Finite-temperature properties of Pb(Zr1-xTi(x))O3 alloys from first principles

Skyrmion nanodomains in ferroelectric-antiferroelectric solid solutions

Polar skyrmions have demonstrated rich physics and exotic properties for developing novel functionalities. However, so far, skyrmion nanodomains exist only in a few material systems, such as ferroelectric/dielectric superlattices, free-standing PbTiO3/SrTiO3 epitaxial bilayers and ultrathin Pb(Zr,Ti)O3/SrTiO3/Pb(Zr,Ti)O3 sandwiches. These heterostructures are fabricated with elaborately designed boundary conditions to meet the delicate energy balance for stabilizing topological phases. This requirement limits the broad applications of skyrmions in electronic devices. Here we show widespread skyrmion nanodomains in ferroelectric-antiferroelectric solid solutions, composed of ferroelectric PbTiO3 and one antiferroelectric PbSnO3 (Pb(Ti1-xSnx)O3), PbHfO3 (Pb(Ti1-xHfx)O3) or PbZrO3 (Pb(Ti1-xZrx)O3). The skyrmionic textures are formed by engineering dipole-dipole and antiferrodistortive-dipole couplings in competition between ferroelectric and antiferroelectric polar orderings, allowing the stabilization of topological phases. A phase diagram is built for the three solid solution series, revealing the stabilization regions of skyrmion nanodomains. In addition, the non-trivial domains also exhibit improved switching character, reversible writing/erasure and long-term retention for the electrical manipulation of polar configurations. These findings open an avenue for the investigation and exploitation of polar skyrmions in ferroelectric-based materials, providing opportunities in topological electronics.

Revisiting Structural and Electromechanical Properties of the Lead-free (K,Na)NbO3 High-Piezoelectric Material

Having lead-free systems with excellent piezoelectric responses is crucial to the development of environmentally friendly electromechanical applications. In this work, we build an effective Hamiltonian model to explore the promising (KxNa1-x)NbO3 system, whose rich phase diagram near x = 50% remains poorly understood meanwhile exhibiting a colossal effective piezoelectric response. Thanks to the numerical implementation of this effective Hamiltonian scheme into a Monte Carlo Metropolis algorithm, we reveal striking features. First, a long-period state can be the ground state at low temperatures for some concentrations while only a short-period conventional polar ground state exists for larger x. Second, the electric field-driven transformation, via a first-order transition, of this long-period state into a short-period polar state creates large electromechanical strains (on the order of the percent) and is likely the origin of the colossal piezoelectric response reported in KNN, for which we evaluate an effective piezoelectric coefficient of several thousands of pC/N.

Dynamics of Polar Vortex Crystallization

Vortex crystals are commonly observed in ultrathin ferroelectrics. However, a clear physical picture of origin of this topological state is currently lacking. Here, we show that vortex crystallization in ultrathin Pb(Zr_{0.4},Ti_{0.6})O_{3} films stems from the softening of a phonon mode and can be described as a Z_{2}×SU(1) symmetry-breaking transition. This result sheds light on the topology of the polar vortex patterns and bridges polar vortices with smectic phases, spin spirals, and other modulated states. Finally, we predict a resonant switching of the vortex tube orientation driven by midinfrared laser light which could enable new technologies.

Ferroelectricity in Ultrathin Halide Perovskites

Ferroelectricity has recently been demonstrated in germanium-based halide perovskites. We use first-principles-based simulations to study 4-18 nm CsGeBr3 films and develop a theory for ferroelectric ultrathin films. The theory introduces (i) a local order parameter, which identifies phase transitions into both monodomain and polydomain phases, and (ii) a dipole pattern classifier, which allows efficient and reliable identification of dipole patterns. Application of the theory to both halides CsGeBr3 and CsGeI3 and oxide BiFeO3 ultrathin ferroelectrics reveals two distinct scenarios. First, the films transition into a monodomain phase below the critical value of the residual depolarizing field. Above this critical value, the second scenario occurs, and the film undergoes a transition into a nanodomain phase. The two scenarios exhibit opposite responses of Curie temperature to thickness reduction. Application of a dipole pattern classifier reveals rich nanodomain phases in halide films: nanostripes, labyrinths, zig-zags, pillars, and lego domains.

Crossover from Linear to Quadratic Electro-optic Behavior in BaTiO_{3} and (Ba, Sr)TiO_{3} Solid Solution

We derive a numerical method based on coupled density functional theory and effective Hamiltonian schemes to calculate the linear and quadratic electro-optic response of ferroelectrics at finite temperature and in different frequency ranges. By applying the developed method to BaTiO_{3}, we successfully resolve apparent discrepancies in the experimental literature that reported a linear or quadratic electro-optic response when visible or terahertz radiation was employed to measure the optical index, respectively. We further demonstrate that (and explain why), in the case of the Ba_{1-x}Sr_{x}TiO_{3} disordered solid solutions, structural phase transitions not only lead to larger linear electro-optic constants, as previously demonstrated in the literature, but also significantly enhance the quadratic electro-optic constants.

Atomistic Origin of Diverse Charge Density Wave States in CsV_{3}Sb_{5}

Kagome metals AV_{3}Sb_{5} (A=K, Rb, or Cs) exhibit intriguing charge density wave (CDW) instabilities, which interplay with superconductivity and band topology. However, despite firm observations, the atomistic origins of the CDW phases, as well as hidden instabilities, remain elusive. Here, we adopt our newly developed symmetry-adapted cluster expansion method to construct a first-principles-based effective Hamiltonian of CsV_{3}Sb_{5}, which not only reproduces the established inverse star of David (ISD) phase, but also predict a series of D_{3h}-n states under mild tensile strains. With such atomistic Hamiltonians, the microscopic origins of different CDW states are revealed as the competition of the second-nearest neighbor V-V pairs versus the first-nearest neighbor V-V and V-Sb couplings. Interestingly, the effective Hamiltonians also reveal the existence of ionic Dzyaloshinskii-Moriya interaction in the high-symmetry phase of CsV_{3}Sb_{5} and drives the formation of noncollinear CDW patterns. Our work thus not only deepens the understanding of the CDW formation in AV_{3}Sb_{5}, but also demonstrates that the effective Hamiltonian is a suitable approach for investigating CDW mechanisms, which can be extended to various CDW systems.

Dynamical Control of Topology in Polar Skyrmions via Twisted Light

Twisted light carries a nonzero orbital angular momentum, that can be transferred from light to electrons and particles ranging from nanometers to micrometers. Up to now, the interplay between twisted light with dipolar systems has scarcely been explored, though the latter bear abundant forms of topologies such as skyrmions and embrace strong light-matter coupling. Here, using first-principles-based simulations, we show that twisted light can excite and drive dynamical polar skyrmions and transfer its nonzero winding number to ferroelectric ultrathin films. The skyrmion is successively created and annihilated alternately at the two interfaces, and experiences a periodic transition from a markedly "Bloch" to "Néel" character, accompanied with the emergence of a "Bloch point" topological defect with vanishing polarization. The dynamical evolution of skyrmions is connected to a constant jump of topological number between "0" and "1" over time. These intriguing phenomena are found to have an electrostatic origin. Our study thus demonstrates that, and explains why this unique light-matter interaction can be very powerful in creating and manipulating topological solitons in functional materials.

Motion and teleportation of polar bubbles in low-dimensional ferroelectrics

Electric bubbles are sub-10nm spherical vortices of electric dipoles that can spontaneously form in ultra-thin ferroelectrics. While the static properties of electric bubbles are well established, little to nothing is known about the dynamics of these particle-like structures. Here, we reveal pathways to realizing both the spontaneous and controlled dynamics of electric bubbles in ultra-thin Pb(Zr0.4Ti0.6)O3 films. In low screening conditions, we find that electric bubbles exhibit thermally-driven chaotic motion giving rise to a liquid-like state. In the high screening regime, we show that bubbles remain static but can be continuously displaced by a local electric field. Additionally, we predict and experimentally demonstrate the possibility of bubble teleportation - a process wherein a bubble is transferred to a new location via a single electric field pulse of a PFM tip. Finally, we attribute the discovered phenomena to the hierarchical structure of the energy landscape.

Toward Ecofriendly Piezoelectric Ceramics-Reduction of Energy and Environmental Footprint from Conceptualization to Deployment

Piezoelectric materials are widely used in electromechanical coupling components including actuators, kinetic sensors, and transducers, as well as in kinetic energy harvesters that convert mechanical energy into electricity and thus can power wireless sensing networks and the Internet of Things (IoT). Because the number of deployed energy harvesting powered systems is projected to explode, the supply of piezoelectric energy harvesters is also expected to be boosted. However, despite being able to produce green electricity from the ambient environment, high-performance piezoelectrics (i.e., piezoelectric ceramics) are energy intensive in research and manufacturing. For instance, the design of new piezoceramics relies on experimental trials, which need high process temperatures and thus cause high consumption and waste of energy. Also, the dominant element in high-performance piezoceramics is hazardous Pb, but substituting Pb with other nonhazardous elements may lead to a compromise of performance, extending the energy payback time and imposing a question of trade-offs between energy and environmental benefits. Meanwhile, piezoceramics are not well recycled, raising even more issues in terms of energy saving and environmental protection. This paper discusses these issues and then proposes solutions and provides perspectives to the future development of different aspects of piezoceramic research and industry.

Simulating Terahertz Field-Induced Ferroelectricity in Quantum Paraelectric SrTiO_{3}

Recent experiments have demonstrated that light can induce a transition from the quantum paraelectric to the ferroelectric phase of SrTiO_{3}. Here, we investigate this terahertz field-induced ferroelectric phase transition by solving the time-dependent lattice Schrödinger equation based on first-principles calculations. We find that ferroelectricity originates from a light-induced mixing between ground and first excited lattice states in the quantum paraelectric phase. In agreement with the experimental findings, our study shows that the nonoscillatory second harmonic generation signal can be evidence of ferroelectricity in SrTiO_{3}. We reveal the microscopic details of this exotic phase transition and highlight that this phenomenon is a unique behavior of the quantum paraelectric phase.

Deciphering the phase transition-induced ultrahigh piezoresponse in (K,Na)NbO3-based piezoceramics

Here, we introduce phase change mechanisms in lead-free piezoceramics as a strategy to utilize attendant volume change for harvesting large electrostrain. In the newly developed (K,Na)NbO₃ solid-solution at the polymorphic phase boundary we combine atomic mapping of the local polar vector with in situ synchrotron X-ray diffraction and density functional theory to uncover the phase change and interpret its underlying nature. We demonstrate that an electric field-induced phase transition between orthorhombic and tetragonal phases triggers a dramatic volume change and contributes to a huge effective piezoelectric coefficient of 1250 pm V⁻¹ along specific crystallographic directions. The existence of the phase transition is validated by a significant volume change evidenced by the simultaneous recording of macroscopic longitudinal and transverse strain. The principle of using phase transition to promote electrostrain provides broader design flexibility in the development of high-performance piezoelectric materials and opens the door for the discovery of high-performance future functional oxides.

Functional oxides with coexisting states of comparable energy typically exhibit extraordinary responses to external stimuli. Here, the authors demonstrate that coexisting phase structures provide large electric field-triggered volume change.

Evolution from Lead-Based to Lead-Free Piezoelectrics: Engineering of Lattices, Domains, Boundaries, and Defects Leading to Giant Response

Piezoelectric materials are known to mankind for more than a century, with numerous advancements made in both scientific understandings and practical applications. In the last two decades, in particular, the research on piezoelectrics has largely been driven by the constantly changing technological demand, and the drive toward a sustainable society. Hence, environmental-friendly "lead-free piezoelectrics" have emerged in the anticipation of replacing lead-based counterparts with at least comparable performance. However, there are still obstacles to be overcome for realizing this objective, while the efforts in this direction already seem to culminate. Therefore, novel structural strategies need to be designed to address these issues and for further breakthrough in this field. Here, various strategies to enhance piezoelectric properties in lead-free systems with fundamental and historical context, and from atomic to macroscopic scale, are explored. The main challenges currently faced in the transition from lead-based to lead-free piezoelectrics are identified and key milestones for future research in this field are suggested. These include: i) decoding the fundamental mechanisms; ii) large temperature-stable piezoresponse; and iii) fabrication-friendly and tailorable composition. Strategic insights and general guidelines for the synergistic design of new piezoelectric materials for obtaining a large piezoelectric response are also provided.

Grain Growth Behavior and Electrical Properties of 0.96(K0.46-xNa0.54-x)Nb0.95Sb0.05O3-0.04Bi0.5(Na0.82K0.18)0.5ZrO3 Ceramics

This study investigated the causes of microstructural changes and the resultant electrical properties according to the sintering temperature of 0.96(K_0.46−xNa_0.54−x)Nb_0.95Sb_0.05O₃-0.04Bi_0.5(Na_0.82K_0.18)_0.5ZrO₃ lead-free ceramics by analyzing the correlation between vacancy concentrations and 2D nucleation. When sintered for 4 h, no grain growth occurred for the x = 0.000 composition over a wide temperature range, demonstrating that the existence of initial vacancies is essential for grain growth. As x increased, that is, as the vacancy concentration increased, the critical driving force (ΔG_C) for 2D nucleation decreased, and abnormal grain growth was promoted. The number and size of these abnormal grains increased as the sintering temperature increased, but at sintering temperatures above 1100 °C, they decreased again owing to a large drop in ΔG_C. The x = 0.005 specimen sintered at 1085 °C exhibited excellent piezoelectric properties of d₃₃ = 498 pC/N and k_p = 0.45 due to the large number of large abnormal grains with an 83% tetragonal phase fraction. The x = 0.000 specimen sintered at 1130 °C with suppressed grain growth exhibited good energy storage properties because of its very high relative density and small grain size of 300 to 400 nm.

High-density switchable skyrmion-like polar nanodomains integrated on silicon

Topological domains in ferroelectrics^1-5 have received much attention recently owing to their novel functionalities and potential applications^6,7 in electronic devices. So far, however, such topological polar structures have been observed only in superlattices grown on oxide substrates, which limits their applications in silicon-based electronics. Here we report the realization of room-temperature skyrmion-like polar nanodomains in lead titanate/strontium titanate bilayers transferred onto silicon. Moreover, an external electric field can reversibly switch these nanodomains into the other type of polar texture, which substantially modifies their resistive behaviours. The polar-configuration-modulated resistance is ascribed to the distinct band bending and charge carrier distribution in the core of the two types of polar texture. The integration of high-density (more than 200 gigabits per square inch) switchable skyrmion-like polar nanodomains on silicon may enable non-volatile memory applications using topological polar structures in oxides.

Designing Monoclinic Heterophase Coexistence for the Enhanced Piezoelectric Performance in Ternary Lead-Based Relaxor Ferroelectrics

Enhanced piezoelectric, dielectric properties and thermal stability in ternary relaxor-PbTiO₃ based ferroelectric crystals are expected to develop the next-generation of electromechanical devices. However, due to their increased disorder compared to other ferroelectrics, designing a controllable phase boundary structure and engineered domain remains a challenging task. Here, we construct a monoclinic heterophase coexisting in a ternary Pb(In_1/2Nb_1/2)O₃-Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ single crystal with optimized composition and an ultrahigh piezoelectric coefficient of 1400 pC N^-1, to quantify the correlation between spontaneous nanopolarity and phase heterogeneity, in an attempt to understand the origin of the exceptional functionalities. By designing an in situ high-resolution spectroscopic-microscopic technique, we have observed M_a and M_c heterophase mixtures spatially separated by the monoclinic heterophase boundary (MHB), which are responsible for the ferroelectric-dominated and relaxor-ferroelectric-dominated nanodomain structure, respectively. Internal energy mapping from optical soft mode dynamics reveals the inhomogeneous polarization and local symmetry on both sides of the MHB. Various molecular polarizabilities and localized octahedral distortions correlate directly with monoclinic regions and electromechanical contribution. This work clarifies the heterogeneity between structure, energy, and polar order and provides a new design freedom for advanced relaxor ferroelectrics.

Anisotropic epitaxial stabilization of a low-symmetry ferroelectric with enhanced electromechanical response

Piezoelectrics interconvert mechanical energy and electric charge and are widely used in actuators and sensors. The best performing materials are ferroelectrics at a morphotropic phase boundary, where several phases coexist. Switching between these phases by electric field produces a large electromechanical response. In ferroelectric BiFeO₃, strain can create a morphotropic-phase-boundary-like phase mixture and thus generate large electric-field-dependent strains. However, this enhanced response occurs at localized, randomly positioned regions of the film. Here, we use epitaxial strain and orientation engineering in tandem-anisotropic epitaxy-to craft a low-symmetry phase of BiFeO₃ that acts as a structural bridge between the rhombohedral-like and tetragonal-like polymorphs. Interferometric displacement sensor measurements reveal that this phase has an enhanced piezoelectric coefficient of ×2.4 compared with typical rhombohedral-like BiFeO₃. Band-excitation frequency response measurements and first-principles calculations provide evidence that this phase undergoes a transition to the tetragonal-like polymorph under electric field, generating an enhanced piezoelectric response throughout the film and associated field-induced reversible strains. These results offer a route to engineer thin-film piezoelectrics with improved functionalities, with broader perspectives for other functional oxides.

Freestanding Ferroelectric Bubble Domains

Bubble-like domains, typically a precursor to the electrical skyrmions, arise in ultrathin complex oxide ferroelectric-dielectric-ferroelectric heterostructures epitaxially clamped with flat substrates. Here, it is reported that these specially ordered electric dipoles can also be retained in a freestanding state despite the presence of inhomogeneously distributed structural ripples. By probing local piezo and capacitive responses and using atomistic simulations, this study analyzes these ripples, sheds light on how the bubbles are stabilized in the modified electromechanical energy landscape, and discusses the difference in morphology between bubbles in freestanding and as-grown states. These results are anticipated to be the starting point of a new paradigm for the exploration of electric skyrmions with arbitrary boundaries and physically flexible topological orders in ferroelectric curvilinear space.

Direct Observation of Polarization Rotation in the Monoclinic MB Phase under Electrical Loading

The monoclinic phase has received a lot of research because of its importance in explaining the origin of high piezoelectric and ferroelectric performances around the morphotropic phase boundary. In the present study, we have investigated the detailed structural evolution in monoclinic PbZr_0.535Ti_0.465O₃ ferroelectric ceramics induced by an electric field with in situ high-energy synchrotron diffraction combined with two-dimensional (2D) geometry scattering technology. It has been discovered that an electric-field-induced single monoclinic M_B phase persists indefinitely. The lattice, unit cell volume, and spontaneous polarization of the monoclinic M_B structure exhibit significant and flexible responses to the external electric field, i.e., the spontaneous polarization rotates continuously and the lattice and unit cell volume present a butterfly form under the influence of the bipolar electric field. Particularly, direct experimental evidence demonstrates that the macropolarization of PbZr_0.535Ti_0.465O₃ is derived from the spontaneous polarization rotation rather than domain switching, and its volume expansion plays a vital role in the piezoelectric response.

Topotactic Growth of Free-Standing Two-Dimensional Perovskite Niobates with Low Symmetry Phase

Here, we report a novel topotactic method to grow 2D free-standing perovskite using KNbO₃ (KN) as a model system. Perovskite KN with monoclinic phase, distorted by as large as ∼6 degrees compared with orthorhombic KN, is obtained from 2D KNbO₂ after oxygen-assisted annealing at relatively low temperature (530 °C). Piezoresponse force microscopy (PFM) measurements confirm that the 2D KN sheets show strong spontaneous polarization (P_s) along [101̅]_pc direction and a weak in-plane polarization, which is consistent with theoretical predictions. Thickness-dependent stripe domains, with increased surface displacement and PFM phase changes, are observed along the monoclinic tilt direction, indicating the preserved strain in KN induces the variation of nanoscale ferroelectric properties. 2D perovskite KN with low symmetry phase stable at room temperature will provide new opportunities in the exploration of nanoscale information storage devices and better understanding of ferroelectric/ferroelastic phenomena in 2D perovskite oxides.

PASP: Property analysis and simulation package for materials

We have developed a software package, namely, PASP (Property Analysis and Simulation Package for materials), to analyze the structural, electronic, magnetic, and thermodynamic properties of complex condensed matter systems. Our package integrates several functionalities including symmetry analysis, global structure searching methods, effective Hamiltonian methods, and Monte Carlo simulation methods. In conjunction with first-principles calculations, PASP has been successfully applied to diverse physical systems. In this paper, we give a brief introduction to its main features and underlying theoretical formulism. Some typical applications are provided to demonstrate the usefulness, high efficiency, and reliability of PASP. We expect that further developments will make PASP a general-purpose tool for material simulation and property calculation of condensed matters.

Topology and control of self-assembled domain patterns in low-dimensional ferroelectrics

Whilst often discussed as non-trivial phases of low-dimensional ferroelectrics, modulated polar phases such as the dipolar maze and the nano-bubble state have been appraised as essentially distinct. Here we emphasize their topological nature and show that these self-patterned polar states, but also additional mesophases such as the disconnected labyrinthine phase and the mixed bimeron-skyrmion phase, can be fathomed in their plurality through the unifying canvas of phase separation kinetics. Under compressive strain, varying the control parameter, i.e., the external electric field, conditions the nonequilibrium self-assembly of domains, and bridges nucleation and spinodal decomposition via the sequential onset of topological transitions. The evolutive topology of these polar textures is driven by the (re)combination of the elementary topological defects, merons and antimerons, into a plethora of composite topological defects such as the fourfold junctions, the bimeron and the target skyrmion. Moreover, we demonstrate that these manipulable defects are stable at room temperature and feature enhanced functionalities, appealing for devising future topological-based nanoelectronics.

Understanding the processes underlying the self-assembly of polar textures is pivotal for the development of future technologies. Here, the authors reveal the dynamics of nonequilibrium phase transitions in low-dimensional ferroelectrics and emphasize their topological nature.

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.

Mechanism of phosphate adsorption on superparamagnetic microparticles modified with transitional elements: Experimental observation and computational modelling

Microparticle sorbents (MPSs) containing nano-Fe₃O₄ core, nano-layered double hydroxides shell modified with different transitional elements (TE-MPSs) are effective for capturing phosphate from wastewater. In present article, different TE-MPSs loaded with Ce, La, Zr and Hf were synthesized and the phosphorous removal performances were compared. The molecular-level mechanism of phosphate adsorption was successfully simulated by pseudo-atom model based on virtual crystal approximation method, which was in line with the spectroscopic data. The results confirmed the inter-sphere complexation reaction between phosphate and TE-MPSs under neutral pH. And the adsorption mechanism probably changed during cycles of adsorption/regeneration. As revealed by elemental composition analysis, ion exchange mechanism probably played an important part in phosphate adsorption in Cycle 1 while the ligand complexation became dominant after regenerated with NaOH in the following cycles. This work indicates that the highly effective, easily separable and repeatedly usable TE-MPSs has the potential for phosphate sequestration and recovery from sewage wastewater.

Photoinduced Phase Transitions in Ferroelectrics

Ferroic materials naturally exhibit a rich number of functionalities, which often arise from thermally, chemically, or mechanically induced symmetry breakings or phase transitions. Based on density functional calculations, we demonstrate here that light can drive phase transitions as well in ferroelectric materials such as the perovskite oxides lead titanate and barium titanate. Phonon analysis and total energy calculations reveal that the polarization tends to vanish under illumination, to favor the emergence of nonpolar phases, potentially antiferroelectric, and exhibiting a tilt of the oxygen octahedra. Strategies to tailor photoinduced phases based on phonon instabilities in the electronic ground state are also discussed.

Monte-Carlo simulation combined with density functional theory to investigate the equilibrium thermodynamics of electrode materials: lithium titanates as model compounds

By using lithium titanate (LTO) as a model electrode material, the present study proposes a method to describe its equilibrium thermodynamics based on the Monte-Carlo simulation (MC), for which the energetic parameters are determined by the density functional theory (DFT). The electrochemical potential profile is simulated by a simple topological model which consists only of three parameters representing the Li site energies; namely, the potential energy of the 8a site (ε8a), the difference in the site energy between the 8a and 16c sites (Δε) and the repulsion between two Li atoms situated at the adjacent 8a and 16c sites (J). Parameter physics by the MC revealed that the term Δε plays a decisive role, with a collateral effect from J, for characterizing the shape of the potential profile whereas the term ε8a determines its position along the electrochemical potential. For instance, if Δε exceeds the thermal energy at the temperature under consideration, i.e., if Δε > 3kT, the first-order phase transition takes place during which two phases coexist, resulting in a plateau region in the potential profile. On the other hand, if Δε < 3kT, the lithiation of LTO is viewed as a phenomenon above the critical point, above which the material is in a homogeneous uniphasic state. A multiple regression analysis of a set of the total energy calculated by DFT allows us to determine these energetic terms. The MC simulation with the determined parameters well reproduces the shape and position of the experimental potential profile of LTO. Since the determined value, Δε/eV ∼ 0.4, far exceeds the thermal energy at ambient temperature, the potential plateau of LTO is explained by the first-order phase transition as long as the equilibrium state is concerned.

Giant piezoelectricity of Sm-doped Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals

High-performance piezoelectrics benefit transducers and sensors in a variety of electromechanical applications. The materials with the highest piezoelectric charge coefficients (d ₃₃) are relaxor-PbTiO₃ crystals, which were discovered two decades ago. We successfully grew Sm-doped Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (Sm-PMN-PT) single crystals with even higher d ₃₃ values ranging from 3400 to 4100 picocoulombs per newton, with variation below 20% over the as-grown crystal boule, exhibiting good property uniformity. We characterized the Sm-PMN-PT on the atomic scale with scanning transmission electron microscopy and made first-principles calculations to determine that the giant piezoelectric properties arise from the enhanced local structural heterogeneity introduced by Sm³⁺ dopants. Rare-earth doping is thus identified as a general strategy for introducing local structural heterogeneity in order to enhance the piezoelectricity of relaxor ferroelectric crystals.

Ferroelectric Problem beyond the Conventional Scaling Law

Ferroelectric (FE) size effects against the scaling law were reported recently in ultrathin group-IV monochalcogenides, and extrinsic effects (e.g., defects and lattice strains) were often resorted to. Via first-principles based finite-temperature (T) simulations, we reveal that these abnormalities are intrinsic to their unusual symmetry breaking from bulk to thin film. Changes of the electronic structures result in different order parameters characterizing the FE phase transition in bulk and in thin films, and invalidation of the scaling law. Beyond the scaling law T_{c} limit, this mechanism can help predict materials that are promising for room-T ultrathin FE devices of broad interest.

Intrinsic Origin of Enhancement of Ferroelectricity in SnTe Ultrathin Films

Previous studies showed that, as ferroelectric films become thinner, their Curie temperature (T_{c}) and polarization below T_{c} both typically decrease. In contrast, a recent experiment [Chang et al., Science 353, 274 (2016)SCIEAS0036-807510.1126/science.aad8609] observed that atomic-thick SnTe films have a higher T_{c} than their bulk counterpart, which was attributed to extrinsic effects. We find, using first-principles calculations, that the 0-K energy barrier for the polarization switching (which is a quantity directly related to T_{c}) is higher in most investigated defect-free SnTe ultrathin films than that in bulk SnTe, and that the 5-unit-cell (UC) SnTe thin film has the largest energy barrier as a result of an interplay between hybridization interactions and Pauli repulsions. Further simulations, employing a presently developed effective Hamiltonian, confirm that freestanding, defect-free SnTe thin films have a higher T_{c} than bulk SnTe, except for the 1-UC case. Our work, therefore, demonstrates the possibility to intrinsically enhance ferroelectricity of ultrathin films by reducing their thickness.

Development of Bismuth Ferrite as a Piezoelectric and Multiferroic Material by Cobalt Substitution

Bismuth ferrite (BiFeO3 ) is the most widely studied multiferroic material with robust ferroelectricity and antiferromagnetic ordering at room temperature. One of the possible device applications of this material is one that utilizes the ferroelectric/piezoelectric property itself such as ferroelectric memory components, actuators, and so on. Other applications are more challenging and make full use of its multiferroic property to realize novel spintronics and magnetic memory devices, which can be addressed electrically as well as magnetically. This progress report summarizes the recent attempt to control the piezoelectric and magnetic properties of BiFeO3 by cobalt substitution.

Local deformation gradients in epitaxial Pb(Zr0.2Ti0.8)O3 layers investigated by transmission electron microscopy

Lead zirconate titanate samples are used for their piezoelectric and ferroelectric properties in various types of micro-devices. Epitaxial layers of tetragonal perovskites have a tendency to relax by forming [Formula: see text] ferroelastic domains. The accommodation of the a/c/a/c polydomain structure on a flat substrate leads to nanoscale deformation gradients which locally influence the polarization by flexoelectric effect. Here, we investigated the deformation fields in epitaxial layers of Pb(Zr_0.2Ti_0.8)O₃ grown on SrTiO₃ substrates using transmission electron microscopy (TEM). We found that the deformation gradients depend on the domain walls inclination ([Formula: see text] or [Formula: see text] to the substrate interface) of the successive [Formula: see text] domains and we describe three different a/c/a domain configurations: one configuration with parallel a-domains and two configurations with perpendicular a-domains (V-shaped and hat-[Formula: see text]-shaped). In the parallel configuration, the c-domains contain horizontal and vertical gradients of out-of-plane deformation. In the V-shaped and hat-[Formula: see text]-shaped configurations, the c-domains exhibit a bending deformation field with vertical gradients of in-plane deformation. Each of these configurations is expected to have a different influence on the polarization and so the local properties of the film. The deformation gradients were measured using dark-field electron holography, a TEM technique, which offers a good sensitivity (0.1%) and a large field-of-view (hundreds of nanometers). The measurements are compared with finite element simulations.

Cooperative Couplings between Octahedral Rotations and Ferroelectricity in Perovskites and Related Materials

The structure of ABO_{3} perovskites is dominated by two types of unstable modes, namely, the oxygen octahedral rotation (AFD) and ferroelectric (FE) mode. It is generally believed that such AFD and FE modes tend to compete and suppress each other. Here we use first-principles methods to show that a dual nature of the FE-AFD coupling, which turns from competitive to cooperative as the AFD mode strengthens, occurs in numerous perovskite oxides. We provide a unified model of such a dual interaction by introducing novel high-order coupling terms and explain the atomistic origin of the resulting new form of ferroelectricity in terms of universal steric mechanisms. We also predict that such a novel form of ferroelectricity leads to atypical behaviors, such as an enhancement of all the three Cartesian components of the electric polarization under hydrostatic pressure and compressive epitaxial strain.

Photostriction and elasto-optic response in multiferroics and ferroelectrics from first principles

The present work reviews a series of recent first-principles studies devoted to the description of the interaction of light and strain in ferroelectric and multiferroic materials. Specifically, the modelling schemes used in these works to describe the so-called photostriction and elasto-optic effects are presented, in addition to the results and analysis provided by these ab initio calculations. In particular, the large importance of the piezoelectric effect in the polar direction in the photostriction of ferroelectric materials is stressed. Similarly, the occurrence of low-symmetry phases in lead titanate thin films under tensile strain is demonstrated to result in large elasto-optic constants. In addition, first-principle calculations allow to gain microscopic knowledge of subtle effects, for instance in the case of photostriction, where the deformation potential effect in directions perpendicular to the polar axis is shown to be almost as significant as the piezoelectric effect. As a result, the numerical methods presented here could propel the design of efficient opto-mechanical devices.

Modelling the structure of Zr-rich Pb(Zr1-xTix)O3, x = 0.4 by a multiphase approach

Solid solution perovskite Pb(Zr_1-xTi_x)O₃ (PZT) is an industrially important material. Despite the long history of experimental and theoretical studies, the structure of this material is still under intensive discussion. In this work, we have applied structure searching coupled with density functional theory methods to provide a multiphase description of this material at x = 0.4. We demonstrate that the permutational freedom of B-site cations leads to the stabilisation of a variety of local phases reflecting a relatively flat energy landscape of PZT. Using a set of predicted local phases we reproduce the experimental pair distribution function (PDF) profile with high accuracy. We introduce a complex multiphase picture of the structure of PZT and show that additional monoclinic and rhombohedral phases account for a better description of the experimental PDF profile. We propose that such a multiphase picture reflects the entropy reached in the sample during the preparation process.

Quantum-mechanical analysis of effect of alloying elements on ε-martensite start temperature of steels

With regard to the transformation mechanism of austenitic high manganese steel, the prediction of the ε-martensite start temperature is a critical consideration in alloy design. Evaluation of the ε-martensite start temperature makes it possible to predict the microstructure and to understand the phase transformation occurring during deformation. Here we use the quantum mechanical calculation of random alloys to understand the physics for ε-martensitic transformation in steels. We could find the linear relationship between the measured ε-martensite start temperatures and the crystal structure stability for various compositions. We also could estimate the effect of several alloying elements. It is expected that the effect of decreasing the temperatures for the same amount of alloying elements addition will be larger moving farther from Group VIII. By creating a free-energy model that reflects the temperature effect, we were able to calculate the average driving force required for the ε-martensitic transformations.

Nanoscale Bubble Domains and Topological Transitions in Ultrathin Ferroelectric Films

Observation of a new type of nanoscale ferroelectric domains, termed as "bubble domains"-laterally confined spheroids of sub-10 nm size with local dipoles self-aligned in a direction opposite to the macroscopic polarization of a surrounding ferroelectric matrix-is reported. The bubble domains appear in ultrathin epitaxial PbZr_0.2 Ti_0.8 O₃ /SrTiO₃ /PbZr_0.2 Ti_0.8 O₃ ferroelectric sandwich structures due to the interplay between charge and lattice degrees of freedom. The existence of the bubble domains is revealed by high-resolution piezoresponse force microscopy (PFM), and is corroborated by aberration-corrected atomic-resolution scanning transmission electron microscopy mapping of the polarization displacements. An incommensurate phase and symmetry breaking is found within these domains resulting in local polarization rotation and hence impart a mixed Néel-Bloch-like character to the bubble domain walls. PFM hysteresis loops for the bubble domains reveal that they undergo an irreversible phase transition to cylindrical domains under the electric field, accompanied by a transient rise in the electromechanical response. The observations are in agreement with ab-initio-based calculations, which reveal a very narrow window of electrical and elastic parameters that allow the existence of bubble domains. The findings highlight the richness of polar topologies possible in ultrathin ferroelectric structures and bring forward the prospect of emergent functionalities due to topological transitions.

Microscopic origins of the large piezoelectricity of leadfree (Ba,Ca)(Zr,Ti)O3

In light of directives around the world to eliminate toxic materials in various technologies, finding lead-free materials with high piezoelectric responses constitutes an important current scientific goal. As such, the recent discovery of a large electromechanical conversion near room temperature in (1-x)Ba(Zr_0.2Ti_0.8)O₃-x(Ba_0.7Ca_0.3)TiO₃ compounds has directed attention to understanding its origin. Here, we report the development of a large-scale atomistic scheme providing a microscopic insight into this technologically promising material. We find that its high piezoelectricity originates from the existence of large fluctuations of polarization in the orthorhombic state arising from the combination of a flat free-energy landscape, a fragmented local structure, and the narrow temperature window around room temperature at which this orthorhombic phase is the equilibrium state. In addition to deepening the current knowledge on piezoelectricity, these findings have the potential to guide the design of other lead-free materials with large electromechanical responses.

The origin of ultrahigh piezoelectricity in relaxor-ferroelectric solid solution crystals

The discovery of ultrahigh piezoelectricity in relaxor-ferroelectric solid solution single crystals is a breakthrough in ferroelectric materials. A key signature of relaxor-ferroelectric solid solutions is the existence of polar nanoregions, a nanoscale inhomogeneity, that coexist with normal ferroelectric domains. Despite two decades of extensive studies, the contribution of polar nanoregions to the underlying piezoelectric properties of relaxor ferroelectrics has yet to be established. Here we quantitatively characterize the contribution of polar nanoregions to the dielectric/piezoelectric responses of relaxor-ferroelectric crystals using a combination of cryogenic experiments and phase-field simulations. The contribution of polar nanoregions to the room-temperature dielectric and piezoelectric properties is in the range of 50–80%. A mesoscale mechanism is proposed to reveal the origin of the high piezoelectricity in relaxor ferroelectrics, where the polar nanoregions aligned in a ferroelectric matrix can facilitate polarization rotation. This mechanism emphasizes the critical role of local structure on the macroscopic properties of ferroelectric materials.

Combining a perovskite ferroelectric with moderate piezoelectric properties and a nonpiezoelectric pervoskite relaxor can create a highly piezoelectric material. Here, the authors help explain this unusual result by quantifying how polar nanoregions in the material contribute to its piezoelectric response.

Special quasirandom structures for perovskite solid solutions

Special quasirandom structures (SQS) are presently generated for disordered (A'1-x [Formula: see text] x )BX3 and A(B'1-x [Formula: see text] x )X3 perovskite solid solutions, with x  =  1/2 as well as 1/3 and 2/3. These SQS configurations are obtained by imposing that the so-called Cowley parameters are as close to zero as possible for the three nearest neighboring shells. Moreover, these SQS configurations are slightly larger in size than those available in the literature for x  =  1/2, mostly because of the current capabilities of atomistic techniques. They are used here within effective Hamiltonian schemes to predict various properties, which are then compared to those associated with large random supercells, in a variety of compounds, namely (Ba1-x Sr x )TiO3, Pb(Zr1-x Ti x )O3, Pb(Sc0.5Nb0.5)O3, Ba(Zr1-x Ti x )O3, Pb(Mg1/3Nb2/3)O3 and (Bi1-x Nd x )FeO3. It is found that these SQS configurations can reproduce many properties of large random supercells of most of these disordered perovskite alloys, below some finite material-dependent temperature. Examples of these properties are electrical polarization, anti-phase and in-phase octahedral tiltings, antipolar motions, antiferromagnetism, strain, piezoelectric coefficients, dielectric response, specific heat and even the formation of polar nanoregions (PNRs) in some relaxors. Some limitations of these SQS configurations are also pointed out and explained.

Enhanced Piezoelectric Response due to Polarization Rotation in Cobalt-Substituted BiFeO3 Epitaxial Thin Films

Polarization rotation induced by an external electric field in piezoelectric materials such as PbZr_1-x Ti_x O₃ is generally regarded as the origin of their large piezoelectric responses. Here, the piezoelectric responses of high-quality cobalt-substituted BiFeO₃ epitaxial thin films with monoclinic distortions are systematically examined. It is demonstrated that polarization rotation plays a crucial role in improving the piezoelectric responses in this material.

Two-step polarization switching mediated by a nonpolar intermediate phase in Hf0.4Zr0.6O2 thin films

The broken ferroelectric hysteresis loop achieved from a Hf0.4Zr0.6O2 film was interpreted based on the first order phase transition theory. The two-step polarization switching, which was expected from the theory, could be observed by dynamic pulse switching measurement. The variations in the interfacial capacitance values along with switching time and number of switching cycles could also be estimated from the pulse switching test. Being different from the one-step polarization switching in other ferroelectric films, two-step polarization switching produced two slanted plateau regions where the estimated interfacial capacitance values were different from each other. This could be understood based on the quantitative model of the two-step polarization switching with the involvement of an intermediate nonpolar phase. The Hf0.4Zr0.6O2 film was changed from antiferroelectric-like to ferroelectric-like with the increasing number of electric field cycles, which could be induced by the field driven phase change.

New modalities of strain-control of ferroelectric thin films

Ferroelectrics, with their spontaneous switchable electric polarization and strong coupling between their electrical, mechanical, thermal, and optical responses, provide functionalities crucial for a diverse range of applications. Over the past decade, there has been significant progress in epitaxial strain engineering of oxide ferroelectric thin films to control and enhance the nature of ferroelectric order, alter ferroelectric susceptibilities, and to create new modes of response which can be harnessed for various applications. This review aims to cover some of the most important discoveries in strain engineering over the past decade and highlight some of the new and emerging approaches for strain control of ferroelectrics. We discuss how these new approaches to strain engineering provide promising routes to control and decouple ferroelectric susceptibilities and create new modes of response not possible in the confines of conventional strain engineering. To conclude, we will provide an overview and prospectus of these new and interesting modalities of strain engineering helping to accelerate their widespread development and implementation in future functional devices.

Emergence of ferroelectricity in antiferroelectric nanostructures

First-principles-based finite-temperature simulations are used to predict the emergence of ferroelectricity in antiferroelectric nanostructures made of PbZrO3. The phenomenon is expected to occur in antiferroelectric nanodots, nanowires, and thin films with good surface charge compensation and can be explained by the recently proposed surface effect. Our computations provide a microscopic insight into the equilibrium phases, phase competition, and electrical properties of PbZrO3 nanostructures. The dependence of these properties on the electrical boundary conditions and nanostructure size is investigated.

Topological Point Defects in Relaxor Ferroelectrics

First-principles-based effective Hamiltonian simulations are used to reveal the hidden connection between topological defects (hedgehogs and antihedgehogs) and relaxor behavior. Such defects are discovered to predominantly lie at the border of polar nanoregions in both Ba(Zr_{0.5}Ti_{0.5})O_{3} (BZT) and Pb(Sc_{0.5}Nb_{0.5})O_{3} (PSN) systems, and the temperature dependency of their density allows us to distinguish between noncanonical (PSN) and canonical (BZT) relaxor behaviors (via the presence or absence of a crossing of a percolation threshold). This density also possesses an inflection point at precisely the temperature for which the dielectric response peaks. Moreover, hedgehogs and antihedgehogs are found to be mobile excitations, and the dynamical nature of their annihilation is demonstrated (using simple hydrodynamical arguments) to follows laws, such as those of Vogel-Fulcher and Arrhenius, that are characteristic of dipolar relaxation kinetics of relaxor ferroelectrics.

Frustration and Self-Ordering of Topological Defects in Ferroelectrics

A first-principles-based effective Hamiltonian technique is used to investigate the interplay between geometrical frustration and the ordering of topological defects in a ferroelectric nanocomposite consisting of a square array of BaTiO_{3} nanowires embedded in a Ba_{0.15}Sr_{0.85}TiO_{3} matrix. Different arrangements of the wires' chiralities geometrically frustrate the matrix, which in response exhibits point topological defects featuring self-assembled ordered structures spatially fluctuating down to the lowest temperatures. These fluctuations thereby endow the system with residual configurational entropy from which many properties characteristic of geometric frustration, such as the ground state degeneracy and the broadness of the dielectric response, are further found to originate.

Unique Piezoelectric Properties of the Monoclinic Phase in Pb(Zr,Ti)O_{3} Ceramics: Large Lattice Strain and Negligible Domain Switching

The origin of the excellent piezoelectric properties at the morphotropic phase boundary is generally attributed to the existence of a monoclinic phase in various piezoelectric systems. However, there exist no experimental studies that reveal the role of the monoclinic phase in the piezoelectric behavior in phase-pure ceramics. In this work, a single monoclinic phase has been identified in Pb(Zr,Ti)O_{3} ceramics at room temperature by in situ high-energy synchrotron x-ray diffraction, and its response to electric field has been characterized for the first time. Unique piezoelectric properties of the monoclinic phase in terms of large intrinsic lattice strain and negligible domain switching have been observed. The extensional strain constant d_{33} and the transverse strain constant d_{31} are calculated to be 520 and -200  pm/V, respectively. These large piezoelectric coefficients are mainly due to the large intrinsic lattice strain, with very little extrinsic contribution from domain switching. The unique properties of the monoclinic phase provide new insights into the mechanisms responsible for the piezoelectric properties at the morphotropic phase boundary.

Large Elasto-Optic Effect in Epitaxial PbTiO(3) Films

First-principles calculations are performed to investigate the elasto-optic properties of four different structural phases in (001) epitaxial PbTiO(3) films under tensile strain: a tetragonal (T) phase and an orthorhombic (O) phase, which are the ground states for small and large strain, respectively, and two low-symmetry, monoclinic phases of Cm and Pm symmetries that have low total energy in the intermediate strain range. It is found that the refractive indices of the T and O phases respond differently to epitaxial strain, evidenced by a change of sign of their effective elasto-optic coefficients, and as a result of presently discovered correlations between refractive index, axial ratio, and magnitude of the ferroelectric polarization. The difference in refractive indices between T and O and the existence of such correlations naturally lead to large elasto-optic coefficients in the Cm and Pm states in the intermediate strain range, because Cm structurally bridges the T and O phases (via polarization rotation and a rapid change of its axial ratio) and Pm adopts a similar axial ratio and polarization magnitude to Cm. The present results therefore broaden the palette of functionalities of ferroelectric materials, and suggest new routes to generate systems with unprecedentedly large elasto-optic conversion.