Machine learning has emerged as a powerful tool for the analysis of mesoscopic and atomically resolved images and spectroscopy in electron and scanning probe microscopy, with the applications ranging from feature extraction to information compression and elucidation of relevant order parameters to inversion of imaging data to reconstruct structural models. However, the fundamental limitation of machine learning methods is their correlative nature, leading to extreme susceptibility to confounding factors. Here, we implement the workflow for causal analysis of structural scanning transmission electron microscopy (STEM) data and explore the interplay between physical and chemical effects in ferroelectric perovskite across the ferroelectric-antiferroelectric phase transitions. The combinatorial library of the Sm-doped BiFeO3 is grown to cover the composition range from pure ferroelectric BFO to orthorhombic 20% Sm-doped BFO. Atomically resolved STEM images are acquired for selected compositions and are used to create a set of local compositional, structural, and polarization field descriptors. The information-geometric causal inference (IGCI) and additive noise model (ANM) analysis are used to establish the pairwise causal directions between the descriptors, ordering the data set in the causal direction. The causal chain for IGCI and ANM across the composition is compared and suggests the presence of common causal mechanisms across the composition series. Ultimately, we believe that the causal analysis of the multimodal data will allow exploring the causal links between multiple competing mechanisms that control the emergence of unique functionalities of morphotropic materials and ferroelectric relaxors.
An atomistic approach is used to investigate finite-temperature properties of ferroelectric nanodots that are embedded in a polarizable medium. Different phases are predicted, depending on the ferroelectric strengths of the material constituting the dot and of the system forming the medium. In particular, novel states, exhibiting a coexistence between two kinds of order parameters or possessing a peculiar order between dipole vortices of adjacent dots, are discovered. We also discuss the origins of these phases, e.g. depolarizing fields and medium-driven interactions between dots.
An {\it atomistic} approach allowing an accurate and efficient treatment of depolarizing energy and field in {\it any} low-dimensional ferroelectric structure is developed. Application of this approach demonstrates the limits of the widely used continuum model (even) for simple test cases. Moreover, implementation of this approach within a first-principles-based model reveals an unusual phase transition -- from a state exhibiting a spontaneous polarization to a phase associated with a toroid moment of polarization -- in a ferroelectric nanodot for a critical value of the depolarizing field.
A parameterized effective Hamiltonian approach is used to investigate KTaO$_3$. We find that the experimentally observed anomalous dielectric response of this incipient ferroelectric is well reproduced by this approach, once quantum effects are accounted for. Quantum fluctuations suppress the paraelectric--to--ferroelectric phase transition; it is unnecessary to introduce defects to explain the dielectric behavior. The resulting quantum-induced local structure exhibits off-center atomic displacements that display {\sl longitudinal, needle-like correlations} extending a few lattice constants.
We provide a fundamental insight into the microscopic mechanisms of the ageing processes. Using large scale molecular dynamics simulations of the prototypical ferroelectric material PbTiO3, we demonstrate that the experimentally observed ageing phenomena can be reproduced from intrinsic interactions of defect-dipoles related to dopant-vacancy associates, even in the absence of extrinsic effects. We show that variation of the dopant concentration modifies the material's hysteretic response. We identify a universal method to reduce loss and tune the electromechanical properties of inexpensive ce…
Atomistic effective Hamiltonian simulations are used to investigate electrocaloric (EC) effects in the lead-free Ba(Zr$_{0.5}$Ti$_{0.5}$)O$_{3}$ (BZT) relaxor ferroelectric. We find that the EC coefficient varies non-monotonically with the field at any temperature, presenting a maximum that can be traced back to the behavior of BZT's polar nanoregions. We also introduce a simple Landau-based model that reproduces the EC behavior of BZT as a function of field and temperature, and which is directly applicable to other compounds. Finally, we confirm that, for low temperatures (i.e., in non-ergodi…
An atomistic effective Hamiltonian is used to investigate electrocaloric (EC) effects of Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) relaxor ferroelectrics in its ergodic regime, and subject to electric fields applied along the pseudocubic [111] direction. Such Hamiltonian qualitatively reproduces (i) the electric field-versus-temperature phase diagram, including the existence of a critical point where first-order and second-order transitions meet each other; and (ii) a giant EC response near such critical point. It also reveals that such giant response around this critical point is microscopically …
We have developed first-principles models, based on a general parametrization of the full potential-energy surface, to investigate the lattice-dynamical properties of perovskite oxides. We discuss the application of our method to prototypic ferroelectric PbTiO3, showing that its properties are drastically affected by a competition between structural instabilities. Indeed, we confirm previous indications that the destructive interaction between the ferroelectric and antiferrodistortive (involving rotations of the O6 octahedra) soft modes shifts PbTiO3's Curie temperature by hundreds of degrees.…
We report a first-principles study of (BaTiO${_3}$)$_m$/(BaO)$_n$ superlattices for a wide range of periodicities $m/n$. We show that such a system develops a polar zone-center instability for sufficiently large \textit{m}/\textit{n} ratio, which can be understood, at least qualitatively, from a simple electrostatic model and should lead to a ferroelectric ground-state. However, the analysis of the phonon dispersion curves also points out the appearance of stronger antiferroelectric instabilities at the zone boundaries around $m=4$, before the critical ratio for ferroelectricity is reached and…
Neutron diffraction studies using powder samples have been used to understand the complex sequence of low temperature phase transitions of NaNbO3 in the temperature range from 12 K-350 K. Detailed Rietveld analysis of the diffraction data reveal that the antiferroelectric to ferroelectric phase transition occurs on cooling around 73 K while the reverse ferroelectric to antiferroelectric transition occurs on heating at 245 K. However, the former transformation is not complete till down to 12 K and there is unambiguous evidence for the presence of the ferroelectric R3c phase coexisting with an a…
Hafnia (HfO$_2$)-based thin films have promising applications in nanoscale electronic devices due to their robust ferroelectricity and integration with silicon. However, HfO$_2$ has various stable and metastable polymorphs with quite similar structures and energies. Identifying and stabilizing the ferroelectric functional phases of HfO$_2$ have attracted intensive research interest in recent years. In this work, first-principles calculations on (111)-oriented HfO$_2$ are used to discover that imposing an in-plane shear strain on the tetragonal phase induces a nonpolar to polar phase transition…
Neutron and x-ray scattering studies on relaxor ferroelectric systems Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$ (PZN), Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$ (PMN), and their solid solutions with PbTiO$_3$ (PT) have shown that inhomogeneities and disorder play important roles in the materials properties. Although a long-range polar order can be established at low temperature - sometimes with the help of an external electric field; short-range local structures called the ``polar nano-regions'' (PNR) still persist. Both the bulk structure and the PNR have been studied in details. The coexistence and competition of l…
We have performed molecular dynamics simulations using a shell model potential developed by fitting first principles results to describe the behavior of the relaxor-ferroelectric (1-x)PbMg1/3Nb2/3O3-xPbTiO3 (PMN-xPT) as function of concentration and temperature, using site occupancies within the random site model. In our simulations, PMN is cubic at all temperatures and behaves as a polar glass. As a small amount of Ti is added, a weak polar state develops, but structural disorder dominates, and the symmetry is rhombohedral. As more Ti is added the ground state is clearly polar and the system …
The role of defects in solids of mixed ionic-covalent bonds such as ferroelectric oxides is complex. Current understanding of defects on ferroelectric properties at the single-defect level remains mostly at the empirical level, and the detailed atomistic mechanisms for many defect-mediated polarization-switching processes have not been convincingly revealed quantum mechanically. We simulate the polarization-electric field (P-E) and strain-electric field ({$ε$}-E) hysteresis loops for BaTiO3 in the presence of generic defect dipoles with large-scale molecular dynamics and provide a detailed ato…
Properties of (BaTiO$_3$)$_1$/(BaZrO$_3$)$_n$ ferroelectric superlattices (SLs) with $n = {}$1--7 grown in the [001] direction are calculated from first principles within the density functional theory. It is revealed that the quasi-two-dimensional ferroelectricity occurs in these SLs in the barium titanate layers with a thickness of one unit cell; the polarization is oriented in the layer plane and weakly interacts with the polarization in neighboring layers. The ferroelectric ordering energy and the height of the barrier separating different orientational states of polarization in these SLs a…
We present a first-principles study of model domain walls (DWs) in prototypic ferroelectric PbTiO3. At high temperature the DW structure is somewhat trivial, with atoms occupying high- symmetry positions. However, upon cooling the DW undergoes a symmetry-breaking transition characterized by a giant dielectric anomaly and the onset of a large and switchable polarization. Our results thus corroborate previous arguments for the occurrence of ferroic orders at structural DWs, providing a detailed atomistic picture of a temperature-driven DW-confined transformation. Beyond its relevance to the fiel…
The geometrically frustrated magnet Ni3V2O8 undergoes a series of competing magnetic ordering at low temperatures. Most importantly, one of the incommensurate phases has been reported to develop a ferroelectric correlation caused by spin frustration. Here we report an extensive thermodynamic, dielectric and magnetic study on clean polycrystalline samples of this novel multiferroic compound. Our low temperature specific heat data at high fields up to 14 Tesla clearly identify the development of a new magnetic field induced phase transition below 2 K that shows signatures of simultaneous electri…
Machine learning has been establishing its potential in multiple areas of condensed matter physics and materials science. Here we develop and use an unsupervised machine learning workflow within a framework of first-principles-based atomistic simulations to investigate phases, phase transitions, and their structural origins in ferroelectric relaxors, Ba(Ti$_{1-x}$,Zr$_x$)O$_3$. We first demonstrate the applicability of the workflow to identify phases and phase transitions in the parent compound, a prototypical ferroelectric BaTiO$_3$. We then apply the workflow on Ba(Ti$_{1-x}$,Zr$_x$)O$_3$, w…
We study the antiferrodistortive instability and its interaction with ferroelectricity in cubic perovskite compounds. Our first-principles calculations show that coexistence of both instabilities is very common. We develop a first-principles scheme to study the thermodynamics of these compounds when both instabilities are present, and apply it to SrTiO$_3$. We find that increased pressure enhances the antiferrodistortive instability while suppressing the ferroelectric one. Moreover, the presence of one instability tends to suppress the other. A very rich $P$--$T$ phase diagram results.
Excess charge on polar surfaces of ionic compounds is commonly described by the two-dimensional electron gas (2DEG) model, a homogeneous distribution of charge, spatially-confined in a few atomic layers. Here, by combining scanning probe microscopy with density functional theory calculations, we show that excess charge on the polar TaO$_2$ termination of KTaO$_3$(001) forms more complex electronic states with different degrees of spatial and electronic localization: charge density waves (CDW) coexist with strongly-localized electron polarons and bipolarons. These surface electronic reconstruct…
The mechanocaloric effect is the temperature change of a material upon application or removal of an external stress. Beyond its fundamental interest, this caloric response represents a promising and ecofriendly alternative to current cooling technologies. To obtain large mechanocaloric effects, we need materials whose elastic properties (e.g., strain, elastic compliance) are strongly temperature dependent. This is the case of ferroelectric perovskite oxides, where the development of the spontaneous electric polarization is accompanied by significant strains and lattice softening. Thus, in this…
Multiscale Modelling of Ferroelectrics using a Physics-Informed Neural Network Driven by Molecular Dynamics Data: Parameter Identification and Field Reconstruction
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Nagoya Institute of Technology（名古屋工业大学）
The structural and polar properties of BiFeO3 at finite temperature are investigated using an atomistic shell model fitted to first-principles calculations. Molecular Dynamics simulations show a direct transition from the low-temperature R3c ferroelectric phase to the Pbnm orthorhombic phase without evidence of any intermediate bridging phase between them. The high-temperature phase is characterized by the presence of two sublattices with opposite polarizations, and it displays the characteristic double-hysteresis loop under the action of an external electric field. The microscopic analysis re…
Neutron pair distribution function analysis and first principles calculations have been employed to study short-range correlations in heavily disordered dielectric material Sr$_x$Ba$_{1-x}$Nb$_2$O$_6$ ($x=0.35, 0.5$ and 0.61). The combination of methods has been fruitful in pinpointing main local-structure features, their temperature behaviour and interrelation. A rather complex system of tilts is found to be both temperature and Sr-content sensitive with the biggest tilt magnitudes reached at low temperatures and high $x$. Relative Nb-O$_6$ displacements, directly responsible for material's f…
Recent observations of unusual ferroelectricity in thin films of HfO_2 and related materials have attracted broad interest to the materials and led to the emergence of a number of competing models for observed behaviors. Here we develop the electrochemical mechanism of observed ferroelectric-like behaviors, namely the collective phenomena of elastic and electric dipoles originated from oxygen vacancies formation in the vicinity of film surfaces, as well as from grain boundaries and other types of inhomogeneities inside the film. The ferroelectric phase is induced by the "electrochemical" coupl…
The physics of ferroelectric domain walls is explored using the Bayesian inference analysis of atomically resolved STEM data. We demonstrate that domain wall profile shapes are ultimately sensitive to the nature of the order parameter in the material, including the functional form of Ginzburg-Landau-Devonshire expansion, and numerical value of the corresponding parameters. The preexisting materials knowledge naturally folds in the Bayesian framework in the form of prior distributions, with the different order parameters forming competing (or hierarchical) models. Here, we explore the physics o…
This paper combines experimental and modelling studies to provide a detailed examination of the influence of porosity volume fraction and morphology on the polarisation-electric field response of ferroelectric materials. The broadening of the electric field distribution and a decrease in the electric field experienced by the ferroelectric ceramic medium due to the presence of low-permittivity pores is examined and its implications on the shape of the hysteresis loop, remnant polarisation and coercive field is discussed. The variation of coercive field with porosity level is seen to be complex …
Static and dynamic critical behavior of Sn$_2$P$_2$S$_6$ type ferroelectrics and (Pb$_y$Sn$_{1-y}$)$_2$P$_2$(Se$_x$S$_{1-x}$)$_6$ mixed crystals with line of tricritical points and line of Lifshitz points on the $T-x-y$ phase diagram, which meet at the tricritical Lifshitz point, can be described in a combined BEG-ANNNI model. Such the model considers first and second neighbor interactions for pseudospins in a local three-well potential. Below the temperature of tricritical Lifshitz point, the "chaotic" state accompanied by the coexistence of ferroelectric, metastable paraelectric and modulate…
Design of novel artificial materials based on ferroelectric perovskites relies on the basic principles of electrostatic coupling and in-plane lattice matching. These rules state that the out-of-plane component of the electric displacement field and the in-plane components of the strain are preserved across a layered superlattice, provided that certain growth conditions are respected. Intense research is currently directed at optimizing materials functionalities based on these guidelines, often with remarkable success. Such principles, however, are of limited practical use unless one disposes o…
A thorough understanding of native oxides is essential for designing semiconductor devices. Here we report a study of the rate and mechanisms of spontaneous oxidation of bulk single crystals of ZrS$_x$Se$_{2-x}$ alloys and MoS$_2$. ZrS$_x$Se$_{2-x}$ alloys oxidize rapidly, and the oxidation rate increases with Se content. Oxidation of basal surfaces is initiated by favorable O$_2$ adsorption and proceeds by a mechanism of Zr-O bond switching, that collapses the van der Waals gaps, and is facilitated by progressive redox transitions of the chalcogen. The rate-limiting process is the formation a…
We extend our previous first-principles theory for perovskite ferroelectric phase transitions to treat also antiferrodistortive phase transitions. Our approach involves construction of a model Hamiltonian from a Taylor expansion, first-principles calculations to determine expansion parameters, and Monte Carlo simulations to study the resulting system. We apply this approach to three cubic perovskite compounds, SrTiO3, CaTiO3, and NaNbO3, that are known to undergo antiferrodistortive phase transitions. We calculate their transition sequences and transition temperatures at the experimental latti…
We develop and implement an automated experiment in multimodal imaging to probe structural, chemical, and functional behaviors in complex materials and elucidate the dominant physical mechanisms that control device function. Here the emergence of non-linear electromechanical responses in piezoresponse force microscopy (PFM) is explored. Non-linear responses in PFM can originate from multiple mechanisms, including intrinsic material responses often controlled by domain structure, surface topography that affects the mechanical phenomena at the tip-surface junction, and, potentially, the presence…
We use atomistic simulations to study the interactions between two-dimensional domain walls and Sr inclusions in the prototypical ferroelectric BaTiO$_3$. Based on nudged elastic band calculations we predict that the energy barrier for domain wall movement increases in the vicinity of small planar Sr inclusions which may act as pinning centers. We link this observation to the local increase in polarization by larger oxygen off-centering and validate our predictions by molecular dynamics simulations of field-driven domain walls at finite temperatures.
