Creating polar antivortex in PbTiO3/SrTiO3 superlattice

Ferroelectric Texture of Individual Barium Titanate Nanocrystals

Ferroelectric materials display exotic polarization textures at the nanoscale that could be used to improve the energetic efficiency of electronic components. The vast majority of studies were conducted in two dimensions on thin films that can be further nanostructured, but very few studies address the situation of individual isolated nanocrystals (NCs) synthesized in solution, while such structures could have other fields of applications. In this work, we experimentally and theoretically studied the polarization texture of ferroelectric barium titanate (BaTiO3, BTO) NCs attached to a conductive substrate and surrounded by air. We synthesized NCs of well-defined quasicubic shape and 160 nm average size that conserve the tetragonal structure of BTO at room temperature. We then investigated the inverse piezoelectric properties of such pristine individual NCs by vector piezoresponse force microscopy (PFM), taking particular care to suppress electrostatic artifacts. In all of the NCs studied, we could not detect any vertical PFM signal, and the maps of the lateral response all displayed larger displacement amplitude on the edges with deformations converging toward the center. Using field phase simulations dedicated to ferroelectric nanostructures, we were able to predict the equilibrium polarization texture. These simulations revealed that the NC core is composed of 180° up and down domains defining the polar axis that rotate by 90° in the two facets orthogonal to this axis, eventually lying within these planes forming a layer of about 10 nm thickness mainly composed of 180° domains along an edge. From this polarization distribution, we predicted the lateral PFM response, which was revealed to be in very good qualitative agreement with the experimental observations. This work positions PFM as a relevant tool to evaluate the potential of complex ferroelectric nanostructures to be used as sensors.

Atomic-Scale Tracking Topological Phase Transition Dynamics of Polar Vortex-Antivortex Pairs

Non-trivial topological structures, such as vortex-antivortex (V-AV) pairs, have garnered significant attention in the field of condensed matter physics. However, the detailed topological phase transition dynamics of V-AV pairs, encompassing behaviors like self-annihilation, motion, and dissociation, have remained elusive in real space. Here, polar V-AV pairs are employed as a model system, and their transition pathways are tracked with atomic-scale resolution, facilitated by in situ (scanning) transmission electron microscopy and phase field simulations. This investigation reveals that polar vortices and antivortices can stably coexist as bound pairs at room temperature, and their polarization decreases with heating. No dissociation behavior is observed between the V-AV phase at room temperature and the paraelectric phase at high temperature. However, the application of electric fields can promote the approach of vortex and antivortex cores, ultimately leading to their annihilation near the interface. Revealing the transition process mediated by polar V-AV pairs at the atomic scale, particularly the role of polar antivortex, provides new insights into understanding the topological phases of matter and their topological phase transitions. Moreover, the detailed exploration of the dynamics of polar V-AV pairs under thermal and electrical fields lays a solid foundation for their potential applications in electronic devices.

Tuning Topology Phases by Controlling Effective Screening and Depolarization in Oxide Superlattices

Polar topological phases in oxide superlattices attracted significant attention due to their unique properties. Previous work revealed that a polar vortex and polar skyrmions exist in (PTO)/(STO) superlattices under different elastic constraints, i.e., on different substrates. Here, our phase-field simulation demonstrates that manipulating the PTO and STO layers' thickness can control the effective screening provided by STO and the depolarization degree in PTO, thus switching the system among the polar skyrmions, vortex labyrinth, or paraelectric phase without changing elastic constraints. Additionally, reducing the STO thickness creates interlayer coupling among PTO layers, generating the long-range order of topological phases within superlattices. Furthermore, we construct a PTO-STO thickness topological phase diagram. These findings offer insights into the polar topological phases' formation in oxide superlattices, elucidating the roles of ferroelectric and paraelectric layers in their formation.

Revealing the three-dimensional arrangement of polar topology in nanoparticles

In the early 2000s, low dimensional ferroelectric systems were predicted to have topologically nontrivial polar structures, such as vortices or skyrmions, depending on mechanical or electrical boundary conditions. A few variants of these structures have been experimentally observed in thin film model systems, where they are engineered by balancing electrostatic charge and elastic distortion energies. However, the measurement and classification of topological textures for general ferroelectric nanostructures have remained elusive, as it requires mapping the local polarization at the atomic scale in three dimensions. Here we unveil topological polar structures in ferroelectric BaTiO3 nanoparticles via atomic electron tomography, which enables us to reconstruct the full three-dimensional arrangement of cation atoms at an individual atom level. Our three-dimensional polarization maps reveal clear topological orderings, along with evidence of size-dependent topological transitions from a single vortex structure to multiple vortices, consistent with theoretical predictions. The discovery of the predicted topological polar ordering in nanoscale ferroelectrics, independent of epitaxial strain, widens the research perspective and offers potential for practical applications utilizing contact-free switchable toroidal moments.

Large Polarization Near 50 μC/cm2 in a Single Unit Cell Layer SrTiO3

The generally nonpolar SrTiO3 has attracted more attention recently because of its possibly induced novel polar states and related paraelectric-ferroelectric phase transitions. By using controlled pulsed laser deposition, high-quality, ultrathin, and strained SrTiO3 layers were obtained. Here, transmission electron microscopy and theoretical simulations have unveiled highly polar states in SrTiO3 films even down to one unit cell at room temperature, which were stabilized in the PbTiO3/SrTiO3/PbTiO3 sandwich structures by in-plane tensile strain and interfacial coupling, as evidenced by large tetragonality (∼1.05), notable polar ion displacement (0.019 nm), and thus ultrahigh spontaneous polarization (up to ∼50 μC/cm2). These values are nearly comparable to those of the strong ferroelectrics as the PbZrxTi1-xO3 family. Our findings provide an effective and practical approach for integrating large strain states into oxide films and inducing polarization in nonpolar materials, which may broaden the functionality of nonpolar oxides and pave the way for the discovery of new electronic materials.

Interlayer Coupling Controlled Ordering and Phases in Polar Vortex Superlattices

The recent discovery of polar topological structures has opened the door for exciting physics and emergent properties. There is, however, little methodology to engineer stability and ordering in these systems, properties of interest for engineering emergent functionalities. Notably, when the surface area is extended to arbitrary thicknesses, the topological polar texture becomes unstable. Here we show that this instability of the phase is due to electrical coupling between successive layers. We demonstrate that this electrical coupling is indicative of an effective screening length in the dielectric, similar to the conductor-ferroelectric interface. Controlling the electrostatics of the superlattice interfaces, the system can be tuned between a pure topological vortex state and a mixed classical-topological phase. This coupling also enables engineering coherency among the vortices, not only tuning the bulk phase diagram but also enabling the emergence of a 3D lattice of polar textures.

Electrically and mechanically driven rotation of polar spirals in a relaxor ferroelectric polymer

Topology created by quasi-continuous spatial variations of a local polarization direction represents an exotic state of matter, but field-driven manipulation has been hitherto limited to creation and destruction. Here we report that relatively small electric or mechanical fields can drive the non-volatile rotation of polar spirals in discretized microregions of the relaxor ferroelectric polymer poly(vinylidene fluoride-ran-trifluoroethylene). These polar spirals arise from the asymmetric Coulomb interaction between vertically aligned helical polymer chains, and can be rotated in-plane through various angles with robust retention. Given also that our manipulation of topological order can be detected via infrared absorption, our work suggests a new direction for the application of complex materials.

The emergence of three-dimensional chiral domain walls in polar vortices

Chirality or handedness of a material can be used as an order parameter to uncover the emergent electronic properties for quantum information science. Conventionally, chirality is found in naturally occurring biomolecules and magnetic materials. Chirality can be engineered in a topological polar vortex ferroelectric/dielectric system via atomic-scale symmetry-breaking operations. We use four-dimensional scanning transmission electron microscopy (4D-STEM) to map out the topology-driven three-dimensional domain walls, where the handedness of two neighbor topological domains change or remain the same. The nature of the domain walls is governed by the interplay of the local perpendicular (lateral) and parallel (axial) polarization with respect to the tubular vortex structures. Unique symmetry-breaking operations and the finite nature of domain walls result in a triple point formation at the junction of chiral and achiral domain walls. The unconventional nature of the domain walls with triple point pairs may result in unique electrostatic and magnetic properties potentially useful for quantum sensing applications.

Pure Chiral Polar Vortex Phase in PbTiO3/SrTiO3 Superlattices with Tunable Circular Dichroism

Nontrivial polarization textures have been demonstrated in ferroelectric/dielectric superlattices, where the electrostatic, elastic, and different gradient energies compete in a delicate balance. When PbTiO₃/SrTiO₃ superlattices are grown on DyScO₃, the coexistence of ferroelectric domains and vortex structure is observed for n = 12-20 unit cells. Here, we report an approach to achieve single-phase vortex structures in superlattices by controlling the epitaxial strain using Sr_1.04Al_0.12Ga_0.35Ta_0.50O₃ substrates. The domain width follows Kittel's law with the thickness of the ferroelectric PbTiO₃ layers. A phase transition from vortex to a disordered phase with temperature is characterized by the correlation length. Resonant soft X-ray diffraction circular dichroism at the titanium L-edge reveals enhanced chirality with the thickness of the ferroelectric layer. These results are supported by second-principles simulations, which demonstrate that the integrated helicity increases with n. The stabilization of chiral single-phase polar vortices in ferroelectric/dielectric superlattices can enable novel optoelectronic devices with enhanced ferroelectric-light interaction.

Ferroelectric solitons crafted in epitaxial bismuth ferrite superlattices

In ferroelectrics, complex interactions among various degrees of freedom enable the condensation of topologically protected polarization textures. Known as ferroelectric solitons, these particle-like structures represent a new class of materials with promise for beyond-CMOS technologies due to their ultrafine size and sensitivity to external stimuli. Such polarization textures have scarcely been demonstrated in multiferroics. Here, we present evidence for ferroelectric solitons in (BiFeO₃)/(SrTiO₃) superlattices. High-resolution piezoresponse force microscopy and Cs-corrected high-angle annular dark-field scanning transmission electron microscopy reveal a zoo of topologies, and polarization displacement mapping of planar specimens reveals center-convergent/divergent topological defects as small as 3 nm. Phase-field simulations verify that some of these structures can be classed as bimerons with a topological charge of ±1, and first-principles-based effective Hamiltonian computations show that the coexistence of such structures can lead to non-integer topological charges, a first observation in a BiFeO₃-based system. Our results open new opportunities in multiferroic topotronics.

Absence of critical thickness for polar skyrmions with breaking the Kittel's law

The period of polar domain (d) in ferroics was commonly believed to scale with corresponding film thicknesses (h), following the classical Kittel's law of d ∝ [Formula: see text]. Here, we have not only observed that this relationship fails in the case of polar skyrmions, where the period shrinks nearly to a constant value, or even experiences a slight increase, but also discovered that skyrmions have further persisted in [(PbTiO3)2/(SrTiO3)2]10 ultrathin superlattices. Both experimental and theoretical results indicate that the skyrmion periods (d) and PbTiO3 layer thicknesses in superlattice (h) obey the hyperbolic function of d = Ah + [Formula: see text] other than previous believed, simple square root law. Phase-field analysis indicates that the relationship originates from the different energy competitions of the superlattices with PbTiO3 layer thicknesses. This work exemplified the critical size problems faced by nanoscale ferroelectric device designing in the post-Moore era.

Thermodynamics of Light-Induced Nanoscale Polar Structures in Ferroelectric Superlattices

We study the thermodynamics of nanoscale polar structures in PbTiO₃/SrTiO₃ ferroelectric superlattices induced by above-bandgap optical excitation using a phase-field model explicitly considering both structural and electronic processes. We demonstrate that the light-excited carriers provide the charge compensation of polarization bound charges and the lattice thermal energy, both of which are key to the thermodynamic stabilization of a previously observed supercrystal, a three-dimensionally periodic nanostructure, within a window of substrate strains, while different mechanical and electrical boundary conditions can stabilize a number of other nanoscale polar structures by balancing the competing short-range exchange interactions responsible for the domain wall energy and long-range electrostatic and elastic interactions. The insights into the light-induced formation and richness of nanoscale structures from this work offer theoretical guidance for exploring and manipulating the thermodynamic stability of nanoscale polar structures employing a combination of thermal, mechanical, and electrical stimuli as well as light.

Optimizing experimental parameters of integrated differential phase contrast (iDPC) for atomic resolution imaging

Integrated differential phase contrast scanning transmission electron microscopy (iDPC-STEM) technique has been well developed for studying atomic structures at sub-Å resolution with the capability of simultaneously imaging heavy and light atoms even at an extremely low electron dose. As a direct phase contrast imaging technique, atomic resolution iDPC-STEM is sensitive to the imaging conditions. Although great achievements have been made both in aspect of theory and experiments, the influence of experimental parameters on the contrast of atomic resolution iDPC-STEM images has not been systematically investigated. Here, we perform the iDPC-STEM simulations on the prototypical example of SrTiO₃ with respect to the routine experimental factors, including the defocus, specimen thickness, accelerating voltage, convergence angle, collection angle, sample tilt and electron dose. Through the evaluation of image contrast and atom column intensity, the parameters are discussed to improve the image contrast and the visibility of light elements. Moreover, the dose-dependent simulations demonstrate the advantage of low dose iDPC-STEM imaging over other conventional STEM modes. Our results provide a practical guideline to experimentally obtain accessible atomic resolution iDPC-STEM images.

Nonabelian Ginzburg-Landau theory for ferroelectrics

The Ginzburg-Landau theory, which was introduced to phenomenologically describe the destruction of superconductivity by a magnetic field at the beginning, has brought up much more knowledge beyond the original one as a mean-field theory of thermodynamics states. There the complex order parameter plays an important role. Here we propose a macroscopic theory to describe the features of ferroelectrics by a two-component complex order parameter coupled to nonabelian gauge potentials that provide more freedom to reflect interplays between different measurables. Within this theoretical framework, some recently discovered empirical static and time-independent phenomena, such as vortex, anti-vortex, spiral orders can be obtained as solutions for different gauge potentials. It is expected to bring in a new angle of view with more elucidation than the traditional one that takes the polarization as order parameter.

Density Functional Theory Study on the Enhancement Mechanism of the Photocatalytic Properties of the g-C3N4/BiOBr(001) Heterostructure

The van der Waals heterostructures fabricated in two semiconductors are currently attracting considerable attention in various research fields. Our study uses density functional theory calculations within the Heyd-Scuseria-Ernzerhof hybrid functional to analyze the geometric structure and electronic structure of the g-C₃N₄/BiOBr(001) heterojunction in order to gain a better understanding of its photocatalytic properties. The calculated band alignments show that g-C₃N₄/BiOBr can function as a type-II heterojunction. In this heterojunction, the electrons and holes can effectively be separated at the interface. Moreover, we find that the electronic structure and band alignment of g-C₃N₄/BiOBr(001) can be tuned using external electric fields. It is also noteworthy that the optical absorption peak in the visible region is enhanced under the action of the electric field. The electric field may even improve the optical properties of the g-C₃N₄/BiOBr(001) heterostructure. Given the results of our calculations, it seems that g-C₃N₄/BiOBr(001) may be significantly superior to visible light photocatalysis.

Dynamics of Polar Skyrmion Bubbles under Electric Fields

Room-temperature polar skyrmions, which have been recently discovered in oxide superlattice, have received considerable attention for their potential applications in nanoelectronics owing to their nanometer size, emergent chirality, and negative capacitance. For practical applications, their manipulation using external stimuli is a prerequisite. Herein, we study the dynamics of individual polar skyrmions at the nanoscale via in situ scanning transmission electron microscopy. By monitoring the electric-field-driven creation, annihilation, shrinkage, and expansion of topological structures in real space, we demonstrate the reversible transformation among skyrmion bubbles, elongated skyrmions, and monodomains. The underlying mechanism and interactions are discussed in conjunction with phase-field simulations. The electrical manipulation of nanoscale polar skyrmions allows the tuning of their dielectric permittivity at the atomic scale, and the detailed knowledge of their phase transition behaviors provides fundamentals for their applications in nanoelectronics.

Theoretical Understanding of Polar Topological Phase Transitions in Functional Oxide Heterostructures: A Review

The exotic topological phase is attracting considerable attention in condensed matter physics and materials science over the past few decades due to intriguing physical insights. As a combination of "topology" and "ferroelectricity," the ferroelectric (polar) topological structures are a fertile playground for emergent phenomena and functionalities with various potential applications. Herein, the review starts with the universal concept of the polar topological phase and goes on to briefly discuss the important role of computational tools such as phase-field simulations in designing polar topological phases in oxide heterostructures. In particular, the history of the development of phase-field simulations for ferroelectric oxide heterostructures is highlighted. Then, the current research progress of polar topological phases and their emergent phenomena in ferroelectric functional oxide heterostructures is reviewed from a theoretical perspective, including the topological polar structures, the establishment of phase diagrams, their switching kinetics and interconnections, phonon dynamics, and various macroscopic properties. Finally, this review offers a perspective on the future directions for the discovery of novel topological phases in other ferroelectric systems and device design for next-generation electronic device applications.

Ferroelectric/paraelectric superlattices for energy storage

The polarization response of antiferroelectrics to electric fields is such that the materials can store large energy densities, which makes them promising candidates for energy storage applications in pulsed-power technologies. However, relatively few materials of this kind are known. Here, we consider ferroelectric/paraelectric superlattices as artificial electrostatically engineered antiferroelectrics. Specifically, using high-throughput second-principles calculations, we engineer PbTiO₃/SrTiO₃ superlattices to optimize their energy storage performance at room temperature (to maximize density and release efficiency) with respect to different design variables (layer thicknesses, epitaxial conditions, and stiffness of the dielectric layer). We obtain results competitive with the state-of-the-art antiferroelectric capacitors and reveal the mechanisms responsible for the optimal properties.

Chiral structures of electric polarization vectors quantified by X-ray resonant scattering

Resonant elastic X-ray scattering (REXS) offers a unique tool to investigate solid-state systems providing spatial knowledge from diffraction combined with electronic information through the enhanced absorption process, allowing the probing of magnetic, charge, spin, and orbital degrees of spatial order together with electronic structure. A new promising application of REXS is to elucidate the chiral structure of electrical polarization emergent in a ferroelectric oxide superlattice in which the polarization vectors in the REXS amplitude are implicitly described through an anisotropic tensor corresponding to the quadrupole moment. Here, we present a detailed theoretical framework and analysis to quantitatively analyze the experimental results of Ti L-edge REXS of a polar vortex array formed in a PbTiO₃/SrTiO₃ superlattice. Based on this theoretical framework, REXS for polar chiral structures can become a useful tool similar to x-ray resonant magnetic scattering (XRMS), enabling a comprehensive study of both electric and magnetic REXS on the chiral structures.

The polar chiral texture of the vortex or skyrmion structure in ferroelectric oxide PbTiO₃/SrTiO₃ superlattice attracts attention. Here, the authors report a theoretical framework to probe emergent chirality of electrical polarization textures.

Phase-Field Simulations of Tunable Polar Topologies in Lead-Free Ferroelectric/Paraelectric Multilayers with Ultrahigh Energy-Storage Performance

Dielectric capacitors are emerging energy-storage components that require both high energy-storage density and high efficiency. The conventional approach to energy-storage enhancement is polar nanodomain engineering via chemical modification. Here, a new approach of domain engineering is proposed by exploiting the tunable polar topologies that have been observed recently in ferroelectric/paraelectric multilayer films. Using phase-field simulations, it is demonstrated that vortex, spiral, and in-plane polar structures can be stabilized in BiFeO₃ /SrTiO₃ (BFO/STO) multilayers by tailoring the strain state and layer thickness. Various switching dynamics are realized in these polar topologies, resulting in relaxor-ferroelectric-, antiferroelectric-, and paraelectric-like polarization behaviors, respectively. Ultrahigh energy-storage densities above 170 J cm^-3 and efficiencies above 95% are achievable in STO/BFO/STO trilayers. This strategy should be generally implementable in other multilayer dielectrics and offers a new avenue to enhancing energy storage by tuning the polar topology and thus the polarization characteristics.

Tunable Nanoscale Evolution and Topological Phase Transitions of a Polar Vortex Supercrystal

Understanding the phase transitions and domain evolutions of mesoscale topological structures in ferroic materials is critical to realizing their potential applications in next-generation high-performance storage devices. Here, the behaviors of a mesoscale supercrystal are studied with 3D nanoscale periodicity and rotational topology phases in a PbTiO₃ /SrTiO₃ (PTO/STO) superlattice under thermal and electrical stimuli using a combination of phase-field simulations and X-ray diffraction experiments. A phase diagram of temperature versus polar state is constructed, showing the formation of the supercrystal from a mixed vortex and a-twin state and a temperature-dependent erasing process of a supercrystal returning to a classical a-twin structure. Under an in-plane electric field bias at room temperature, the vortex topology of the supercrystal irreversibly transforms to a new type of stripe-like supercrystal. Under an out-of-plane electric field, the vortices inside the supercrystal undergo a topological phase transition to polar skyrmions. These results demonstrate the potential for the on-demand manipulation of polar topology and transformations in supercrystals using electric fields. The findings provide a theoretical understanding that may be utilized to guide the design and control of mesoscale polar structures and to explore novel polar structures in other systems and their topological nature.

Control of upconversion luminescence by tailoring energy migration in doped perovskite superlattices

We describe an experimental investigation of photon upconversion (UC) in a series of perovskite BaTiO₃/SrTiO₃ superlattices doped with different lanthanide compositions. We show that UC emission can be effectively enhanced by precisely incorporating a set of lanthanide ions into separated layers rather than homogeneously distributing the dopant ions in the host lattice. The use of an inert layer in the superlattice can suppress deleterious energy cross-relaxation. Furthermore, UC emission can be rendered by controlling the energy migration mediated by the Yb-doped sublattice. These results demonstrate the opportunity to modulate energy migration and transfer processes through the rational design of superlattice structures.

Thickness-Dependent Polar Domain Evolution in Strained, Ultrathin PbTiO3 Films

Ferroelectric ultrathin films have great potential in electronic devices and device miniaturization with the innovation of technology. In the process of product commercialization, understanding the domain evolution and topological properties of ferroelectrics is a prerequisite for high-density storage devices. In this work, a series of ultrathin PbTiO₃ (PTO) films with varying thicknesses were deposited on cubic KTaO₃ substrates by pulsed laser deposition and were researched by Cs-corrected scanning transmission electron microscopy (STEM), reciprocal space mapping (RSM), and piezoresponse force microscopy (PFM). RSM experiments indicate the existence of a/c domains and show that the lattice constant varies continuously, which is further confirmed by atomic-scale STEM imaging. Diffraction contrast analysis clarifies that with the decrease in PTO film thickness, the critical thickness for the formation of a/c domains could be missing. When the thickness of PTO films is less than 6 nm, the domain configurations in the ultrathin PTO films are the coexistence of a/c domains and bowl-like topological structures, where the latter ones were identified as convergent and divergent types of meron. In addition, abundant 90° charged domain walls in these ultrathin PTO films were identified. PFM studies reveal clear ferroelectric properties for these ultrathin PTO films. These results may shed light on further understanding the domain evolution and topological properties in ultrathin ferroelectric PTO films.

Emergence of non-trivial polar topologies hidden in singular stress field in SrTiO3: topological strain-field engineering

Discovery of non-trivial topological structures in condensed matters holds promise in novel technological paradigms. In contrast to ferromagnetics, where a variety of topological structures such as vortex, meron, and skyrmion have been discovered, only few topological structures can exist in ferroelectrics due to the lack of non-collinear interaction like the Dzyaloshinskii-Moriya interaction in ferromagnetics. Here, we demonstrate that polarization structures with a wide range of topological numbers (winding numbernfrom -3 to +1) can be mechanically excited and designed by the mode-I singular stress field formed near the crack-tip in incipient ferroelectric SrTiO₃. Our phase-field simulations based on Ginzburg-Landau theory successfully reveals that the near-tip polar topology is driven by the flexoelectric coupling with intense strain gradient at the tip, while a variety of the far-field topological structures is triggered by a collaboration between the electrostrictive and flexoelectric effects. The strain (gradient) field analysis further shows that the unexpected topological characters are implied in the singular stress field, which develops a variety of polar topologies near the crack tip. Therefore, our work provides a novel insight into the unusual interplay between mechanical- and ferroelectric-topologies, i.e. 'topological strain-field engineering', which paves the way to the mechanical design of functional topologies in the matter.

Engineering polar vortex from topologically trivial domain architecture

Topologically nontrivial polar structures are not only attractive for high-density data storage, but also for ultralow power microelectronics thanks to their exotic negative capacitance. The vast majority of polar structures emerging naturally in ferroelectrics, however, are topologically trivial, and there are enormous interests in artificially engineered polar structures possessing nontrivial topology. Here we demonstrate reconstruction of topologically trivial strip-like domain architecture into arrays of polar vortex in (PbTiO3)10/(SrTiO3)10 superlattice, accomplished by fabricating a cross-sectional lamella from the superlattice film. Using a combination of techniques for polarization mapping, atomic imaging, and three-dimensional structure visualization supported by phase field simulations, we reveal that the reconstruction relieves biaxial epitaxial strain in thin film into a uniaxial one in lamella, changing the subtle electrostatic and elastostatic energetics and providing the driving force for the polar vortex formation. The work establishes a realistic strategy for engineering polar topologies in otherwise ordinary ferroelectric superlattices.

Periodic Polarization Waves in a Strained, Highly Polar Ultrathin SrTiO3

SrTiO₃ is generally paraelectric with centrosymmetric structure exhibiting unique quantum fluctuation related ferroelectricity. Here we reveal highly polar and periodic polarization waves in SrTiO₃ at room temperature, which is stabilized by periodic tensile strains in a sandwiched PbTiO₃/SrTiO₃/PbTiO₃ structure. Scanning transmission electron microscopy reveals that periodic a/c domain structures in PbTiO₃ layers exert unique periodic tensile strains in the ultrathin SrTiO₃ layer and consequently make the highly polar and periodic states of SrTiO₃. The as-received polar SrTiO₃ layer features peak polar ion displacement of ∼0.01 nm and peak tetragonality of ∼1.07. These peak values are larger than previous results, which are comparable to that of bulk ferroelectric PbTiO₃. Our results suggest that it is possible to integrate large and periodic strain state in oxide films with exotic properties, which in turn could be useful in optical applications and information addressing when used as memory unit.