Surface-Symmetry-Driven Dzyaloshinskii-Moriya Interaction and Canted Ferrimagnetism in Collinear Magnetoelectric Antiferromagnet Cr_{2}O_{3}.

Antiferromagnets are normally thought of as materials with compensated magnetic sublattices. This adds to their technological advantages but complicates readout of the antiferromagnetic state. We demonstrate theoretically the existence of a Dzyaloshinskii-Moriya interaction (DMI), which is determined by the magnetic symmetry classes of Cr_{2}O_{3} surfaces with an in-plane magnetic easy axis. The DMI explains a previously predicted out-of-plane magnetization at the nominally compensated surfaces of chromia, leading to a surface-localized canted ferrimagnetism. This is in agreement with magnetotransport measurements and with density functional theory predictions that further allow us to quantify the strength of DMI. The temperature dependence of the transversal resistance for these planes shows distinct behavior in comparison with that of the Cr_{2}O_{3} c plane, which we attribute to the influence of DMI. Our Letter provides a framework to analyze surface-driven phenomena in antiferromagnets, and motivates the use of nominally compensated chromia surfaces for antiferromagnetic spintronics and magnonics.

Three-dimensional domain identification in a single hexagonal manganite nanocrystal.

The three-dimensional domain structure of ferroelectric materials significantly influences their properties. The ferroelectric domain structure of improper multiferroics, such as YMnO3, is driven by a non-ferroelectric order parameter, leading to unique hexagonal vortex patterns and topologically protected domain walls. Characterizing the three-dimensional structure of these domains and domain walls has been elusive, however, due to a lack of suitable imaging techniques. Here, we present a multi-peak Bragg coherent x-ray diffraction imaging determination of the domain structure in single YMnO3 nanocrystals. We resolve two ferroelectric domains separated by a domain wall and confirm that the primary atomic displacements occur along the crystallographic c-axis. Correlation with atomistic simulations confirms the Mexican hat symmetry model of domain formation, identifying two domains with opposite ferroelectric polarization and adjacent trimerization, manifesting in a clockwise arrangement around the hat's brim.

On the sign of the linear magnetoelectric coefficient in Cr2O3.

We establish the sign of the linear magnetoelectric (ME) coefficient,α, in chromia, Cr2O3. Cr2O3is the prototypical linear ME material, in which an electric (magnetic) field induces a linearly proportional magnetization (polarization), and a single magnetic domain can be selected by annealing in combined magnetic (H) and electric (E) fields. Opposite antiferromagnetic (AFM) domains have opposite ME responses, and which AFM domain corresponds to which sign of response has previously been unclear. We use density functional theory (DFT) to calculate the magnetic response of a single AFM domain of Cr2O3to an applied in-plane electric field at zero kelvin. We find that the domain with nearest neighbor magnetic moments oriented away from (towards) each other has a negative (positive) in-plane ME coefficient,α⊥, at zero kelvin. We show that this sign is consistent with all other DFT calculations in the literature that specified the domain orientation, independent of the choice of DFT code or functional, the method used to apply the field, and whether the direct (magnetic field) or inverse (electric field) ME response was calculated. Next, we reanalyze our previously published spherical neutron polarimetry data to determine the AFM domain produced by annealing in combinedEandHfields oriented along the crystallographic symmetry axis at room temperature. We find that the AFM domain with nearest-neighbor magnetic moments oriented away from (towards) each other is produced by annealing in (anti-)parallelEandHfields, corresponding to a positive (negative) axial ME coefficient,α∥, at room temperature. Sinceα⊥at zero kelvin andα∥at room temperature are known to be of opposite sign, our computational and experimental results are consistent.

First-principles calculation of electron-phonon coupling in doped KTaO3.

Background: Motivated by the recent experimental discovery of strongly surface-plane-dependent superconductivity at surfaces of KTaO 3 single crystals, we calculate the electron-phonon coupling strength, λ, of doped KTaO 3 along the reciprocal-space high-symmetry directions. Methods:Using the Wannier-function approach implemented in the EPW package, we calculate λ across the experimentally covered doping range and compare its mode-resolved distribution along the [001], [110] and [111] reciprocal-space directions. Results: We find that the electron-phonon coupling is strongest in the optical modes around the Γ point, with some distribution to higher k values in the [001] direction. The electron-phonon coupling strength as a function of doping has a dome-like shape in all three directions and its integrated total is largest in the [001] direction and smallest in the [111] direction, in contrast to the experimentally measured trends in critical temperatures. Conclusions: This disagreement points to a non-BCS character of the superconductivity. Instead, the strong localization of λ in the soft optical modes around Γ suggests an importance of ferroelectric soft-mode fluctuations, which is supported by our findings that the mode-resolved λ values are strongly enhanced in polar structures. The inclusion of spin-orbit coupling has negligible influence on our calculated mode-resolved λ values.

Chiral phonons in quartz probed by X-rays.

The concept of chirality is of great relevance in nature, from chiral molecules such as sugar to parity transformations in particle physics. In condensed matter physics, recent studies have demonstrated chiral fermions and their relevance in emergent phenomena closely related to topology1-3. The experimental verification of chiral phonons (bosons) remains challenging, however, despite their expected strong impact on fundamental physical properties4-6. Here we show experimental proof of chiral phonons using resonant inelastic X-ray scattering with circularly polarized X-rays. Using the prototypical chiral material quartz, we demonstrate that circularly polarized X-rays, which are intrinsically chiral, couple to chiral phonons at specific positions in reciprocal space, allowing us to determine the chiral dispersion of the lattice modes. Our experimental proof of chiral phonons demonstrates a new degree of freedom in condensed matter that is both of fundamental importance and opens the door to exploration of new emergent phenomena based on chiral bosons.

Characterizing and Overcoming Surface Paramagnetism in Magnetoelectric Antiferromagnets.

We use a combination of density functional theory and Monte Carlo methods to calculate the surface magnetization in magnetoelectric Cr_{2}O_{3} at finite temperatures. Such antiferromagnets, lacking both inversion and time-reversal symmetries, are required by symmetry to possess an uncompensated magnetization density on particular surface terminations. Here, we first show that the uppermost layer of magnetic moments on the ideal (001) surface remains paramagnetic at the bulk Néel temperature, bringing the theoretical estimate of surface magnetization density in line with experiment. We demonstrate that the lower surface ordering temperature compared to bulk is a generic feature of surface magnetization when the termination reduces the effective Heisenberg coupling. We then propose two methods by which the surface magnetization in Cr_{2}O_{3} could be stabilized at higher temperatures. Specifically, we show that the effective coupling of surface magnetic ions can be drastically increased either by a different choice of surface Miller plane, or by Fe doping. Our findings provide an improved understanding of surface magnetization properties in AFMs.

Experimental and theoretical thermodynamic studies in Ba2MgReO6-the ground state in the context of Jahn-Teller effect.

We address the degeneracy of the ground state multiplet on the 5d1Re6+ion in double perovskite Ba2MgReO6using a combination of specific heat measurements and density functional calculations. For Ba2MgReO6, two different ground state multiplets have previously been proposed-a quartet (with degeneracyN= 4) (Hirai and Hiroi 2019J. Phys. Soc. Japan88064712) and a doublet (N= 2) (Marjerrisonet al2016Inorg. Chem.5510701). Here we employ two independent methods for the estimation of phonon contribution in heat capacity data to obtain the magnetic entropySmag, which reflects the degeneracy of the ground state multipletNthroughSmag=RlnN. In both cases, we obtain that in the temperature range covering 2 to 120 K the released entropy is better described bySmag=Rln2. The detailed nature of the ground state multiplet in Ba2MgReO6remains an open question.

Origin of the Critical Thickness in Improper Ferroelectric Thin Films.

Improper ferroelectrics are expected to be more robust than conventional ferroelectrics against depolarizing field effects and to exhibit a much-desired absence of critical thickness. Recent studies, however, revealed the loss of ferroelectric response in epitaxial improper ferroelectric thin films. Here, we investigate improper ferroelectric hexagonal YMnO3 thin films and find that the polarization suppression, and hence functionality, in the thinner films is due to oxygen off-stoichiometry. We demonstrate that oxygen vacancies form on the film surfaces to provide the necessary charge to screen the large internal electric field resulting from the positively charged YMnO3 surface layers. Additionally, we show that by modifying the oxygen concentration of the films, the phase transition temperatures can be substantially tuned. We anticipate that our findings are also valid for other ferroelectric oxide films and emphasize the importance of controlling the oxygen content and cation oxidation states in ferroelectrics for their successful integration in nanoscale applications.

Non-volatile electric-field control of inversion symmetry.

Competition between ground states at phase boundaries can lead to significant changes in properties under stimuli, particularly when these ground states have different crystal symmetries. A key challenge is to stabilize and control the coexistence of symmetry-distinct phases. Using BiFeO3 layers confined between layers of dielectric TbScO3 as a model system, we stabilize the mixed-phase coexistence of centrosymmetric and non-centrosymmetric BiFeO3 phases at room temperature with antipolar, insulating and polar semiconducting behaviour, respectively. Application of orthogonal in-plane electric (polar) fields results in reversible non-volatile interconversion between the two phases, hence removing and introducing centrosymmetry. Counterintuitively, we find that an electric field 'erases' polarization, resulting from the anisotropy in octahedral tilts introduced by the interweaving TbScO3 layers. Consequently, this interconversion between centrosymmetric and non-centrosymmetric phases generates changes in the non-linear optical response of over three orders of magnitude, resistivity of over five orders of magnitude and control of microscopic polar order. Our work establishes a platform for cross-functional devices that take advantage of changes in optical, electrical and ferroic responses, and demonstrates octahedral tilts as an important order parameter in materials interface design.

Physics-Guided Descriptors for Prediction of Structural Polymorphs.

We develop a method combining machine learning (ML) and density functional theory (DFT) to predict low-energy polymorphs by introducing physics-guided descriptors based on structural distortion modes. We systematically generate crystal structures utilizing the distortion modes and compute their energies with single-point DFT calculations. We then train a ML model to identify low-energy configurations on the material's high-dimensional potential energy surface. Here, we use BiFeO3 as a case study and explore its phase space by tuning the amplitudes of linear combinations of a finite set of distinct distortion modes. Our procedure is validated by rediscovering several known metastable phases of BiFeO3 with complex crystal structures, and its efficiency is proved by identifying 21 new low-energy polymorphs. This approach proposes a new avenue toward accelerating the prediction of low-energy polymorphs in solid-state materials.

Magnetoelectric Classification of Skyrmions.

We develop a general theory to classify magnetic skyrmions and related spin textures in terms of their magnetoelectric multipoles. Since magnetic skyrmions are now established in insulating materials, where the magnetoelectric multipoles govern the linear magnetoelectric response, our classification provides a recipe for manipulating the magnetic properties of skyrmions using applied electric fields. We apply our formalism to skyrmions and antiskyrmions of different helicities, as well as to magnetic bimerons, which are topologically, but not geometrically, equivalent to skyrmions. We show that the nonzero components of the magnetoelectric multipole and magnetoelectric response tensors are uniquely determined by the topology, helicity, and geometry of the spin texture. Therefore, we propose straightforward linear magnetoelectric response measurements as an alternative to Lorentz microscopy for characterizing insulating skyrmionic textures.

Hidden k-Space Magnetoelectric Multipoles in Nonmagnetic Ferroelectrics.

In condensed matter systems, the electronic degrees of freedom are often entangled to form complex composites, known as hidden orders, which give rise to unusual properties, while escaping detection in conventional experiments. Here we demonstrate the existence of hidden k-space magnetoelectric multipoles in nonmagnetic systems with broken space-inversion symmetry. These k-space magnetoelectric multipoles are reciprocal to the real-space charge dipoles associated with the broken inversion symmetry. Using the prototypical ferroelectric PbTiO_{3} as an example, we show that their origin is a spin asymmetry in momentum space resulting from the broken space inversion symmetry associated with the ferroelectric polarization. In PbTiO_{3}, the k-space spin asymmetry corresponds to a pure k-space magnetoelectric toroidal moment, which can be detected using magnetic Compton scattering, an established tool for probing magnetism in ferromagnets or ferrimagnets with a net spin polarization, which has not been exploited to date for nonmagnetic systems. In particular, the k-space magnetoelectric toroidal moment combined with the spin-orbit interaction manifest in an antisymmetric magnetic Compton profile that can be reversed using an electric field. Our work suggests an experimental route to directly measuring and tuning hidden k-space magnetoelectric multipoles via specially designed magnetic Compton scattering measurements.

Magnetoelectric Effect in Hydrogen Harvesting: Magnetic Field as a Trigger of Catalytic Reactions.

Magnetic fields have been regarded as an additional stimulus for electro- and photocatalytic reactions, but not as a direct trigger for catalytic processes. Multiferroic/magnetoelectric materials, whose electrical polarization and surface charges can be magnetically altered, are especially suitable for triggering and control of catalytic reactions solely with magnetic fields. Here, it is demonstrated that magnetic fields can be employed as an independent input energy source for hydrogen harvesting by means of the magnetoelectric effect. Composite multiferroic CoFe2 O4 -BiFeO3 core-shell nanoparticles act as catalysts for the hydrogen evolution reaction (HER), which is triggered when an alternating magnetic field is applied to an aqueous dispersion of the magnetoelectric nanocatalysts. Based on density functional calculations, it is proposed that the hydrogen evolution is driven by changes in the ferroelectric polarization direction of BiFeO3 caused by the magnetoelectric coupling. It is believed that the findings will open new avenues toward magnetically induced renewable energy harvesting.

Liberating a hidden antiferroelectric phase with interfacial electrostatic engineering.

Antiferroelectric materials have seen a resurgence of interest because of proposed applications in a number of energy-efficient technologies. Unfortunately, relatively few families of antiferroelectric materials have been identified, precluding many proposed applications. Here, we propose a design strategy for the construction of antiferroelectric materials using interfacial electrostatic engineering. We begin with a ferroelectric material with one of the highest known bulk polarizations, BiFeO3. By confining thin layers of BiFeO3 in a dielectric matrix, we show that a metastable antiferroelectric structure can be induced. Application of an electric field reversibly switches between this new phase and a ferroelectric state. The use of electrostatic confinement provides an untapped pathway for the design of engineered antiferroelectric materials with large and potentially coupled responses.

Interplay between ferroelectricity and metallicity in BaTiO3.

We explore the interplay between ferroelectricity and metallicity, which are generally considered to be contra-indicated properties, in the prototypical ferroelectric barium titanate, BaTiO3. Using first-principles density functional theory, we calculate the effects of electron and hole doping, first by introducing a hypothetical background charge, and second through the introduction of explicit impurities (La, Nb and V for electron doping, and K, Al and Sc for hole doping). We find that, apart from a surprising increase in polarization at small hole concentrations, both charge-carrier types decrease the tendency towards ferroelectricity, with the strength of the polarization suppression, which is different for electrons and holes, determined by the detailed structure of the conduction and valence bands. Doping with impurity atoms increases the complexity and allows us to identify three factors that influence the ferroelectricity: structural effects arising largely from the size of the impurity ion, electronic effects from the introduction of charge carriers, and changes in unit-cell volume and shape. A competing balance between these contributions can result in an increase or decrease in ferroelectricity with doping.

Magnetoelectric coupling of domains, domain walls and vortices in a multiferroic with independent magnetic and electric order.

Magnetically induced ferroelectrics exhibit rigidly coupled magnetic and electric order. The ordering temperatures and spontaneous polarization of these multiferroics are notoriously low, however. Both properties can be much larger if magnetic and ferroelectric order occur independently, but the cost of this independence is that pronounced magnetoelectric interaction is no longer obvious. Using spatially resolved images of domains and density-functional theory, we show that in multiferroics with separately emerging magnetic and ferroelectric order, the microscopic magnetoelectric coupling can be intrinsically strong even though the macroscopic leading-order magnetoelectric effect is forbidden by symmetry. We show, taking hexagonal ErMnO3 as an example, that a strong bulk coupling between the ferroelectric and antiferromagnetic order is realized because the structural distortions that lead to the ferroelectric polarization also break the balance of the competing superexchange contributions. We observe the manifestation of this coupling in uncommon types of topological defects like magnetoelectric domain walls and vortex-like singularities.

Layer and spontaneous polarizations in perovskite oxides and their interplay in multiferroic bismuth ferrite.

We review the concept of surface charge, first, in the context of the polarization in ferroelectric materials and, second, in the context of layers of charged ions in ionic insulators. While the former is traditionally discussed in the ferroelectrics community and the latter in the surface science community, we remind the reader that the two descriptions are conveniently unified within the modern theory of polarization. In both cases, the surface charge leads to electrostatic instability-the so-called "polar catastrophe"-if it is not compensated, and we review the range of phenomena that arise as a result of different compensation mechanisms. We illustrate these concepts using the example of the prototypical multiferroic bismuth ferrite, BiFeO3, which is unusual in that its spontaneous ferroelectric polarization and the polarization arising from its layer charges can be of the same magnitude. As a result, for certain combinations of polarization orientation and surface termination, its surface charge is self-compensating. We use density functional calculations of BiFeO3 slabs and superlattices, analysis of high-resolution transmission electron micrographs, and examples from the literature to explore the consequences of this peculiarity.

On the happiness of ferroelectric surfaces and its role in water dissociation: The example of bismuth ferrite.

We investigate, using density functional theory, how the interaction between the ferroelectric polarization and the chemical structure of the (001) surfaces of bismuth ferrite influences the surface properties and reactivity of this material. A precise understanding of the surface behavior of ferroelectrics is necessary for their use in surface science applications such as catalysis as well as for their incorporation in microelectronic devices. Using the (001) surface of bismuth ferrite as a model system, we show that the most energetically favored surface geometries are combinations of surface termination and polarization direction that lead to uncharged stable surfaces. On the unfavorable charged surfaces, we explore the compensation mechanisms of surface charges provided by the introduction of point defects and adsorbates, such as water. Finally, we propose that the special surface properties of bismuth ferrite (001) could be used to produce an effective water splitting cycle through cyclic polarization switching.

Anti-symmetric Compton scattering in LiNiPO 4: Towards a direct probe of the magneto-electric multipole moment.

BACKGROUND: Magnetoelectric multipoles, which break both space-inversion and time-reversal symmetries, play an important role in the magnetoelectric response of a material. Motivated by uncovering the underlying fundamental physics of the magnetoelectric multipoles and the possible technological applications of magnetoelectric materials, understanding as well as detecting such magnetoelectric multipoles has become an active area of research in condensed matter physics. Here we employ the well-established Compton scattering effect as a possible probe for the magnetoelectric toroidal moments in LiNiPO 4. METHODS: We employ combined theoretical and experimental techniques to compute as well as detect the antisymmetric Compton profile in LiNiPO 4. For the theoretical investigation we use density functional theory to compute the anti-symmetric part of the Compton profile for the magnetic and structural ground state of LiNiPO 4. For the experimental verification, we measure the Compton signals for a single magnetoelectric domain sample of LiNiPO 4, and then again for the same sample with its magnetoelectric domain reversed. We then take the difference between these two measured signals to extract the antisymmetric Compton profile in LiNiPO 4. RESULTS: Our theoretical calculations indicate an antisymmetric Compton profile in the direction of the t y toroidal moment in momentum space, with the computed antisymmetric profile around four orders of magnitude smaller than the total profile. The difference signal that we measure is consistent with the computed profile, but of the same order of magnitude as the statistical errors and systematic uncertainties of the experiment. CONCLUSIONS: While the weak difference signal in the measurements prevents an unambiguous determination of the antisymmetric Compton profile in LiNiPO 4, our results motivate  further theoretical work to understand the factors that influence the size of the antisymmetric Compton profile, and to identify materials exhibiting larger effects.

In-situ monitoring of interface proximity effects in ultrathin ferroelectrics.

The development of energy-efficient nanoelectronics based on ferroelectrics is hampered by a notorious polarization loss in the ultrathin regime caused by the unscreened polar discontinuity at the interfaces. So far, engineering charge screening at either the bottom or the top interface has been used to optimize the polarization state. Yet, it is expected that the combined effect of both interfaces determines the final polarization state; in fact the more so the thinner a film is. The competition and cooperation between interfaces have, however, remained unexplored so far. Taking PbTiO3 as a model system, we observe drastic differences between the influence of a single interface and the competition and cooperation of two interfaces. We investigate the impact of these configurations on the PbTiO3 polarization when the interfaces are in close proximity, during thin-film synthesis in the ultrathin limit. By tailoring the interface chemistry towards a cooperative configuration, we stabilize a robust polarization state with giant polarization enhancement. Interface cooperation hence constitutes a powerful route for engineering the polarization in thin-film ferroelectrics towards improved integrability for oxide electronics in reduced dimension.