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

Quantitative evaluation of nuclear quantum effects on the phase transitions in BaTiO3using large-scale molecular dynamics simulations based on machine learning potentials

The machine learning potential (MLP) based molecular dynamics (MD) method (MLPMD) was applied for constructing the pressure-temperature phase diagram in the barium titanate (BaTiO3) crystals. The nuclear quantum effects (NQEs) on the phase transitions were quantitatively evaluated from the difference in the phase transition pressures between the NQEs-incorporated and classical simulations. In this study, the quantum thermal bath (QTB) method was used for incorporating the NQEs. The constructed phase diagrams verified that the NQEs lower the phase transition temperatures and pressures. The NQEs are more significant at lower temperatures but cannot be ignored even at room temperature. The phase diagram in the QTB-based MLPMD is in good agreement with those of the previous studies based on dielectric measurements and path-integral based simulations. The displacement distributions of Ti and O ions in the QTB-MLPMD suggest that the pressure-induced tetragonal-cubic phase transition is the displacive type, in contrast to the order-disorder type reported in the literature. Possible reasons for the discrepancy in the microscopic behavior are the differences in the simulation cell size and restriction for lattice dynamics. In contrast to the relatively small simulation cell (12 × 12 × 12 supercell or smaller) with some restriction to the degrees of freedom (DOFs) for lattice dynamics in the previous studies, the large cell (20 × 20 × 20 supercell) without any DOF restriction was employed in the present study.

Ferroelectric Phase Transition in Barium Titanate Revisited with Ab Initio Molecular Dynamics

The ferroelectric phase transition of the perovskite barium titanate as well as its technical importance regarding the switching of respective polar properties is well known and has been thoroughly studied, both experimentally and on theoretical grounds. While details about the phase diagram as well as transition temperatures are experimentally well known, the theoretical approaches still face difficulties in contributing a detailed description of these phase transitions. Within this work, a new methodological approach is introduced to revisit the ferroelectric phase transition with first-principles methods. With the chosen ab initio molecular dynamics (AIMD) method in combination with the applied NpT ensemble, we are able to join the accuracy of density functional theory (DFT) with ambient conditions, realized using a thermostat and barostat in an MD simulation. The derived phase diagram confirms recent corrections in the theoretical models and reproduces the phase boundary pressure dependence of TC. In conclusion of the statistical atomistic dynamics, the nature of the transition can be described in a more detailed way. In addition, this work paves the way towards locally patterned piezoelectrica by means of acoustic standing waves as well as piezoelectrically induced acoustic resonators.

Quantum criticality at cryogenic melting of polar bubble lattices

Quantum fluctuations (QFs) caused by zero-point phonon vibrations (ZPPVs) are known to prevent the occurrence of polar phases in bulk incipient ferroelectrics down to 0 K. On the other hand, little is known about the effects of QFs on the recently discovered topological patterns in ferroelectric nanostructures. Here, by using an atomistic effective Hamiltonian within classical Monte Carlo (CMC) and path integral quantum Monte Carlo (PI-QMC), we unveil how QFs affect the topology of several dipolar phases in ultrathin Pb(Zr0.4Ti0.6)O3 (PZT) films. In particular, our PI-QMC simulations show that the ZPPVs do not suppress polar patterns but rather stabilize the labyrinth, bimeron and bubble phases within a wider range of bias field magnitudes. Moreover, we reveal that quantum fluctuations induce a quantum critical point (QCP) separating a hexagonal bubble lattice from a liquid-like state characterized by spontaneous motion, creation and annihilation of polar bubbles at cryogenic temperatures. Finally, we show that the discovered quantum melting is associated with anomalous physical response, as, e.g., demonstrated by a negative longitudinal piezoelectric coefficient.

Electrostatics and domains in ferroelectric superlattices

The electrostatics arising in ferroelectric/dielectric two-dimensional heterostructures and superlattices is revisited within a Kittel model in order to define and complete a clear paradigmatic reference for domain formation. The screening of the depolarizing field in isolated ferroelectric or polar thin films via the formation of 180° domains is well understood, where the width of the domains w grows as the square-root of the film thickness d, following Kittel's Law for thick enough films (w ≪ d). For thinner films, a minimum is reached for w before diverging to a monodomain. Although this behaviour is known to be qualitatively unaltered when the dielectric environment of the film is modified, we consider the quantitative changes in that behaviour induced on the ferroelectric film by different dielectric settings: as deposited on a dielectric substrate, sandwiched between dielectrics, and in a superlattice of alternating ferroelectric/dielectric films. The model assumes infinitely thin domain walls, and therefore is not expected to be reliable for film thickness in the nanometre scale. The polarization field P(r) does vary in space, deviating from ±P _S , following the depolarizing field in linear response, but the model does not include a polarization-gradient term as would appear in a Ginzburg-Landau free energy. The model is, however, worth characterizing, both as paradigmatic reference, and as applicable to not-so-thin films. The correct renormalization of parameters is obtained for the thick-film square-root behaviour in the mentioned settings, and the sub-Kittel regime is fully characterized. New results are presented alongside well-known ones for a comprehensive description. Among the former, a natural separation between strong and weak ferroelectric coupling in superlattices is found, which depends exclusively on the dielectric anisotropy of the ferroelectric layer.

Direct and indirect methods based on effective Hamilton for electrocaloric effect of BaTiO3 nanoparticle

Low dimensional ferroelectric materials, including nano thin films, nanowires and nanoparticules, exhibit excellent electrocaloric effect (ECE) and have potential application in solid-state cooling devices. Predicting the ECE property of nanoscale ferroelectrics is of scientific significance and practice importance. Here, the direct and indirect methods based on effective Hamilton are employed to study the ECE in BaTiO₃ nanoparticle under different electric fields and temperatures. In indirect method, the Monte Carlo simulation is used to obtain the polarization changes with temperature under different electric fields. The ECE is calculated indirectly based on the Maxwell relation. In direct method, the demon energy is introduced into the system in order to obtain the ECE directly. The results shows that the difference between the peak values of direct method and indirect method is less than 5%, which means both direct method and indirect method can be used to simulate the ECE of ferroelectric nanoparticle.

Revisiting the zero-temperature phase diagram of stoichiometric SrCoO3 with first-principles methods

By using first-principles methods based on density functional theory we revisited the zero-temperature phase diagram of stoichiometric SrCoO₃, a ferromagnetic metallic perovskite that undergoes significant structural, electronic, and magnetic changes as its content of oxygen is decreased. We considered both bulk and epitaxial thin film geometries. In the bulk case, we found that a tetragonal P4/mbm phase with moderate Jahn-Teller distortions and a c/a ratio of is consistently predicted to have a lower energy than the thus far assumed ground-state cubic Pm3[combining macron]m phase. In thin films, we found two phase transitions occurring at compressive and tensile epitaxial strains. However, in contrast to previous theoretical predictions, our results show that: (i) the phase transition induced by tensile strain is isostructural and involves only a change in magnetic spin order (that is, not a metallic to insulator transformation), and (ii) the phase transition induced by compressive strain comprises simultaneous structural, electronic and magnetic spin order changes, but the required epitaxial stress is so large (<-6%) that is unlikely to be observed in practice. Our findings call for a revision of the crystallographic data obtained in fully oxidised SrCoO₃ samples at low temperatures, as well as of previous first-principles studies.

Theoretical Methods of Domain Structures in Ultrathin Ferroelectric Films: A Review

This review covers methods and recent developments of the theoretical study of domain structures in ultrathin ferroelectric films. The review begins with an introduction to some basic concepts and theories (e.g., polarization and its modern theory, ferroelectric phase transition, domain formation, and finite size effects, etc.) that are relevant to the study of domain structures in ultrathin ferroelectric films. Basic techniques and recent progress of a variety of important approaches for domain structure simulation, including first-principles calculation, molecular dynamics, Monte Carlo simulation, effective Hamiltonian approach and phase field modeling, as well as multiscale simulation are then elaborated. For each approach, its important features and relative merits over other approaches for modeling domain structures in ultrathin ferroelectric films are discussed. Finally, we review recent theoretical studies on some important issues of domain structures in ultrathin ferroelectric films, with an emphasis on the effects of interfacial electrostatics, boundary conditions and external loads.

The stabilization of a single domain in free-standing ferroelectric nanocrystals

High resolution electron microscopy, electron diffraction and electron holography were used to study individual free-standing ∼ 30 nm barium titanate nanocrystals. Large unidirectional variations in the tetragonal distortion were mapped across the smaller nanocrystals, peaking to anomalously large values of up to 4% at the centers of the nanocrystals. This indicated that the nanocrystals consist of highly strained single ferroelectric domains. Simulations using an effective Hamiltonian for modeling a nanocrystal under a small depolarizing field and negative pressure qualitatively confirm this picture. These simulations, along with the development of a phenomenological model, show that the tetragonal distortion variation is a combined effect of: (i) electrostrictive coupling between the spontaneous polarization and strain inside the nanocrystal, and (ii) a surface-induced effective stress existing inside the nanodot. As a result, a 'strain skin layer', having a smaller tetragonal distortion relative to the core of the nanocrystal, is created.

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.

Off-center displacements and hydrostatic pressure induced phase transition in perovskites

Pressure has a profound effect on the paraelectric and ferroelectric properties of perovskite crystals. In this paper we theoretically investigate the effect of pressure on the cubic-to-tetragonal phase transition and on the soft mode dynamics of some classical perovskite crystals: BaTiO(3), PbTiO(3), and KNbO(3). We use a model consisting of three subsystems: electrons, phonons, and off-center displacements treated as spins. Experiments show that pressure has a large effect on the tunneling and hopping of the off-center displacements, that in turn strongly affect the pressure dependence of the transition temperature and the soft mode frequency. This model, with a very small number of adjustable parameters, accounts quantitatively for the experimentally measured nonlinear pressure dependence of the cubic-to-tetragonal phase transition temperature, up to the critical pressure where the transition temperature is zero. It also accounts quantitatively for the pressure dependence of the soft mode frequency, which is finite at the phase transition in spite of the fact that the phase transition at elevated pressures is second order, and for the pressure dependence of the electronic gap energy.

Low-symmetry phases in ferroelectric nanowires

Ferroelectric nanostructures have recently attracted much attention due to the quest of miniaturizing devices and discovering novel phenomena. In particular, studies conducted on two-dimensional and zero-dimensional ferroelectrics have revealed original properties and their dependences on mechanical and electrical boundary conditions. Meanwhile, researches aimed at discovering and understanding properties of one-dimensional ferroelectric nanostructures are scarce. The determination of the structural phase and of the direction of the polarization in one-dimensional ferroelectrics is of technological importance, since, e.g., a low-symmetry phase in which the polarization lies away from a highly symmetric direction typically generates phenomenal dielectric and electromechanical responses. Here, we investigate the phase transition sequence of nanowires made of KNbO(3) and BaTiO(3) perovskites, by combining X-ray diffraction, Raman spectroscopy, and first-principles-based calculations. We provide evidence of a previously unreported ferroelectric ground state of monoclinic symmetry and the tuning of the polarization's direction by varying factors inherent to the nanoscale.

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.

Anomalous phase diagram of ferroelectric (Ba,Ca)TiO3 single crystals with giant electromechanical response

We report the anomalous phase evolution in ferroelectric single crystals Ba1-xCaxTiO3 (0.02<x<0.34), and demonstrate the significant effects of quantum fluctuation on the ferroelectric phase transition. In addition, large electromechanical responses in this class of crystals are also demonstrated. Our results indicate that an effective approach to control the ferroelectricity of perovskite oxide can be realized not only by the covalency between A site atom and oxygen but also by the substitution of A site with small ions with off-centering nature. Theoretical calculations support the idea that the off-center displacements of the smaller Ca ions in the Ba-site play an important role in the exotic natures of Ba1-xCaxTiO3.

Origin of the relaxor state in Pb(B{x}B{1-x}{'})O(3) perovskites

Molecular dynamics simulations of first-principles-based effective Hamiltonians for Pb(Sc{1/2}Nb{1/2})O(3) under hydrostatic pressure and for Pb(Mg{1/3}Nb{2/3})O(3) at ambient pressure show clear evidence of a relaxor state in both systems. The Burns temperature is identified as the temperature below which dynamic nanoscale polar clusters form, pinned to regions of quenched chemical short-range order. The effect of pressure in Pb(Sc{1/2}Nb{1/2})O(3) demonstrates that the stability of the relaxor state depends on a delicate balance between the energetics that stabilize normal ferroelectricity and the average strength of random local fields which promote the relaxor state.

Spontaneous polarization in one-dimensional Pb(ZrTi)O3 nanowires

Formation of spontaneous polarization in one-dimensional (1D) structures is a key phenomenon that reveals collective behaviors in systems of reduced dimensions, but has remained unsolved for decades. Here we report ab initio studies on finite-temperature structural properties of infinite-length nanowires of Pb(Zr0.5Ti0.5)O3 solid solution. Whereas existing studies have ruled out the possibility of phase transition in 1D chains, our atomistic simulations demonstrate a different conclusion, characterized by the occurrence of a ferroelectric polarization and critical behaviors of dielectric and piezoelectric responses. The difference is accounted for by the use of depolarizing effects associated with finite thickness of wires. Our results suggest no fundamental constraint that limits the use of ferroelectric nanowires and nanotubes arising from the absence of spontaneous ordering.

Pressure-induced anomalous phase transitions and colossal enhancement of piezoelectricity in PbTiO3

We find an unexpected tetragonal-to-monoclinic-to-rhombohedral-to-cubic phase transition sequence induced by pressure, and a morphotropic phase boundary in a pure compound using first-principles calculations. Huge dielectric and piezoelectric coupling constants occur in the transition regions, comparable to those observed in the new complex single-crystal solid-solution piezoelectrics such as Pb(Mg(1/3)Nb(2/3))O3-PbTiO3, which are expected to revolutionize electromechanical applications. Our results show that morphotropic phase boundaries and giant piezoelectric effects do not require intrinsic disorder, and open the possibility of studying this effect in simple systems.

Ferroelectricity in barium titanate quantum dots and wires

Properties of BaTiO3 colloidal quantum dots and wires are simulated using a first-principles-based approach. Large atomic off-center displacements (that are robust against capping matrix materials) are found to exist in very small (<5 nm) dots. We further determine the size dependences of electrical and electromechanical responses in the studied nanostructures, as well as provide microscopic understanding of these responses.