Effect of quantum fluctuations on structural phase transitions in SrTiO3 and BaTiO3

Intrinsic-strain-induced ferroelectric order and ultrafine nanodomains in SrTiO3

Nano ferroelectrics holds the potential application promise in information storage, electro-mechanical transformation, and novel catalysts but encounters a huge challenge of size limitation and manufacture complexity on the creation of long-range ferroelectric ordering. Herein, as an incipient ferroelectric, nanosized SrTiO3 was indued with polarized ordering at room temperature from the nonpolar cubic structure, driven by the intrinsic three-dimensional (3D) tensile strain. The ferroelectric behavior can be confirmed by piezoelectric force microscopy and the ferroelectric TO1 soft mode was verified with the temperature stability to 500 K. Its structural origin comes from the off-center shift of Ti atom to oxygen octahedron and forms the ultrafine head-to-tail connected 90° nanodomains about 2 to 3 nm, resulting in an overall spontaneous polarization toward the short edges of nanoparticles. According to the density functional theory calculations and phase-field simulations, the 3D strain-related dipole displacement transformed from [001] to [111] and segmentation effect on the ferroelectric domain were further proved. The topological ferroelectric order induced by intrinsic 3D tensile strain shows a unique approach to get over the nanosized limitation in nanodevices and construct the strong strain-polarization coupling, paving the way for the design of high-performance and free-assembled ferroelectric devices.

Insights into Strain Engineering: From Ferroelectrics to Related Functional Materials and Beyond

Ferroelectrics have become indispensable components in various application fields, including information processing, energy harvesting, and electromechanical conversion, owing to their unique ability to exhibit electrically or mechanically switchable polarization. The distinct polar noncentrosymmetric lattices of ferroelectrics make them highly responsive to specific crystal structures. Even slight changes in the lattice can alter the polarization configuration and response to external fields. In this regard, strain engineering has emerged as a prevalent regulation approach that not only offers a versatile platform for structural and performance optimization within ferroelectrics but also unlocks boundless potential in various functional materials. In this review, we systematically summarize the breakthroughs in ferroelectric-based functional materials achieved through strain engineering and progress in method development. We cover research activities ranging from fundamental attributes to wide-ranging applications and novel functionalities ranging from electromechanical transformation in sensors and actuators to tunable dielectric materials and information technologies, such as transistors and nonvolatile memories. Building upon these achievements, we also explore the endeavors to uncover the unprecedented properties through strain engineering in related chemical functionalities, such as ferromagnetism, multiferroicity, and photoelectricity. Finally, through discussions on the prospects and challenges associated with strain engineering in the materials, this review aims to stimulate the development of new methods for strain regulation and performance boosting in functional materials, transcending the boundaries of ferroelectrics.

Brownian Electric Bubble Quasiparticles

Recent works on electric bubbles (including the experimental demonstration of electric skyrmions) constitute a breakthrough akin to the discovery of magnetic skyrmions some 15 years ago. So far research has focused on obtaining and visualizing these objects, which often appear to be immobile (pinned) in experiments. Thus, critical aspects of magnetic skyrmions-e.g., their quasiparticle nature, Brownian motion-remain unexplored (unproven) for electric bubbles. Here we use predictive atomistic simulations to investigate the basic dynamical properties of these objects in pinning-free model systems. We show that it is possible to find regimes where the electric bubbles can present long lifetimes (∼ns) despite being relatively small (diameter <2  nm). Additionally, we find that they can display stochastic dynamics with large and highly tunable diffusion constants. We thus establish the quasiparticle nature of electric bubbles and put them forward for the physical effects and applications (e.g., in token-based probabilistic computing) considered for magnetic skyrmions.

Modeling Temperature-Dependent Electron Thermal Diffuse Scattering via Machine-Learned Interatomic Potentials and Path-Integral Molecular Dynamics

Electron thermal diffuse scattering is shown to be sensitive to subtle changes in atomic vibrations and shows promise in assessing lattice dynamics at nanometer resolution. Here, we demonstrate that machine-learned interatomic potentials (MLIPs) and path-integral molecular dynamics can accurately capture the potential energy landscape and lattice dynamics needed to describe electron thermal diffuse scattering. Using SrTiO_{3} as a test bed at cryogenic and room temperatures, we compare electron thermal diffuse scattering simulations using different approximations to incorporate thermal motion. Only when the simulations are based on quantum mechanically accurate MLIPs in combination with path-integral molecular dynamics that include nuclear quantum effects is there excellent agreement with experiments.

Comprehensive review of micro/nanostructured ZnSnO3: characteristics, synthesis, and diverse applications

Generally, zinc stannate (ZnSnO3) is a fascinating ternary oxide compound, which has attracted significant attention in the field of materials science due to its unique properties such high sensitivity, large specific area, non-toxic nature, and good compatibility. Furthermore, in terms of both its structure and properties, it is the most appealing category of nanoparticles. The chemical stability of ZnSnO3 under normal conditions contributes to its applicability in various fields. To date, its potential as a luminescent and photovoltaic material and application in supercapacitors, batteries, solar cells, biosensors, gas sensors, and catalysts have been extensively studied. Additionally, the efficient energy storage capacity of ZnSnO3 makes it a promising candidate for the development of energy storage systems. This review focuses on the notable progress in the structural features of ZnSnO3 nanocomposites, including the synthetic processes employed for the fabrication of various ZnSnO3 nanocomposites, their intrinsic characteristics, and their present-day uses. Specifically, we highlight the recent progress in ZnSnO3-based nanomaterials, composites, and doped materials for their utilization in Li-ion batteries, photocatalysis, gas sensors, and energy storage and conversion devices. The further exploration and understanding of the properties of ZnSnO3 will undoubtedly lead to its broader implementation and contribute to the advancement of next-generation materials and devices.

Lamellar Fluctuations Melt Ferroelectricity

We consider a standard Ginzburg-Landau model of a ferroelectric whose electrical polarization is coupled to gradients of elastic strain. At the harmonic level, such flexoelectric interaction is known to hybridize acoustic and optic phonon modes and lead to phases with modulated lattice structures that precede the state with spontaneously broken inversion symmetry. Here, we use the self-consistent phonon approximation to calculate the effects of thermal and quantum polarization fluctuations on the bare hybridized modes to show that such long-range modulated order is unstable at all temperatures. We discuss the implications for the nearly ferroelectric SrTiO_{3} and KTaO_{3}, and we propose that these systems are melted versions of an underlying modulated state that is dominated by nonzero momentum thermal fluctuations except at the very lowest temperatures.

Signatures of enhanced out-of-plane polarization in asymmetric BaTiO3 superlattices integrated on silicon

In order to bring the diverse functionalities of transition metal oxides into modern electronics, it is imperative to integrate oxide films with controllable properties onto the silicon platform. Here, we present asymmetric LaMnO₃/BaTiO₃/SrTiO₃ superlattices fabricated on silicon with layer thickness control at the unit-cell level. By harnessing the coherent strain between the constituent layers, we overcome the biaxial thermal tension from silicon and stabilize c-axis oriented BaTiO₃ layers with substantially enhanced tetragonality, as revealed by atomically resolved scanning transmission electron microscopy. Optical second harmonic generation measurements signify a predominant out-of-plane polarized state with strongly enhanced net polarization in the tricolor superlattices, as compared to the BaTiO₃ single film and conventional BaTiO₃/SrTiO₃ superlattice grown on silicon. Meanwhile, this coherent strain in turn suppresses the magnetism of LaMnO₃ as the thickness of BaTiO₃ increases. Our study raises the prospect of designing artificial oxide superlattices on silicon with tailored functionalities.

Integrating multifunctional oxides on silicon is highly desirable. Here, the authors present asymmetric BaTiO3 superlattices on silicon exhibiting enhanced out-of-plane polarization by harnessing the interfacial strain and broken inversion symmetry.

Universal Structural Influence on the 2D Electron Gas at SrTiO3 Surfaces

The 2-dimensional electron gas (2DEG) found at the surface of SrTiO3 and related interfaces has attracted significant attention as a promising basis for oxide electronics. In order to utilize its full potential, the response of this 2DEG to structural changes and surface modification must be understood in detail. Here, a study of the detailed electronic structure evolution of the 2DEG as a function of sample temperature and surface step density is presented. By comparing the experimental results with ab initio calculations, it is shown that local structure relaxations cause a metal-insulator transition of the system around 135 K. This study presents a new and simple way of tuning the 2DEG via surface vicinality and identifies how the operation of prospective devices will respond to changes in temperature.

The ferroelectric photo ground state of SrTiO3: Cavity materials engineering

Controlling collective phenomena in quantum materials is a promising route toward engineering material properties on demand. Strong THz lasers have been successful at inducing ferroelectricity in SrTiO3. Here we demonstrate, from atomistic calculations, that cavity quantum vacuum fluctuations induce a change in the collective phase of SrTiO3 in the strong light–matter coupling regime. Under these conditions, the ferroelectric phase is stabilized as the ground state, instead of the quantum paraelectric one. We conceptualize this light–matter hybrid state as a material photo ground state: Fundamental properties such as crystal structure, phonon frequencies, and the collective phase of a material are determined by the quantum light–matter coupling in equilibrium conditions. Cavity-coupling adds a new dimension to the phase diagram of SrTiO3.

Optical cavities confine light on a small region in space, which can result in a strong coupling of light with materials inside the cavity. This gives rise to new states where quantum fluctuations of light and matter can alter the properties of the material altogether. Here we demonstrate, based on first-principles calculations, that such light–matter coupling induces a change of the collective phase from quantum paraelectric to ferroelectric in the SrTiO3 ground state, which has thus far only been achieved in out-of-equilibrium strongly excited conditions [X. Li et al., Science 364, 1079–1082 (2019) and T. F. Nova, A. S. Disa, M. Fechner, A. Cavalleri, Science 364, 1075–1079 (2019)]. This is a light–matter hybrid ground state which can only exist because of the coupling to the vacuum fluctuations of light, a photo ground state. The phase transition is accompanied by changes in the crystal structure, showing that fundamental ground state properties of materials can be controlled via strong light–matter coupling. Such a control of quantum states enables the tailoring of materials properties or even the design of novel materials purely by exposing them to confined light.

Strong Room-Temperature Ferroelectricity in Strained SrTiO3 Homoepitaxial Film

Although the discovery of exceptional ferroelectricity in paraelectrics offers great opportunities to enrich the diversity of the ferroelectric family and promote the development of novel functionalities, transformation of paraelectric phases into ferroelectric phases remains challenging. Herein, a method is presented for driving paraelectrics into ferroelectric states via the introduction of M/O-deficient (M for metal) perovskite nanoregions. Using this method, strong ferroelectricity, equivalent to that of classic ferroelectrics, is achieved in a prototype paraelectric strontium titanate (SrTiO₃ ) homoepitaxial film embedded with Ti/O-deficient perovskite nanoregions. It is shown that these unique nanoregions impose large out-of-plane tensile strain and electron-doping effects on the matrix to form a tetragonal structure (tetragonality = 1.038), driving the off-center movements of Ti and Sr atoms. This leads to a significant room-temperature ferroelectric polarization (maximum polarization = 41.6 µC cm^-2 and spontaneous polarization = 25.2 µC cm^-2 at 1.60 MV cm^-1 ) with a high thermal stability (T_stable  ≈ 1098 K). The proposed approach can be applied to various paraelectrics for creating ferroelectricity and generating emergent physical properties, opening the door to a new realm of materials design.

Influence of Sr deficiency on structural and electrical properties of SrTiO3 thin films grown by metal-organic vapor phase epitaxy

Homoepitaxial growth of SrTiO3 thin films on 0.5 wt% niobium doped SrTiO3 (100) substrates with high structural perfection was developed using liquid-delivery spin metal-organic vapor phase epitaxy (MOVPE). Exploiting the advantage of adjusting the partial pressures of the individual constituents independently, we tuned the Sr/Ti ratio of the gas phase for realizing, stoichiometric, as well as Sr deficient layers. Quantitative energy dispersive X-ray spectroscopy in a scanning transmission electron microscope confirm Sr deficiency of up to 20% in nominally off-stoichiometrically grown films. Our MOVPE process allows to grow such layers in phase pure state and without extended defect formation. Indications for oxygen deficiency could not be identified. Sr deficient layers exhibit an increased permittivity of ɛr = 202 and a larger vertical lattice parameter. Current-voltage characteristics (IVCs) of metal-oxide-semiconductor (Pt/SrTiO3/SrTiO3:Nb) structures reveal that Sr deficient SrTiO3 films show an intrinsic resistive switching with on-off ratios of three orders of magnitude at RT and seven orders of magnitude at 10 K. There is strong evidence that a large deviation from stoichiometry pronounces the resistive switching behavior. IVCs conducted at 10 K indicate a defect-based mechanism instead of mass transport by ion diffusion. This is supported by in-situ STEM investigations that show filaments to form at significant higher voltages than those were resistive switching is observed in our samples.

Ferroelectricity, Superconductivity, and SrTiO3—Passions of K.A. Müller

SrTiO3 is an insulating material which, using chemical doping, pressure, strain or isotope substitution, can be turned into a ferroelectric material or into a superconductor. The material itself, and the two aforementioned phenomena, have been subjects of intensive research of Karl Alex Müller and have been a source of inspiration, among other things, for his Nobel prize-winning research on high temperature superconductivity. An intriguing outstanding question is whether the occurrence of ferroelectricity and superconductivity in the same material is just a coincidence, or whether a deeper connection exists. In addition there is the empirical question of how these two phenomena interact with each other. Here we show that it is possible to induce superconductivity in a two-dimensional layer at the interface of SrTiO3 and LaAlO3 when we make the SrTiO3 ferroelectric by means of 18O substitution. Our experiments indicate that the ferroelectricity is perfectly compatible with having a superconducting two-dimensional electron system at the interface. This provides a promising avenue for manipulating superconductivity in a non centrosymmetric environment.

Anharmonic Eigenvectors and Acoustic Phonon Disappearance in Quantum Paraelectric SrTiO_{3}

Pronounced anomalies in the SrTiO_{3} dynamical structure factor, S(Q,E), including the disappearance of acoustic phonon branches at low temperatures, were uncovered with inelastic neutron scattering (INS) and simulations. The striking effect reflects anharmonic couplings between acoustic and optic phonons and the incipient ferroelectric instability near the quantum critical point. It is rationalized using a first-principles renormalized anharmonic phonon approach, pointing to nonlinear Ti-O hybridization causing unusual changes in real-space phonon eigenvectors, frequencies, group velocities, and scattering phase space. Our method is general and establishes how T dependences beyond the harmonic regime, assessed by INS mapping of large reciprocal-space volumes, provide real-space insights into anharmonic atomic dynamics near phase transitions.

Enhancing superconductivity in SrTiO3 films with strain

The nature of superconductivity in SrTiO₃, the first oxide superconductor to be discovered, remains a subject of intense debate several decades after its discovery. SrTiO₃ is also an incipient ferroelectric, and several recent theoretical studies have suggested that the two properties may be linked. To investigate whether such a connection exists, we grew strained, epitaxial SrTiO₃ films, which are known to undergo a ferroelectric transition. We show that, for a range of carrier densities, the superconducting transition temperature is enhanced by up to a factor of two compared to unstrained films grown under the same conditions. Moreover, for these films, superconductivity emerges from a resistive state. We discuss the localization behavior in the context of proximity to ferroelectricity. The results point to new opportunities to enhance superconducting transition temperatures in oxide materials.

Enhanced superconductivity close to a non-magnetic quantum critical point in electron-doped strontium titanate

Studies on quantum critical points (QCP) have focused on magnetic QCPs to date. Remarkable phenomena such as superconductivity due to avoided criticality have been discovered, but we focus here on the non-magnetic counterpart, i.e., the superconductivity of SrTiO3 regarded as being close to a ferroelectric QCP. Here we prepare high-quality Sr1-xLaxTi(16O1-z18Oz)3 single crystals without localisation at low temperatures, which allow us to systematically investigate the La substitution of Sr as an alternative to introducing oxygen vacancies. Analysis of our data based on a theoretical model predicts an appearance of the ferroelectric QCP around 3 × 1018 cm-3. Because of the QCP, the superconducting dome of Sr1-xLaxTiO3 can be raised upwards. Furthermore, remarkable enhancement of Tc (~0.6 K) is achieved by 18O exchange on the Sr1-xLaxTiO3 crystals. These findings provide a new knob for observing intriguing physics around the ferroelectric QCP.

Electron-Phonon Scattering in the Presence of Soft Modes and Electron Mobility in SrTiO_{3} Perovskite from First Principles

Structural phase transitions and soft phonon modes pose a long-standing challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent e-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic SrTiO_{3} is controlled by scattering with longitudinal optical phonons at room temperature and with ferroelectric soft phonons below 200 K. Our calculations can accurately predict the temperature dependence of the electron mobility in SrTiO_{3} between 150-300 K, and reveal the microscopic origin of its roughly T^{-3} trend. Our approach enables first-principles calculations of e-ph interactions and charge transport in broad classes of crystals with phase transitions and strongly anharmonic phonons.

New high-pressure tetragonal polymorphs of SrTiO3-molecular orbital and Raman band change under pressure

The vibrational and structural properties of SrTiO₃ were investigated using Raman spectroscopy, synchrotron x-ray powder diffraction up to 55 GPa at 300 K, and ab initio quantum chemical molecular orbital (MO) calculations. These measurements and calculations revealed the structure transformation from cubic to tetragonal phase at about 9 GPa. Above 9 GPa, sharper new peaks were associated with a tetragonal structure. At about 30 GPa some bands disappeared and several new bands emerged. Structure transformation from I4/mcm to a new structure of P4/mbm was found at above 30 GPa by Rietveld profile fitting analysis. The diffraction pattern gave no indication of a Cmcm orthorhombic phase. Ab initio MO calculation proved the change of the molecular orbital coupling with a structure transformation. The Mulliken charge of Ti is increased with increasing pressure in the cubic phase, but the Sr charge continuously decreased. The d-p-π hybridization of the Ti-O bond and localizing the electron density are decreased with increasing pressure. The Ti-O bond becomes shorted in the P4/mbm phase and the change in the Ti charge accelerated more. All present investigations by x-ray diffraction, Raman spectra study and MO calculation show consistent results.

Prediction of a Large-Gap and Switchable Kane-Mele Quantum Spin Hall Insulator

Fundamental research and technological applications of topological insulators are hindered by the rarity of materials exhibiting a robust topologically nontrivial phase, especially in two dimensions. Here, by means of extensive first-principles calculations, we propose a novel quantum spin Hall insulator with a sizable band gap of ∼0.5  eV that is a monolayer of jacutingaite, a naturally occurring layered mineral first discovered in 2008 in Brazil and recently synthesized. This system realizes the paradigmatic Kane-Mele model for quantum spin Hall insulators in a potentially exfoliable two-dimensional monolayer, with helical edge states that are robust and that can be manipulated exploiting a unique strong interplay between spin-orbit coupling, crystal-symmetry breaking, and dielectric response.

Prospects and applications near ferroelectric quantum phase transitions: a key issues review

The emergence of complex and fascinating states of quantum matter in the neighborhood of zero temperature phase transitions suggests that such quantum phenomena should be studied in a variety of settings. Advanced technologies of the future may be fabricated from materials where the cooperative behavior of charge, spin and current can be manipulated at cryogenic temperatures. The progagating lattice dynamics of displacive ferroelectrics make them appealing for the study of quantum critical phenomena that is characterized by both space- and time-dependent quantities. In this key issues article we aim to provide a self-contained overview of ferroelectrics near quantum phase transitions. Unlike most magnetic cases, the ferroelectric quantum critical point can be tuned experimentally to reside at, above or below its upper critical dimension; this feature allows for detailed interplay between experiment and theory using both scaling and self-consistent field models. Empirically the sensitivity of the ferroelectric T _c's to external and to chemical pressure gives practical access to a broad range of temperature behavior over several hundreds of Kelvin. Additional degrees of freedom like charge and spin can be added and characterized systematically. Satellite memories, electrocaloric cooling and low-loss phased-array radar are among possible applications of low-temperature ferroelectrics. We end with open questions for future research that include textured polarization states and unusual forms of superconductivity that remain to be understood theoretically.

LiNbO3 surfaces from a microscopic perspective

A large number of oxides has been investigated in the last twenty years as possible new materials for various applications ranging from opto-electronics to heterogeneous catalysis. In this context, ferroelectric oxides are particularly promising. The electric polarization plays a crucial role at many oxide surfaces, and it largely determines their physical and chemical properties. Ferroelectrics offer in addition the possibility to control/switch the electric polarization and hence the surface chemistry, allowing for the realization of domain-engineered nanoscale devices such as molecular detectors or highly efficient catalysts. Lithium niobate (LiNbO₃) is a ferroelectric with a high spontaneous polarization, whose surfaces have a huge and largely unexplored potential. Owing to recent advances in experimental techniques and sample preparation, peculiar and exclusive properties of LiNbO₃ surfaces could be demonstrated. For example, water films freeze at different temperatures on differently polarized surfaces, and the chemical etching properties of surfaces with opposite polarization are strongly different. More important, the ferroelectric domain orientation affects temperature dependent surface stabilization mechanisms and molecular adsorption phenomena. Various ab initio theoretical investigations have been performed in order to understand the outcome of these experiments and the origin of the exotic behavior of the lithium niobate surfaces. Thanks to these studies, many aspects of their surface physics and chemistry could be clarified. Yet other puzzling features are still not understood. This review gives a résumé on the present knowledge of lithium niobate surfaces, with a particular view on their microscopic properties, explored in recent years by means of ab initio calculations. Relevant aspects and properties of the surfaces that need further investigation are briefly discussed. The review is concluded with an outlook of challenges and potential payoff for LiNbO₃ based applications.

Room Temperature Tunable Multiferroic Properties in Sol-Gel-Derived Nanocrystalline Sr(Ti1-xFex)O3-δ Thin Films

Sr(Ti_1−xFe_x)O_3−δ (0 ≤ x ≤ 0.2) thin films were grown on Si(100) substrates with LaNiO₃ buffer-layer by a sol-gel process. Influence of Fe substitution concentration on the structural, ferroelectric, and magnetic properties, as well as the leakage current behaviors of the Sr(Ti_1−xFe_x)O_3−δ thin films, were investigated by using the X-ray diffractometer (XRD), atomic force microscopy (AFM), the ferroelectric test system, and the vibrating sample magnetometer (VSM). After substituting a small amount of Ti ion with Fe, highly enhanced ferroelectric properties were obtained successfully in SrTi_0.9Ti_0.1O_3−δ thin films, with a double remanent polarization (2P_r) of 1.56, 1.95, and 9.14 μC·cm⁻², respectively, for the samples were annealed in air, oxygen, and nitrogen atmospheres. The leakage current densities of the Fe-doped SrTiO₃ thin films are about 10⁻⁶–10⁻⁵ A·cm⁻² at an applied electric field of 100 kV·cm⁻¹, and the conduction mechanism of the thin film capacitors with various Fe concentrations has been analyzed. The ferromagnetic properties of the Sr(Ti_1−xFe_x)O_3−δ thin films have been investigated, which can be correlated to the mixed valence ions and the effects of the grain boundary. The present results revealed the multiferroic nature of the Sr(Ti_1−xFe_x)O_3−δ thin films. The effect of the annealing environment on the room temperature magnetic and ferroelectric properties of Sr(Ti_0.9Fe_0.1)O_3−δ thin films were also discussed in detail.

Ultrafast X-ray diffraction probe of terahertz field-driven soft mode dynamics in SrTiO3

We use ultrafast X-ray pulses to characterize the lattice response of SrTiO₃ when driven by strong terahertz fields. We observe transient changes in the diffraction intensity with a delayed onset with respect to the driving field. Fourier analysis reveals two frequency components corresponding to the two lowest energy zone-center optical modes in SrTiO₃. The lower frequency mode exhibits clear softening as the temperature is decreased while the higher frequency mode shows slight temperature dependence.

High-temperature colossal dielectric behavior of BaZrO3 ceramics

BaZrO₃ (BZO) powders were synthesized by solution combustion based on the glycine nitrate process.

Insight into structural phase transitions from the decoupled anharmonic mode approximation

We develop a formalism (decoupled anharmonic mode approximation, DAMA) that allows calculation of the vibrational free energy using density functional theory even for materials which exhibit negative curvature of the potential energy surface with respect to atomic displacements. We investigate vibrational modes beyond the harmonic approximation and approximate the potential energy surface with the superposition of the accurate potential along each normal mode. We show that the free energy can stabilize crystal structures at finite temperatures which appear dynamically unstable at T  =  0. The DAMA formalism is computationally fast because it avoids statistical sampling through molecular dynamics calculations, and is in principle completely ab initio. It is free of statistical uncertainties and independent of model parameters, but can give insight into the mechanism of a structural phase transition. We apply the formalism to the perovskite cryolite, and investigate the temperature-driven phase transition from the P21/n to the Immm space group. We calculate a phase transition temperature between 710 and 950 K, in fair agreement with the experimental value of 885 K. This can be related to the underestimation of the interaction of the vibrational states. We also calculate the main axes of the thermal ellipsoid and can explain the experimentally observed increase of its volume for the fluorine by 200-300% throughout the phase transition. Our calculations suggest the appearance of tunneling states in the high temperature phase. The convergence of the vibrational DOS and of the critical temperature with respect of reciprocal space sampling is investigated using the polarizable-ion model.

Trends in (LaMnO3)n/(SrTiO3)m superlattices with varying layer thicknesses

We investigate the thickness dependence of the structural, electronic, and magnetic properties of (LaMnO₃)_n/(SrTiO₃)_m (n, m = 2, 4, 6, 8) superlattices using density functional theory. The electronic structure turns out to be highly sensitive to the onsite Coulomb interaction. In contrast to bulk SrTiO₃, strongly distorted O octahedra are observed in the SrTiO₃ layers with a systematic off centering of the Ti atoms. The systems favour ferromagnetic spin ordering rather than the antiferromagnetic spin ordering of bulk LaMnO₃ and all show half-metallicity, while a systematic reduction of the minority spin band gaps as a function of the LaMnO₃ and SrTiO₃ layer thicknesses originates from modifications of the Ti d_xy states.

First-principles theory, coarse-grained models, and simulations of ferroelectrics

CONSPECTUS: A ferroelectric crystal exhibits macroscopic electric dipole or polarization arising from spontaneous ordering of its atomic-scale dipoles that breaks inversion symmetry. Changes in applied pressure or electric field generate changes in electric polarization in a ferroelectric, defining its piezoelectric and dielectric properties, respectively, which make it useful as an electromechanical sensor and actuator in a number of applications. In addition, a characteristic of a ferroelectric is the presence of domains or states with different symmetry equivalent orientations of spontaneous polarization that are switchable with large enough applied electric field, a nonlinear property that makes it useful for applications in nonvolatile memory devices. Central to these properties of a ferroelectric are the phase transitions it undergoes as a function of temperature that involve lowering of the symmetry of its high temperature centrosymmetric paraelectric phase. Ferroelectricity arises from a delicate balance between short and long-range interatomic interactions, and hence the resulting properties are quite sensitive to chemistry, strains, and electric charges associated with its interface with substrate and electrodes. First-principles density functional theoretical (DFT) calculations have been very effective in capturing this and predicting material and environment specific properties of ferroelectrics, leading to fundamental insights into origins of ferroelectricity in oxides and chalcogenides uncovering a precise picture of electronic hybridization, topology, and mechanisms. However, use of DFT in molecular dynamics for detailed prediction of ferroelectric phase transitions and associated temperature dependent properties has been limited due to large length and time scales of the processes involved. To this end, it is quite appealing to start with input from DFT calculations and construct material-specific models that are realistic yet simple for use in large-scale simulations while capturing the relevant microscopic interactions quantitatively. In this Account, we first summarize the insights obtained into chemical mechanisms of ferroelectricity using first-principles DFT calculations. We then discuss the principles of construction of first-principles model Hamiltonians for ferroelectric phase transitions in perovskite oxides, which involve coarse-graining in time domain by integrating out high frequency phonons. Molecular dynamics simulations of the resulting model are shown to give quantitative predictions of material-specific ferroelectric transition behavior in bulk as well as nanoscale ferroelectric structures. A free energy landscape obtained through coarse-graining in real-space provides deeper understanding of ferroelectric transitions, domains, and states with inhomogeneous order and points out the key role of microscopic coupling between phonons and strain. We conclude with a discussion of the multiscale modeling strategy elucidated here and its application to other materials such as shape memory alloys.

Competition and cooperation between antiferrodistortive and ferroelectric instabilities in the model perovskite SrTiO3

We use density functional theory to explore the interplay between octahedral rotations and ferroelectricity in the model compound SrTiO3. We find that over the experimentally relevant range octahedral rotations suppress ferroelectricity as is generally assumed in the literature. Somewhat surprisingly, we observe that at larger angles the previously weakened ferroelectric instability strengthens significantly. By analyzing geometry changes, energetics, force constants and charges, we explain the mechanisms behind this transition from competition to cooperation with increasing octahedral rotation angle.

First-principles model potentials for lattice-dynamical studies: general methodology and example of application to ferroic perovskite oxides

We present a scheme to construct model potentials, with parameters computed from first principles, for large-scale lattice-dynamical simulations of materials. We mimic the traditional solid-state approach to the investigation of vibrational spectra, i.e., we start from a suitably chosen reference configuration of the compound and describe its energy as a function of arbitrary atomic distortions by means of a Taylor series. Such a form of the potential-energy surface is general, trivial to formulate for any material, and physically transparent. Further, such models involve clear-cut approximations, their precision can be improved in a systematic fashion, and their simplicity allows for convenient and practical strategies to compute/fit the potential parameters. We illustrate our scheme with two challenging cases in which the model potential is strongly anharmonic, namely, the ferroic perovskite oxides PbTiO3 and SrTiO3. Studying these compounds allows us to better describe the connection between the so-called effective-Hamiltonian method and ours (which may be seen as an extension of the former), and to show the physical insight and predictive power provided by our approach-e.g., we present new results regarding the factors controlling phase-transition temperatures, novel phase transitions under elastic constraints, an improved treatment of thermal expansion, etc.

Correlations and local order parameter in the paraelectric phase of barium titanate

General features of the order parameter distribution in barium titanate in its paraelectric phase and in its ferroelectric phases (tetragonal and orthorhombic) are presented. The density of probability of the polarization [Formula: see text], defined by an average of the local order parameters over regions of various sizes and shapes (L(x) × L(y) × L(z)), is examined by molecular dynamics simulations using a first-principles derived effective Hamiltonian. The free energies [Formula: see text] associated with these probabilities are computed by thermodynamic integration. The evolution of these quantities are explained through the computation of pair correlations, which are found, as stated in several previous works, very anisotropic, 'needle-like', with longitudinal correlations ([Formula: see text]) having much longer range than transverse ones ([Formula: see text]). The correlations explain why the density of probability of the order parameter evolves from a multiple-peaked distribution with maxima along [111] (in the single cell), along [100] for small needle-like regions, towards a single-peaked distribution for larger regions. A useful expression in which the shape-dependence of the free energy is manifest is provided.

Thermodynamic properties of a quasi-harmonic model for ferroelectric transitions

Within a framework of a quasi-harmonic model for quantum particles in a local potential of the double Morse type and within the mean-field approximation for interactions between particles, we investigate the thermodynamic properties of ferroelectric materials. A quantum thermodynamic treatment gives analytic expressions for the internal energy, the entropy, the specific heat, and the static susceptibility. The calculated thermodynamic characteristics are studied as a function of temperature and energy barrier, where it is shown that at the proper choice of the theory parameters, particularly the energy barrier, the model system exhibits characteristic features of either second-order tricritical or first-order phase transitions. Our results indicate that the barrier energy seems to be an important criterion for the character of the structural phase transition. The influence of quantum fluctuations manifested on zero-point energy on the phase transition and thermodynamic properties is analyzed and discussed. This leads to several quantum effects, including the existence of a saturation regime at low temperatures, where the order parameter saturates giving thermodynamic saturation of the calculated thermodynamic quantities. It is found that both quantum effects and energy barrier magnitude have an important influence on the thermodynamic properties of the ferroelectric materials and on driving the phase transition at low temperatures. Also, the analytical parameters' effect on the transition temperature is discussed, which seems to give a general insight into the structural phase transition and its nature.

Ferroelectricity in strain-free SrTiO3 thin films

Biaxial strain is known to induce ferroelectricity in thin films of nominally nonferroelectric materials such as SrTiO3. By a direct comparison of the strained and strain-free SrTiO3 films using dielectric, ferroelectric, Raman, nonlinear optical and nanoscale piezoelectric property measurements, we conclude that all SrTiO3 films and bulk crystals are relaxor ferroelectrics, and the role of strain is to stabilize longer-range correlation of preexisting nanopolar regions, likely originating from minute amounts of unintentional Sr deficiency in nominally stoichiometric samples. These findings highlight the sensitive role of stoichiometry when exploring strain and epitaxy-induced electronic phenomena in oxide films, heterostructures, and interfaces.

Competition between quantum fluctuations and antiferroelectric order in Ru-doped Sr(0.8)Ca(0.2)Ti(1-x)Ru(x)O(3)

The competition between quantum fluctuations and the antiferroelectric state in Sr(0.8)Ca(0.2)Ti(1-x)Ru(x)O(3) is investigated by measuring the low-temperature dielectric permittivity and by Raman spectroscopy. We demonstrate the significant impact of quantum fluctuations on the stability of the antiferroelectric polar order. It is revealed that the structural phase transitions can be modified by the quantum fluctuations, enhancing the stability of the high-symmetry phase and suppressing the antiferroelectric transitions. More importantly, a quantum antiferroelectric state, exhibiting similar behavior as the quantum ferroelectric state in terms of dielectric response, is identified. In addition, the effect of quantum fluctuations on the increasing permittivity at low temperature is also discussed.

Discovery of incipient ferrotoroidics from atomistic simulations

An effective Hamiltonian technique is used to investigate the effect of quantum vibrations on properties of stress-free KTaO3 nanodots under open-circuit electrical boundary conditions. We discover that these vibrations suppress the paraelectric-to-ferrotoroidic transition, or, equivalently, wash out the formation of vortex states. Such suppression leads to the saturation of the so-called ferrotoroidic susceptibility at low temperature, and to a peculiar local structure that exhibits short-range, needlelike correlations of the individual toroidal moments.

Fluctuations and criticality in quantum paraelectrics

The temperature dependence of the static dielectric susceptibility of a system with strongly coupled fluctuating dipoles is calculated within a self-consistent mean fluctuation field approximation. Results are qualitatively in good agreement with a quantum paraelectric SrTiO(3) in the low temperature regime. We identify this system as a gapped quantum paraelectric and suggest a possible experimental realization of a quantum critical paraelectric through the application of hydrostatic pressure or doping by impurity.

Order-disorder component in the phase transition mechanism of 18O enriched strontium titanate

Ti and Sr nuclear magnetic resonance spectra of 18O enriched SrTiO3 (STO-18) provide direct evidence for Ti disorder already in the cubic phase and show that the ferroelectric transition at T(C)=24 K occurs in two steps. Below 70 K rhombohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below T(C). This shows that the elusive ferroelectric transition in STO-18 is indeed connected with local symmetry lowering and implies the existence of an order-disorder component in addition to the displacive soft mode one. Rhombohedral clusters, Ti disorder, and a two-component state are found in the so-called quantum paraelectric state of STO-16 as well. The concentration of the rhombohedral clusters is, however, not high enough to allow for percolation.

First-principles study of the temperature-pressure phase diagram of BaTiO3

We investigate the temperature-pressure phase diagram of BaTiO3 using a first-principles effective-Hamiltonian approach. We find that the zero-point motion of the ions affects the form of the phase diagram dramatically. Specifically, when the zero-point fluctuations are included in the calculations, all the polar (tetragonal, orthorhombic, and rhombohedral) phases of BaTiO3 survive down to 0 K, while only the rhombohedral phase does otherwise. This behavior results from a practical equivalence between thermal and quantum fluctuations. Our work confirms the essential correctness of the phase diagram proposed by Ishidate et al. [Phys. Rev. Lett. 78, 2397 (1997)]].

Ultrafast Optical Excitation of a Combined Coherent-Squeezed Phonon field in SrTiO3

We have simultaneously excited a coherent and a squeezed phonon field in SrTiO3 using femtosecond laser pulses and stimulated Raman scattering. The frequency of the coherent state (a 1.3 THz) is that of the A1g-component of the soft mode responsible for the cubic-tetragonal phase transformation at approximately 110 K. The squeezed field involves a continuum of transverse acoustic phonons dominated by a narrow peak in the density of states at a 6.9 THz.

Giant Piezoelectric Effect in Strontium Titanate at Cryogenic Temperatures

Piezoelectric materials have many applications at cryogenic temperatures. However, the piezoelectric response below 10 kelvin is diminished, making the use of these materials somewhat marginal. Results are presented on strontium titanate (SrTiO3), which exhibits a rapidly increasing piezoelectric response with decreasing temperature below 50 kelvin; the magnitude of its response around 1 kelvin is comparable to that of the best materials at room temperature. This "giant" piezoelectric response may open the way for a broad class of applications including use in ultralow-temperature scanning microscopies and in a magnetic field-insensitive thermometer. These observations, and the possible divergence of the mechanical response to electric fields at even lower temperatures, may arise from an apparent quantum critical point at absolute zero.