Hyperferroelectrics: proper ferroelectrics with persistent polarization

Macroscopic Polarization from Nonlinear Gradient Couplings

We show that a lattice mode of arbitrary symmetry induces a well-defined macroscopic polarization at first order in the momentum and second order in the amplitude. We identify a symmetric flexoelectric-like contribution, which is sensitive to both the electrical and mechanical boundary conditions, and an antisymmetric Dzialoshinskii-Moriya-like term, which is unaffected by either. We develop the first-principles methodology to compute the relevant coupling tensors in an arbitrary crystal, which we illustrate with the example of the antiferrodistortive order parameter in SrTiO_{3}.

Comparison of carrier doping in ZnSnO3 and ZnTiO3 from first principles

Ferroelectric materials have attracted increasing attention due to their rich properties. Unlike perovskite ferroelectric oxides, in the LiNbO3-type ferroelectric oxides of ABO3, ferroelectrically active cations are not necessary. While the effects of carrier doping on perovskite ferroelectric oxides have been extensively studied, the studies on LiNbO3-type ferroelectric oxides are rare. We consider two LiNbO3-type ferroelectric oxides ZnSnO3 and ZnTiO3, where the former has no ferroelectrically active cation and the latter has ferroelectrically active cation Ti4+, and study the effect of carrier doping by performing first-principles calculations. Comparison results indicate that the B-site cation has significant effects on the polar distortion in LN-type ferroelectrics. Our studies show that LN-type materials can maintain the coexistence of ferroelectricity and conductance over a very wide range of concentrations. The polar displacement is even enhanced under hole doping. More importantly, ZnSnO3 can be doped by electrons up to a high level to realize the conducting ferroelectrics of high mobility due to its isolated s conduction band.

Out-of-plane ferroelectricity and robust magnetoelectricity in quasi-two-dimensional materials

Thin-film ferroelectrics have been pursued for capacitive and nonvolatile memory devices. They rely on polarizations that are oriented in an out-of-plane direction to facilitate integration and addressability with complementary metal-oxide semiconductor architectures. The internal depolarization field, however, formed by surface charges can suppress the out-of-plane polarization in ultrathin ferroelectric films that could otherwise exhibit lower coercive fields and operate with lower power. Here, we unveil stabilization of a polar longitudinal optical (LO) mode in the n = 2 Ruddlesden-Popper family that produces out-of-plane ferroelectricity, persists under open-circuit boundary conditions, and is distinct from hyperferroelectricity. Our first-principles calculations show the stabilization of the LO mode is ubiquitous in chalcogenides and halides and relies on anharmonic trilinear mode coupling. We further show that the out-of-plane ferroelectricity can be predicted with a crystallographic tolerance factor, and we use these insights to design a room-temperature multiferroic with strong magnetoelectric coupling suitable for magneto-electric spin-orbit transistors.

Origin of the negative longitudinal piezoelectric effect and electric auxetic effect in hexagonal AIBIVCV semiconductors

Hexagonal ABC semiconductors with a polar structure are potential candidates for piezoelectric applications. The intriguing negative longitudinal piezoelectric effect (NLPE) and electric auxetic effect (EAE) may exist in these materials, and establishing the structure-property relation provides physical insights into the underlying mechanisms responsible for these phenomena. In this work, using first-principles calculations, we investigate the piezoelectric response in a class of hexagonal A^IB^IVC^V (A = Li, Na, and K; B = Ge and Sn; C = N, P, As, and Sb) semiconductors. We demonstrate that the quasi-layered structure with contrasting interlayer and intralayer bonding strengths plays a crucial role in the longitudinal piezoelectric response. In this class of materials, we identify 11 compounds out of the 24 candidates possessing the NLPE. We find that the NLPE tends to occur when the quasi-layered structure is pronounced. Moreover, we identify an unusual coexistence of negative longitudinal and transverse piezoelectric responses, and hence the compounds possessing the NLPE are electric auxetic materials as well. This work provides a simple guide for the search of piezoelectrics with desired responses.

Depolarization induced III-V triatomic layers with tristable polarization states

The integration of ferroelectrics that exhibit high dielectric, piezoelectric, and thermal compatibility with the mainstream semiconductor industry will enable novel device types for widespread applications, and yet there are few silicon-compatible ferroelectrics suitable for device downscaling. We demonstrate with first-principles calculations that the enhanced depolarization field at the nanoscale can be utilized to soften unswitchable wurtzite III-V semiconductors, resulting in ultrathin two-dimensional (2D) sheets possessing reversible polarization states. A 2D sheet of AlSb consisting of three atomic planes is identified to host both ferroelectricity and antiferroelectricity, and the tristate switching is accompanied by a metal-semiconductor transition. The thermodynamic stability and potential synthesizability of the triatomic layer are corroborated with phonon spectrum calculations, ab initio molecular dynamics simulations, and variable-composition evolutionary structure search. We propose a 2D AlSb-based homojunction field effect transistor that supports three distinct and nonvolatile resistance states. This new class of III-V semiconductor-derived 2D materials with dual ferroelectricity and antiferroelectricity opens up the opportunity for nonvolatile multibit-based integrated nanoelectronics.

Flexo-Ferroelectricity and a Work Cycle of a Two-Dimensional-Monolayer Actuator

Well recognized mechanical flexibility of two-dimensional (2D) materials is shown to bring about unexpected behaviors to the recently discovered monolayer ferroelectrics, especially those displaying normal, off-plane polarization. A "ferro-flexo" coupling term is introduced into the energy expression, to account for the connection of ferroelectricity and bending (strain gradient) of the layer, to predict and quantify its spontaneous curvature and how it affects the phase transitions. With InP as a chemically specific representative example, the first-principles calculations indeed reveal strong coupling ∼P·ϰ between the ferroelectric polarization (P) and the curvature of the layer (ϰ ≡ 1/r), having profound consequences for both mechanics and ferroelectricity of the material. Due to flexural relaxation, the spontaneous polarization and the transition barrier rise significantly, leading to large changes in the Curie temperature, coercive field, and domain wall width and energy, based on Monte Carlo simulations. On the other hand, the polarization switching, characteristic to ferroelectrics, does induce an overall layer bending, enabling a conversion of electrical signal to movement as an actuator; its possible work-cycles and maximum work-efficiency are briefly discussed.

Switchable Electric Dipole from Polaron Localization in Dielectric Crystals

Ferroelectricity in crystals is associated with the displacement of ions or rotations of polar units. Here we consider the dipole created by donor doping (D^{+}) and the corresponding bound polaron (e^{-}). A dipole of 6.15 Debye is predicted, from Berry phase analysis, in the Ruddlesden-Popper phase of Sr_{3}Ti_{2}O_{7}. A characteristic double-well potential is formed, which persists for high doping densities. The effective Hubbard U interaction can vary the defect state from metallic, a two-dimensional polaron, through to a zero-dimensional polaron. The ferroelectriclike behavior reported here is localized and distinct from conventional spontaneous lattice polarization.

Effect of chemical substitution and external strain on phase stability and ferroelectricity in two dimensional M2CT2 MXenes

Two dimensional ferroelectric materials are gaining increasing attention for use in ultrathin electronic devices owing to the presence of a spontaneous polarization down to one or two monolayers. However, such materials are difficult to identify, especially those with out-of-plane electric polarizations. Previous work predicted that a metastable ferroelectric phase exists in the 2D MXene Sc₂CO₂, while further studies have predicted that this phase exists in other MXene chemistries. However, questions remain about the origin of ferroelectricity, the stability of this phase relative to other competing phases, and the effect of external stimuli in these materials. In this work, we use density functional theory calculations to investigate 12 M₂CT₂ MXenes (M = transition metal, T = surface terminating group) and determine which have the ferroelectric phase as their ground state. We compute these materials' polarizations, densities of states, phonon band structures, Bader charges, and Born effective charges in the ferroelectric phase to elucidate the reasons for its stabilization. We demonstrate that this ferroelectric phase can be preferentially stabilized in non-ferroelectric MXenes through full chemical substitution of Sc or O, alloying of the Sc sites, or application of epitaxial strain. Finally, we show that these materials have excellent piezoelectric properties as well. This work provides a detailed understanding of ferroelectric MXenes and show how the number of 2D ferroelectric materials can be increased through chemical substitution or application of external stimuli.

The role of lattice dynamics in ferroelectric switching

Reducing the switching energy of ferroelectric thin films remains an important goal in the pursuit of ultralow-power ferroelectric memory and logic devices. Here, we elucidate the fundamental role of lattice dynamics in ferroelectric switching by studying both freestanding bismuth ferrite (BiFeO₃) membranes and films clamped to a substrate. We observe a distinct evolution of the ferroelectric domain pattern, from striped, 71° ferroelastic domains (spacing of ~100 nm) in clamped BiFeO₃ films, to large (10’s of micrometers) 180° domains in freestanding films. By removing the constraints imposed by mechanical clamping from the substrate, we can realize a ~40% reduction of the switching voltage and a consequent ~60% improvement in the switching speed. Our findings highlight the importance of a dynamic clamping process occurring during switching, which impacts strain, ferroelectric, and ferrodistortive order parameters and plays a critical role in setting the energetics and dynamics of ferroelectric switching.

Reducing the switching energy of ferroelectric films remains an important goal. Here, the authors elucidate the fundamental role of lattice dynamics in ferroelectric switching on both freestanding BiFeO₃ membranes and films clamped to a substrate.

Two-dimensional ferroelectric metal for electrocatalysis

The coexistence of metallicity and ferroelectricity has been an intriguing and controversial phenomenon as these two material properties are considered incompatible in bulk. We clarify the concept of the ferroelectric metal by revisiting the original definitions for ferroelectric and metal. Two-dimensional (2D) ferroelectrics with out-of-plane polarization can be engineered via layer stacking to a genuine ferroelectric metal characterized by switchable polarization and non-zero density of states at the Fermi level. We demonstrate that 2D ferroelectric metals can serve as electrically-tunable, high-quality electrocatalysts.

Enhanced bulk photovoltaic effect in two-dimensional ferroelectric CuInP2S6

The photocurrent generation in photovoltaics relies essentially on the interface of p-n junction or Schottky barrier with the photoelectric efficiency constrained by the Shockley-Queisser limit. The recent progress has shown a promising route to surpass this limit via the bulk photovoltaic effect for crystals without inversion symmetry. Here we report the bulk photovoltaic effect in two-dimensional ferroelectric CuInP2S6 with enhanced photocurrent density by two orders of magnitude higher than conventional bulk ferroelectric perovskite oxides. The bulk photovoltaic effect is inherently associated to the room-temperature polar ordering in two-dimensional CuInP2S6. We also demonstrate a crossover from two-dimensional to three-dimensional bulk photovoltaic effect with the observation of a dramatic decrease in photocurrent density when the thickness of the two-dimensional material exceeds the free path length at around 40 nm. This work spotlights the potential application of ultrathin two-dimensional ferroelectric materials for the third-generation photovoltaic cells.

Ferroelectricity and multiferroicity in anti-Ruddlesden-Popper structures

Combining ferroelectricity with other properties such as visible light absorption or long-range magnetic order requires the discovery of new families of ferroelectric materials. Here, through the analysis of a high-throughput database of phonon band structures, we identify a structural family of anti-Ruddlesden-Popper phases [Formula: see text]O (A=Ca, Sr, Ba, Eu, X=Sb, P, As, Bi) showing ferroelectric and antiferroelectric behaviors. The discovered ferroelectrics belong to the new class of hyperferroelectrics that polarize even under open-circuit boundary conditions. The polar distortion involves the movement of O anions against apical A cations and is driven by geometric effects resulting from internal chemical strains. Within this structural family, we show that [Formula: see text]O combines coupled ferromagnetic and ferroelectric order at the same atomic site, a very rare occurrence in materials physics.

Examination of permittivity for depolarization field of ferroelectric by ab initio calculation, suggesting hidden mechanisms

Electrostatics of depolarization field Ed in relation to the polarization is studied. In particular, the value of permittivity for Ed (εd) in prototypical situations of ferroelectrics, including Mehta formula, is examined by ab initio calculations. By using spontaneous polarization PS corresponding to accurate experiment ones, we show εd = 1, which suggests that the results of εd ≫ 1 indicate hidden mechanisms; εd = 1 suggests that the effect of Ed is significant to induce intriguing important phenomena overlooked by εd ≫ 1. A bridge between εd = 1 and εd ≫ 1, i.e. the consistency of εd = 1 with conventional results is presented. The exact electrostatic equality of head-to-head-tail-to-tail domains to free-standing ferroelectrics is deduced. Hence, most stoichiometric clean freestanding monodomain ferroelectrics and head-to-head-tail-to-tail domains are shown unstable regardless of size, unless partially metallic. This verifies the previous results in a transparent manner. This conclusion is shown consistent with a recent hyperferroelectric LiBeSb and "freestanding" monolayer ferroelectrics, of which origin is suggested to be adsorbates. In addition, this restriction is suggested to break in externally strained ultrathin ferroelectrics. The macroscopic formulas of Ed are found valid down to a several unit-cells, when electronic and atomic-scale surface effects are unimportant and accurate PS is used.

A three-order-parameter bistable magnetoelectric multiferroic metal

Using first-principles calculations we predict that the layered-perovskite metal Bi5Mn5O17 is a ferromagnet, ferroelectric, and ferrotoroid which may realize the long sought-after goal of a room-temperature ferromagnetic single-phase multiferroic with large, strongly coupled, primary-order polarization and magnetization. Bi5Mn5O17 has two nearly energy-degenerate ground states with mutually orthogonal vector order parameters (polarization, magnetization, ferrotoroidicity), which can be rotated globally by switching between ground states. Giant cross-coupling magnetoelectric and magnetotoroidic effects, as well as optical non-reciprocity, are thus expected. Importantly, Bi5Mn5O17 should be thermodynamically stable in O-rich growth conditions, and hence experimentally accessible.

Prediction of an Extended Ferroelectric Clathrate

Using first-principles calculations, we predict a lightweight room-temperature ferroelectric carbon-boron framework in a host-guest clathrate structure. This ferroelectric clathrate, with composition ScB_{3}C_{3}, exhibits high polarization density and low mass density compared with widely used commercial ferroelectrics. Molecular dynamics simulations show spontaneous polarization with a moderate above-room-temperature T_{c} of ∼370  K, which implies large susceptibility and possibly large electrocaloric and piezoelectric constants at room temperature. Our findings open the possibility for a new class of ferroelectric materials with potential across a broad range of applications.

Multiband Quantum Criticality of Polar Metals

Motivated by recent experimental realizations of polar metals with broken inversion symmetry, we explore the emergence of strong correlations driven by criticality when the polar transition temperature is tuned to zero. Overcoming previously discussed challenges, we demonstrate a robust mechanism for coupling between the critical mode and electrons in multiband metals. We identify and characterize several novel interacting phases, including non-Fermi liquids, when band crossings are close to the Fermi level and present their experimental signatures for three generic types of band crossings.

Elasticity Modulation Due to Polarization Reversal and Ionic Motion in the Ferroelectric Superionic Conductor KTiOPO4

The coupling between ionic degrees of freedom and ferroelectricity has received renewed attention in recent years, given that surface electrochemical processes have been shown to be intrinsically linked to ferroelectric phase stability in ultrathin ferroelectric films. However, the coupling between bulk ionic transport and local polarization switching has received less attention, as typically the bulk ionic mobilities are low for common ferroelectrics at room temperature. Here, we use the coupled band-excitation method in conjunction with site-correlated time-of-flight secondary ion mass spectrometry, to determine the coupling between ferroelectric switching and ionic motion in single crystal KTiOPO₄. The local scanning probe measurements indicate a substantial softening, as determined by resonant frequency changes, during reversal of polarization along one direction. These changes are correlated with the mass spectrometry measurements, showing a polarization-dependent accumulation of K ions at the polar surfaces, thus corroborating their role in the screening process. These studies shed light on the interplay between ionic dynamics and bulk ferroelectric switching and have implications for studies on domain wall conductivity, chemical switching, and bulk and surface-screening phenomena.

High-throughput first principles search for new ferroelectrics

We use a combination of symmetry analysis and high-throughput density functional theory calculations to search for new ferroelectric materials. We use two search strategies to identify candidate materials. In the first strategy, we start with non-polar materials and look for unrecognized energy-lowering polar distortions. In the second strategy, we consider polar materials and look for related higher symmetry structures. In both cases, if we find new structures with the correct symmetries that are also close in energy to experimentally known structures, then the material is likely to be switchable in an external electric field, making it a candidate ferroelectric. We find sixteen candidate materials, with variety of properties that are rare in typical ferroelectrics, including large polarization, hyperferroelectricity, antiferroelectricity, and multiferroism.

Origin of Negative Longitudinal Piezoelectric Effect

Piezoelectrics with negative longitudinal piezoelectric coefficients will contract in the direction of an applied electric field. Such piezoelectrics are thought to be rare, but there is no fundamental physics preventing the realization of negative longitudinal piezoelectric effect in a single-phase material. Using first-principles calculations, we demonstrate that several hexagonal ABC ferroelectrics possess significant negative longitudinal piezoelectric effects. The data mining of a first-principles-based database of piezoelectrics reveals that this effect is a general phenomenon. The origin of this unusual piezoelectric response relies on the strong ionic bonds associated with small effective charges and rigid potential energy surfaces. Moreover, ferroelectrics with negative longitudinal piezoelectric coefficients show anomalous pressure-enhanced ferroelectricity. Our results offer design principles to aid the search for new piezoelectrics for novel electromechanical device applications.

Antiferroelectric Topological Insulators in Orthorhombic AMgBi Compounds (A=Li, Na, K)

We introduce antiferroelectric topological insulators as a new class of functional materials in which an electric field can be used to control topological order and induce topological phase transitions. Using first principles methods, we predict that several alkali-MgBi orthorhombic members of an ABC family of compounds are antiferroelectric topological insulators. We also show that epitaxial strain and hydrostatic pressure can be used to tune the topological order and the band gap of these ABC compounds. Antiferroelectric topological insulators could enable precise control of topology using electric fields, enhancing the applicability of topological materials in electronics and spintronics.

Stable charged antiparallel domain walls in hyperferroelectrics

Charge-neutral 180° domain walls that separate domains of antiparallel polarization directions are common structural topological defects in ferroelectrics. In normal ferroelectrics, charged 180° domain walls running perpendicular to the polarization directions are highly energetically unfavorable because of the depolarization field and are difficult to stabilize. We explore both neutral and charged 180° domain walls in hyperferroelectrics, a class of proper ferroelectrics with persistent polarization in the presence of a depolarization field, using density functional theory. We obtain zero temperature equilibrium structures of head-to-head and tail-to-tail walls in recently discovered ABC-type hexagonal hyperferroelectrics. Charged domain walls can also be stabilized in canonical ferroelectrics represented by LiNbO₃ without any dopants, defects or mechanical clamping. First-principles electronic structure calculations show that charged domain walls can reduce and even close the band gap of host materials and support quasi-two-dimensional electron(hole) gas with enhanced electrical conductivity.

Computational Screening of All Stoichiometric Inorganic Materials

Forming a four-component compound from the first 103 elements of the periodic table results in more than 10¹² combinations. Such a materials space is intractable to high-throughput experiment or first-principle computation. We introduce a framework to address this problem and quantify how many materials can exist. We apply principles of valency and electronegativity to filter chemically implausible compositions, which reduces the inorganic quaternary space to 10¹⁰ combinations. We demonstrate that estimates of band gaps and absolute electron energies can be made simply on the basis of the chemical composition and apply this to the search for new semiconducting materials to support the photoelectrochemical splitting of water. We show the applicability to predicting crystal structure by analogy with known compounds, including exploration of the phase space for ternary combinations that form a perovskite lattice. Computer screening reproduces known perovskite materials and predicts the feasibility of thousands more. Given the simplicity of the approach, large-scale searches can be performed on a single workstation.

The origin of hyperferroelectricity in LiBO3 (B = V, Nb, Ta, Os)

The electronic and structural properties of LiBO₃ (B = V, Nb, Ta, Os) are investigated via first-principles methods. We show that LiBO₃ belong to the recently proposed hyperferroelectrics (hyperFEs), i.e., they all have unstable longitudinal optic phonon modes. Especially, the ferroelectric-like instability in the metal LiOsO₃, whose optical dielectric constant goes to infinity, is a limiting case of hyperFEs. Via an effective Hamiltonian, we further show that, in contrast to normal proper ferroelectricity, in which the ferroelectric instability usually comes from long-range coulomb interactions, the hyperFE instability is due to the structure instability driven by short-range interactions. This could happen in systems with large ion size mismatches, which therefore provides a useful guidance in searching for novel hyperFEs.

Ferroelectricity and Phase Transitions in Monolayer Group-IV Monochalcogenides

Ferroelectricity usually fades away as materials are thinned down below a critical value. We reveal that the unique ionic-potential anharmonicity can induce spontaneous in-plane electrical polarization and ferroelectricity in monolayer group-IV monochalcogenides MX (M=Ge, Sn; X=S, Se). An effective Hamiltonian has been successfully extracted from the parametrized energy space, making it possible to study the ferroelectric phase transitions in a single-atom layer. The ferroelectricity in these materials is found to be robust and the corresponding Curie temperatures are higher than room temperature, making them promising for realizing ultrathin ferroelectric devices of broad interest. We further provide the phase diagram and predict other potentially two-dimensional ferroelectric materials.

Intertwined Rashba, Dirac, and Weyl Fermions in Hexagonal Hyperferroelectrics

By means of density functional theory based calculations, we study the role of spin-orbit coupling in the new family of ABC hyperferroelectrics [Garrity, Rabe, and Vanderbilt Phys. Rev. Lett. 112, 127601 (2014)]. We unveil an extremely rich physics strongly linked to ferroelectric properties, ranging from the electric control of bulk Rashba effect to the existence of a three-dimensional topological insulator phase, with concomitant topological surface states even in the ultrathin film limit. Moreover, we predict that the topological transition, as induced by alloying, is followed by a Weyl semimetal phase of finite concentration extension, which is robust against disorder, putting forward hyperferroelectrics as promising candidates for spin-orbitronic applications.

Prediction of a native ferroelectric metal

Over 50 years ago, Anderson and Blount discussed symmetry-allowed polar distortions in metals, spawning the idea that a material might be simultaneously metallic and ferroelectric. While many studies have ever since considered such or similar situations, actual ferroelectricity—that is, the existence of a switchable intrinsic electric polarization—has not yet been attained in a metal, and is in fact generally deemed incompatible with the screening by mobile conduction charges. Here we refute this common wisdom and show, by means of first-principles simulations, that native metallicity and ferroelectricity coexist in the layered perovskite Bi₅Ti₅O₁₇. We show that, despite being a metal, Bi₅Ti₅O₁₇ can sustain a sizable potential drop along the polar direction, as needed to reverse its polarization by an external bias. We also reveal striking behaviours, as the self-screening mechanism at work in thin Bi₅Ti₅O₁₇ layers, emerging from the interplay between polar distortions and carriers in this compound.

Ferroelectricity, spontaneous switchable polarization, is usually deemed incompatible with the electronic screening of a metal. Here, the authors use ab initio theory to predict that metallicity natively coexists with ferroelectric polarization and finite depolarizing fields in the perovskite Bi₅Ti₅O₁₇.