and related materials from first-principles calculations

We present a first-principles scheme for computing the magnetoelectric response of multiferroics. We apply our method to BiFeO3 (BFO) and related compounds in which Fe is substituted by other magnetic species. We show that under certain relevant conditions--i.e., in the absence of incommensurate spin modulation, as in BFO thin films and some BFO-based solid solutions--these materials display a large linear magnetoelectric response. Our calculations reveal the atomistic origin of the coupling and allow us to identify the most promising strategies to enhance it.

Multiferroicity in TTF-CA organic molecular crystals predicted through ab initio calculations

We show by means of ab initio calculations that the organic molecular crystal TTF-CA is multiferroic: it has an instability to develop spontaneously both ferroelectric and magnetic ordering. Ferroelectricity is driven by a Peierls transition of the TTF-CA in its ionic state. Subsequent antiferromagnetic ordering strongly enhances the opposing electronic contribution to the polarization. It is so large that it switches the direction of the total ferroelectric moment. Within an extended Hubbard model, we capture the essence of the electronic interactions in TTF-CA, confirm the presence of a multiferroic groundstate, and clarify how this state develops microscopically.

Multiferroicity in rare-earth nickelates RNiO3

We show that charge ordered rare-earth nickelates of the type RNiO3 (R = Ho, Lu, Pr and Nd) are multiferroic with very large magnetically-induced ferroelectric (FE) polarizations. This we determine from first principles electronic structure calculations. The emerging FE polarization is directly tied to the long-standing puzzle of which kind of magnetic ordering is present in this class of materials: its direction and size indicate the type of ground-state spin configuration that is realized. Vice versa, the small energy differences between the different magnetic orderings suggest that a chosen magnetic ordering can be stabilized by cooling the system in the presence of an electric field.

Striped multiferroic phase in double-exchange model for quarter-doped manganites

The phase diagram of quarter-hole-doped perovskite manganites is investigated using the double-exchange model. An exotic striped type-II multiferroic phase, where 25% of the nearest-neighbor spin couplings are orthogonal to each other, is found in the narrow-bandwidth region. Comparing with the spiral-spin ordering phase of undoped manganites, the multiferroic Curie temperature of the new phase is estimated to be approximately 4 times higher, while the ferroelectric polarization is similar in magnitude. Our study provides a path for noncollinear spin multiferroics based on electronic self-organization, different from the traditional approach based on superexchange frustration.

Observation of a multiferroic critical end point

The study of abrupt increases in magnetization with magnetic field known as metamagnetic transitions has opened a rich vein of new physics in itinerant electron systems, including the discovery of quantum critical end points with a marked propensity to develop new kinds of order. However, the electric analogue of the metamagnetic critical end point, a "metaelectric" critical end point, has been rarely studied. Multiferroic materials wherein magnetism and ferroelectricity are cross-coupled are ideal candidates for the exploration of this novel possibility using magnetic-field (H) as a tuning parameter. Herein, we report the discovery of a magnetic-field-induced metaelectric transition in multiferroic BiMn(2)O(5), in which the electric polarization (P) switches polarity along with a concomitant Mn spin-flop transition at a critical magnetic field H(c). The simultaneous metaelectric and spin-flop transitions become sharper upon cooling but remain a continuous cross-over even down to 0.5 K. Near the P = 0 line realized at mu(0)H(c) approximately 18 T below 20 K, the dielectric constant (epsilon) increases significantly over wide field and temperature (T) ranges. Furthermore, a characteristic power-law behavior is found in the P(H) and epsilon(H) curves at T = 0.66 K. These findings indicate that a magnetic-field-induced metaelectric critical end point is realized in BiMn(2)O(5) near zero temperature.

First principles studies of multiferroic materials

Multiferroics, materials where spontaneous long-range magnetic and dipolar orders coexist, represent an attractive class of compounds, which combine rich and fascinating fundamental physics with a technologically appealing potential for applications in the general area of spintronics. Ab initio calculations have significantly contributed to recent progress in this area, by elucidating different mechanisms for multiferroicity and providing essential information on various compounds where these effects are manifestly at play. In particular, here we present examples of density-functional theory investigations for two main classes of materials: (a) multiferroics where ferroelectricity is driven by hybridization or purely structural effects, with BiFeO(3) as the prototype material, and (b) multiferroics where ferroelectricity is driven by correlation effects and is strongly linked to electronic degrees of freedom such as spin-, charge-, or orbital-ordering, with rare-earth manganites as prototypes. As for the first class of multiferroics, first principles calculations are shown to provide an accurate qualitative and quantitative description of the physics in BiFeO(3), ranging from the prediction of large ferroelectric polarization and weak ferromagnetism, over the effect of epitaxial strain, to the identification of possible scenarios for coupling between ferroelectric and magnetic order. For the second class of multiferroics, ab initio calculations have shown that, in those cases where spin-ordering breaks inversion symmetry (e.g. in antiferromagnetic E-type HoMnO(3)), the magnetically induced ferroelectric polarization can be as large as a few µC cm(-2). The examples presented point the way to several possible avenues for future research: on the technological side, first principles simulations can contribute to a rational materials design, aimed at identifying spintronic materials that exhibit ferromagnetism and ferroelectricity at or above room temperature. On the fundamental side, ab initio approaches can be used to explore new mechanisms for ferroelectricity by exploiting electronic correlations that are at play in transition metal oxides, and by suggesting ways to maximize the strength of these effects as well as the corresponding ordering temperatures.

Magnetically induced electronic ferroelectricity in half-doped manganites

Using a joint approach of density functional theory and model calculations, we demonstrate that a prototypical charge ordered half-doped manganite La1/2Ca1/2MnO3 is multiferroic. The combination of a peculiar charge-orbital ordering and a tendency to form spin dimers breaks the inversion symmetry and leads to a ferroelectric ground state with a polarization up to several microC/cm2. The presence of improper ferroelectricity does not depend on the hotly debated structural details of this material: in the Zener-polaron structure we find a similar ferroelectric response with a large polarization of purely magnetic origin.

Superexchange-driven magnetoelectricity in magnetic vortices

We demonstrate that magnetic vortices in which spins are coupled to polar lattice distortions via superexchange exhibit an unusually large linear magnetoelectric response. We show that the periodic arrays of vortices formed by frustrated spins on kagome lattices provide a realization of this concept; our ab initio calculations for such a model structure yield a magnetoelectric coefficient that is 30 times larger than that of prototypical single phase magnetoelectrics. Finally, we identify the design rules required to obtain such a response in a practical material.

Polarization and adiabatic pumping in inhomogeneous crystals

We develop a general theory of electric polarization in crystals with inhomogeneous order. We show that the inhomogeneity-induced polarization can be classified into two parts: a perturbative contribution stemming from a correction to the basis functions and a topological contribution described in terms of the Chern-Simons form of the Berry gauge fields. The latter is determined up to an uncertainty quantum, which is the second Chern number in appropriate units. Our theory provides an exhaustive link between microscopic models and the macroscopic polarization.

Magnetically induced ferroelectricity in TbMnO(3): inverse Goodenough-Kanamori interaction

Improper ferroelectricity in magnets, as induced by non-centrosymmetric spin-, charge- or orbital-ordering, is a branch of the field of multiferroics having fascinating physics and a potentially important technological outcome. We focus here on ferroelectricity in orthorhombic TbMnO(3), where the magnetic field along the a-axis produces a polar collinear spin-arrangement with a rather large in-plane electric polarization. The mechanism, similar to that occurring in orthorhombic HoMnO(3) in the AFM-E phase, is efficiently driven by a large modification of the structural properties (such as MnO bond-lengths and Mn-O-Mn bond-angles) to favor e(g) electron hopping between Mn with parallel spins. A similar mechanism where the t(2g) states are involved is examined through a hypothetical collinear spin-structure, resulting in a weaker out-of-plane ferroelectric polarization.

Origin of electromagnon excitations in multiferroic RMnO3

Electromagnon excitations in multiferroic orthorhombic RMnO3 are shown to result from the Heisenberg coupling between spins despite the fact that the static polarization arises from the much weaker Dzyaloshinskii-Moriya exchange interaction. We present a model incorporating the structural characteristics of this family of manganites that is confirmed by far infrared transmission data as a function of temperature and magnetic field and inelastic neutron scattering results. A deep connection is found between the magnetoelectric dynamics of the spiral phase and the static magnetoelectric coupling in the collinear E phase of this family of manganites.

Ising magnetism and ferroelectricity in Ca3CoMnO6

The origin of both the Ising chain magnetism and ferroelectricity in Ca3CoMnO6 is studied by ab initio electronic structure calculations and x-ray absorption spectroscopy. We find that Ca3CoMnO6 has alternate trigonal prismatic Co2+ and octahedral Mn4+ sites in the spin chain. Both the Co2+ and Mn4+ are in the high-spin state. In addition, the Co2+ has a huge orbital moment of 1.7micro_{B} which is responsible for the significant Ising magnetism. The centrosymmetric crystal structure known so far is calculated to be unstable with respect to exchange striction in the experimentally observed upward arrow upward arrow downward arrow downward arrow antiferromagnetic structure for the Ising chain. The calculated inequivalence of the Co-Mn distances accounts for the ferroelectricity.

Strain-induced effects on antiferromagnetic ordering and magnetocapacitance in orthorhombic HoMnO(3) thin films

We investigated the magnetic and ferroelectric properties of c-axis oriented orthorhombic phase HoMnO(3) (o-HMO in Pbnm symmetry setting) thin films grown on Nb-doped SrTiO(3)(001) substrates. The o-HMO films exhibit an antiferromagnetic ordering near 42 K, irrespective of the orientation of the applied field. However, an additional magnetic ordering occurring around 35 K was observed when the field was applied along the c-axis of o-HMO, which was absent when the field was applied in the ab-plane. The magnetocapacitance measured along the c-axis showed that although there is evidence of dielectric constant enhancement when the temperature is below 35 K the expected abrupt change in dielectric constant appears at a much lower temperature and reaches maximum around 13.5 K, indicating that the low-temperature c-axis polarization might be related to the ordering of the Ho(3+) moment. The lattice constant analyses using x-ray diffraction and the observation of a slight magnetization hysteresis suggest that the weak second magnetic transition along the c-axis at 35 K might be more relevant to the strain-induced effect on antiferromagnetism.

First-principles approach to lattice-mediated magnetoelectric effects

We present a first-principles scheme for the computation of the linear magnetoelectric response of magnetic insulators. We focus on the lattice-mediated part of the response, which we argue can be expected to be dominant in materials displaying strong magnetoelectric couplings. We apply our method to Cr2O3 and show that its low-temperature response has a significant lattice character.

Spin-orbit coupling and ion displacements in multiferroic TbMnO3

The magnetic and ferroelectric (FE) properties of TbMnO3 are investigated on the basis of relativistic density functional theory calculations. We show that, due to spin-orbit coupling, the spin-spiral plane of TbMnO3 can be either the bc or ab plane, but not the ac plane. As for the mechanism of FE polarization, our work reveals that the "pure electronic" model by Katsura, Nagaosa, and Balatsky is inadequate in predicting the absolute direction of FE polarization. Our work indicates that to determine the magnitude and the absolute direction of FE polarization in spin-spiral states, it is crucial to consider the displacements of the ions from their centrosymmetric positions.

First principles study of improper ferroelectricity in TbMnO3

We carry out a first-principles theoretical study of the magnetically induced polarization in orthorhombic TbMnO3, a prototypical material in which a cycloidal-spin structure generates an electric polarization via the spin-orbit interaction. We compute both the electronic and the lattice-mediated contributions to the polarization and find that the latter is strongly dominant. We analyze the spin-orbit induced forces and lattice displacements from both atomic and mode-decomposition viewpoints, and show that a simple model based on nearest Mn-Mn neighbor Dzyaloshinskii-Moriya interactions is not able to account fully for the results. The direction and magnitude of our computed polarization are in good agreement with experiment.