Polar meron lattice in strained oxide ferroelectrics

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

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

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

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

Organic-Inorganic Hybrid Perovskite Ferroelectric Nanosheets Synthesized by a Room-Temperature Antisolvent Method

Over the past years, the application potential of ferroelectric nanomaterials with unique physical properties for modern electronics is highlighted to a large extent. However, it is relatively challenging to fabricate inorganic ferroelectric nanomaterials, which is a process depending on a vacuum atmosphere at high temperatures. As significant complements to inorganic ferroelectric nanomaterials, the nanomaterials of molecular ferroelectrics are rarely reported. Here a low-cost room-temperature antisolvent method is used to synthesize free-standing 2D organic-inorganic hybrid perovskite (OIHP) ferroelectric nanosheets (NSs), that is, (CHA)2PbBr4 NSs (CHA = cyclohexylammonium), with an average lateral size of 357.59 nm and a thickness ranging from 10 to 70 nm. This method shows high repeatability and produces NSs with excellent crystallinity. Moreover, ferroelectric domains in single NSs can be clearly visualized and manipulated using piezoresponse force microscopy (PFM). The domain switching and PFM-switching spectroscopy indicate the robust in-plane ferroelectricity of the NSs. This work not only introduces a feasible, low-cost, and scalable method for preparing molecular ferroelectric NSs but also promotes the research on molecular ferroelectric nanomaterials.

Topological polarons in halide perovskites

Halide perovskites emerged as a revolutionary family of high-quality semiconductors for solar energy harvesting and energy-efficient lighting. There is mounting evidence that the exceptional optoelectronic properties of these materials could stem from unconventional electron-phonon couplings, and it has been suggested that the formation of polarons and self-trapped excitons could be key to understanding such properties. By performing first-principles simulations across the length scales, here we show that halide perovskites harbor a uniquely rich variety of polaronic species, including small polarons, large polarons, and charge density waves, and we explain a variety of experimental observations. We find that these emergent quasiparticles support topologically nontrivial phonon fields with quantized topological charge, making them nonmagnetic analog of the helical Bloch points found in magnetic skyrmion lattices.

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.

Polar Bloch points in strained ferroelectric films

Topological domain structures have drawn great attention as they have potential applications in future electronic devices. As an important concept linking the quantum and classical magnetism, a magnetic Bloch point, predicted in 1960s but not observed directly so far, is a singular point around which magnetization vectors orient to nearly all directions. Here we show polar Bloch points in tensile-strained ultrathin ferroelectric PbTiO3 films, which are alternatively visualized by phase-field simulations and aberration-corrected scanning transmission electron microscopic imaging. The phase-field simulations indicate local steady-state negative capacitance around the Bloch points. The observation of polar Bloch points and their emergent properties consequently implies novel applications in future integrated circuits and low power electronic devices.

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.

Ultralow Strain-Induced Emergent Polarization Structures in a Flexible Freestanding BaTiO3 Membrane

The engineering of ferroic orders, which involves the evolution of atomic structure and local ferroic configuration in the development of next-generation electronic devices. Until now, diverse polarization structures and topological domains are obtained in ferroelectric thin films or heterostructures, and the polarization switching and subsequent domain nucleation are found to be more conducive to building energy-efficient and multifunctional polarization structures. In this work, a continuous and periodic strain in a flexible freestanding BaTiO3 membrane to achieve a zigzag morphology is introduced. The polar head/tail boundaries and vortex/anti-vortex domains are constructed by a compressive strain as low as ≈0.5%, which is extremely lower than that used in epitaxial rigid ferroelectrics. Overall, this study c efficient polarization structures, which is of both theoretical value and practical significance for the development of next-generation flexible multifunctional devices.

Spontaneous Atomic-Scale Polar Skyrmions and Merons on a SrTiO3 (001) Surface: Defect Engineering for Emerging Topological Orders

The emergence of nontrivial topological order in condensed matter has been attracting a great deal of attention owing to its promising technological applications in novel functional nanodevices. In ferroelectrics, the realization of polar topological order at an ultimately small scale is extremely challenging due to the lack of chiral interaction and the critical size of the ferroelectricity. Here, we break through these limitations and demonstrate that the ultimate atomic-scale polar skyrmion and meron (∼2 nm) can be induced by engineering oxygen vacancies on the SrTiO3 (001) surface based on first-principles calculations. The paraelectric-to-antiferrodistortive phase transition leads to a novel topological transition from skyrmion to meron, indicating phase-topology correlations. We also discuss accumulating and driving polar skyrmions based on the oxygen divacancy model; these results and the recent discovery of defect engineering techniques suggest the possibility of arithmetic operations on topological numbers through the natural self-organization and diffusion features of oxygen vacancies.

Mechanical Control of Polar Patterns in Wrinkled Thin Films via Flexoelectricity

Intriguing topological polar structures in oxide nanofilms have drawn growing attention owing to their immense potential applications in nanoscale electronic devices. Here, we report a novel route to mechanically manipulate polar structures via flexoelectricity in wrinkled thin films. Our results present a flexoelectric polar transition from a nonpolar state to uniaxial polar stripes, biaxial meronlike or antimeronlike polar structures, and polar labyrinths by varying wrinkle morphologies. The evolution mechanisms and the outstanding mechanical tunability of these flexoelectric polar patterns were investigated theoretically and numerically. This strategy based on flexoelectricity for generating nontrivial polar structures will no longer rely on the superlattice structure and can be widely applicable to all centrosymmetric or noncentrosymmetric materials, providing a broader range of material and structure candidates for polar topologies.

Mechanical Rippling for Diverse Ferroelectric Topologies in Otherwise Nonferroelectric SrTiO_{3} Nanofilms

Polar topological structures such as skyrmions and merons have become an emerging research field due to their rich functionalities and promising applications in information storage. Up to now, the obtained polar topological structures are restricted to a few limited ferroelectrics with complex heterostructures, limiting their large-scale practical applications. Here, we circumvent this limitation by utilizing a nanoscale ripple-generated flexoelectric field as a universal means to create rich polar topological configurations in nonpolar nanofilms in a controllable fashion. Our extensive phase-field simulations show that a rippled SrTiO_{3} nanofilm with a single bulge activates polarizations that are stabilized in meron configurations, which further undergo topological transitions to Néel-type and Bloch-type skyrmions upon varying the geometries. The formation of these topologies originates from the curvature-dependent flexoelectric field, which extends beyond the common mechanism of geometric confinement that requires harsh energy conditions and strict temperature ranges. We further demonstrate that the rippled nanofilm with three-dimensional ripple patterns can accommodate other unreported modulated phases of ferroelectric topologies, which provide ferroelectric analogs to the complex spin topologies in magnets. The present study not only unveils the intriguing nanoscale electromechanical properties but also opens exciting opportunities to design various functional topological phenomena in flexible materials.

Giant electric field-induced second harmonic generation in polar skyrmions

Electric field-induced second harmonic generation allows electrically controlling nonlinear light-matter interactions crucial for emerging integrated photonics applications. Despite its wide presence in materials, the figures-of-merit of electric field-induced second harmonic generation are yet to be elevated to enable novel device functionalities. Here, we show that the polar skyrmions, a topological phase spontaneously formed in PbTiO3/SrTiO3 ferroelectric superlattices, exhibit a high comprehensive electric field-induced second harmonic generation performance. The second-order nonlinear susceptibility and modulation depth, measured under non-resonant 800 nm excitation, reach ~54.2 pm V-1 and ~664% V-1, respectively, and high response bandwidth (higher than 10 MHz), wide operating temperature range (up to ~400 K) and good fatigue resistance (>1010 cycles) are also demonstrated. Through combined in-situ experiments and phase-field simulations, we establish the microscopic links between the exotic polarization configuration and field-induced transition paths of the skyrmions and their electric field-induced second harmonic generation response. Our study not only presents a highly competitive thin-film material ready for constructing on-chip devices, but opens up new avenues of utilizing topological polar structures in the fields of photonics and optoelectronics.

Surface Effect of Thickness-Dependent Polarization and Domain Evolution in BiFeO3 Epitaxial Ultrathin Films

With the trend of device miniaturization, ultrathin ferroelectric films are gaining more and more attention. However, understanding ferroelectricity in this nanoscale context remains a formidable challenge, primarily due to the heightened relevance of surface effects, which often leads to the loss of net polarization. Here, the influence of surface effects on the polarization as a function of thickness in ultrathin BiFeO3 films is investigated using phase-field simulations. The findings reveal a notable increase in ferroelectric polarization with increasing thickness, with a particularly discernible change occurring below the 10 nm threshold. Upon accounting for surface effects, the polarization is marginally lower than the case without such considerations, with the disparity becoming more pronounced at smaller thicknesses. Moreover, the hysteresis loop and butterfly loop of the ultrathin film were simulated, demonstrating that the ferroelectric properties of films remain robust even down to a thickness of 5 nm. Our investigations provide valuable insights into the significance of ferroelectric thin films in device miniaturization.

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.

Mechanical manipulation for ordered topological defects

Randomly distributed topological defects created during the spontaneous symmetry breaking are the fingerprints to trace the evolution of symmetry, range of interaction, and order parameters in condensed matter systems. However, the effective mean to manipulate topological defects into ordered form is elusive due to the topological protection. Here, we establish a strategy to effectively align the topological domain networks in hexagonal manganites through a mechanical approach. It is found that the nanoindentation strain gives rise to a threefold Magnus-type force distribution, leading to a sixfold symmetric domain pattern by driving the vortex and antivortex in opposite directions. On the basis of this rationale, sizeable mono-chirality topological stripe is readily achieved by expanding the nanoindentation to scratch, directly transferring the randomly distributed topological defects into an ordered form. This discovery provides a mechanical strategy to manipulate topological protected domains not only on ferroelectrics but also on ferromagnets/antiferromagnets and ferroelastics.

Reversible Phase Transition between Vortex Lattice and Hexagonal Polar Skyrmion Crystals

Polar skyrmions in oxide heterostructures have recently attracted extensive interest due to their unique physical properties and potential applications. Here, we report the formation of the vortex lattice and the nanoscale polar skyrmion crystals with two-dimensional hexagonal symmetry in PbTiO3/SrTrO3 (PTO/STO) superlattices. Under an increasing external field, the system transitions from a vortex lattice phase to hexagonal polar skyrmion crystals (PSkC). The formation and annihilation process of the polar skyrmion crystals resemble the structural phase transition observed in atomic crystals. A temperature-electric field topological phase diagram is constructed, demonstrating stabilization of the vortex lattice and polar skyrmion crystals in a wide temperature and electric-field range. This study demonstrates the potential of manipulating the topological phase transition and its long-range order through an external field.

Induction and Ferroelectric Switching of Flux Closure Domains in Strained PbTiO3 with Neural Network Quantum Molecular Dynamics

We have developed an extension of the Neural Network Quantum Molecular Dynamics (NNQMD) simulation method to incorporate electric-field dynamics based on Born effective charge (BEC), called NNQMD-BEC. We first validate NNQMD-BEC for the switching mechanisms of archetypal ferroelectric PbTiO3 bulk crystal and 180° domain walls (DWs). NNQMD-BEC simulations correctly describe the nucleation-and-growth mechanism during DW switching. In triaxially strained PbTiO3 with strain conditions commonly seen in many superlattice configurations, we find that flux-closure texture can be induced with application of an electric field perpendicular to the original polarization direction. Upon field reversal, the flux-closure texture switches via a pair of transient vortices as the intermediate state, indicating an energy-efficient switching pathway. Our NNQMD-BEC method provides a theoretical guidance to study electro-mechano effects with existing machine learning force fields using a simple BEC extension, which will be relevant for engineering applications such as field-controlled switching in mechanically strained ferroelectric devices.

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.

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.

Polar Solomon rings in ferroelectric nanocrystals

Solomon rings, upholding the symbol of wisdom with profound historical roots, were widely used as decorations in ancient architecture and clothing. However, it was only recently discovered that such topological structures can be formed by self-organization in biological/chemical molecules, liquid crystals, etc. Here, we report the observation of polar Solomon rings in a ferroelectric nanocrystal, which consist of two intertwined vortices and are mathematically equivalent to a [Formula: see text] link in topology. By combining piezoresponse force microscopy observations and phase-field simulations, we demonstrate the reversible switching between polar Solomon rings and vertex textures by an electric field. The two types of topological polar textures exhibit distinct absorption of terahertz infrared waves, which can be exploited in infrared displays with a nanoscale resolution. Our study establishes, both experimentally and computationally, the existence and electrical manipulation of polar Solomon rings, a new form of topological polar structures that may provide a simple way for fast, robust, and high-resolution optoelectronic devices.

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.

Hexagonal Close-Packed Polar-Skyrmion Lattice in Ultrathin Ferroelectric PbTiO_{3} Films

Polar skyrmions are topologically stable, swirling polarization textures with particlelike characteristics, which hold promise for next-generation, nanoscale logic and memory. However, the understanding of how to create ordered polar skyrmion lattice structures and how such structures respond to applied electric fields, temperature, and film thickness remains elusive. Here, using phase-field simulations, the evolution of polar topology and the emergence of a phase transition to a hexagonal close-packed skyrmion lattice is explored through the construction of a temperature-electric field phase diagram for ultrathin ferroelectric PbTiO_{3} films. The hexagonal-lattice skyrmion crystal can be stabilized under application of an external, out-of-plane electric field which carefully adjusts the delicate interplay of elastic, electrostatic, and gradient energies. In addition, the lattice constants of the polar skyrmion crystals are found to increase with film thickness, consistent with expectation from Kittel's law. Our studies pave the way for the development of novel ordered condensed matter phases assembled from topological polar textures and related emergent properties in nanoscale ferroelectrics.

Emergent Ferroelectric Switching Behavior from Polar Vortex Lattice

Topologically protected polar textures have provided a rich playground for the exploration of novel, emergent phenomena. Recent discoveries indicate that ferroelectric vortices and skyrmions not only host properties markedly different from traditional ferroelectrics, but also that these properties can be harnessed for unique memory devices. Using a combination of capacitor-based capacitance measurements and computational models, it is demonstrated that polar vortices in dielectric-ferroelectric-dielectric trilayers exhibit classical ferroelectric bi-stability together with the existence of low-field metastable polarization states. This behavior is directly tied to the in-plane vortex ordering, and it is shown that it can be used as a new method of non-destructive readout-out of the poled state.

Polar meron-antimeron networks in strained and twisted bilayers

Out-of-plane polar domain structures have recently been discovered in strained and twisted bilayers of inversion symmetry broken systems such as hexagonal boron nitride. Here we show that this symmetry breaking also gives rise to an in-plane component of polarization, and the form of the total polarization is determined purely from symmetry considerations. The in-plane component of the polarization makes the polar domains in strained and twisted bilayers topologically non-trivial, forming a network of merons and antimerons (half-skyrmions and half-antiskyrmions). For twisted systems, the merons are of Bloch type whereas for strained systems they are of Néel type. We propose that the polar domains in strained or twisted bilayers may serve as a platform for exploring topological physics in layered materials and discuss how control over topological phases and phase transitions may be achieved in such systems.

Accelerating Airy beams with particle-like polarization topologies and free-space bimeronic lattices

Phase and polarization singularities in electromagnetic waves are usually attributed to one-dimensional topologies-lines, knots, and braids. Recently, particle-like structures have been predicted and observed: optical Skyrmions, vortices with spherical polarization, etc. In this article, we devise vector Airy beams with point-like singularity in the focal plane, thus leading to the presence of a particle-like topology. We present an extensive analytical analysis of the spatial spectra and focal structure of such beams. We report on the presence of a free-space lattice of bimerons in such vector Airy beams.

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.

Room-Temperature Ferroelectricity of Paraelectric Oxides Tailored by Nano-Engineering

Inducing clear ferroelectricity in the quantum paraelectric SrTiO₃ is important for triggering methods to discover hidden phases in condensed matter physics. Several methods such as isotope substitution and freestanding membranes could introduce ferroelectricity in SrTiO₃ toward nonvolatile memory applications. However, the stable transformation from quantum paraelectric SrTiO₃ to ferroelectricity SrTiO₃ at room temperature still remains challenging. Here, we used multiple nano-engineering in (SrTiO₃)_0.65/(CeO₂)_0.35 films to achieve an emergent room-temperature ferroelectricity. It is shown that the CeO₂ nanocolumns impose large out-of-plane strains and induce Sr/O deficiency in the SrTiO₃ matrix to form a clear tetragonal structure, which leads to an apparent room-temperature ferroelectric polarization up to 2.5 μC/cm². In collaboration with density functional theory calculations, it is proposed that the compressive strains combined with elemental deficiency give rise to local redistribution of charge density and orbital order, which induce emergent tetragonality of the strained SrTiO₃. Our work thus paves a pathway for architecting functional systems in perovskite oxides using a multiple nano-design.

Squishing Skyrmions: Symmetry-Guided Dynamic Transformation of Polar Topologies Under Compression

Mechanical controllability of recently discovered topological defects (e.g., skyrmions) in ferroelectric materials is of interest for the development of ultralow-power mechano-electronics that are protected against thermal noise. However, fundamental understanding is hindered by the "multiscale quantum challenge" to describe topological switching encompassing large spatiotemporal scales with quantum mechanical accuracy. Here, we overcome this challenge by developing a machine-learning-based multiscale simulation framework─a hybrid neural network quantum molecular dynamics (NNQMD) and molecular mechanics (MM) method. For nanostructures composed of SrTiO₃ and PbTiO₃, we find how the symmetry of mechanical loading essentially controls polar topological switching. We find under symmetry-breaking uniaxial compression a squishing-to-annihilation pathway versus formation of a topological composite named skyrmionium under symmetry-preserving isotropic compression. The distinct pathways are explained in terms of the underlying materials' elasticity and symmetry, as well as the Landau-Lifshitz-Kittel scaling law. Such rational control of ferroelectric topologies will likely facilitate exploration of the rich ferroelectric "topotronics" design space.

Real-Time Transformation of Flux-Closure Domains with Superhigh Thermal Stability

Polar topologies have received extensive attention due to their exotic configurations and functionalities. Understanding their responsive behaviors to external stimuli, especially thermal excitation, is highly desirable to extend their applications to high temperature, which is still unclear. Here, combining in situ transmission electron microscopy and phase-field simulations, the thermal dynamics of the flux-closure domains were illuminated in PbTiO₃/SrTiO₃ multilayers. In-depth analyses suggested that the topological transition processes from a/c domains to flux-closure quadrants were influenced by the boundary conditions of PbTiO₃ layers. The symmetrical boundary condition stabilized the flux-closure domains at higher temperature than in the asymmetrical case. Furthermore, the reversible thermal responsive behaviors of the flux-closure domains displayed superior thermal stability, which maintained robust up to 450 °C (near the Curie temperature). This work provides new insights into the dynamics of polar topologies under thermal excitation and facilitates their applications as nanoelectronics under extreme conditions.

Polarization Topology at the Nominally Charged Domain Walls in Uniaxial Ferroelectrics

Ferroelectric domain walls provide a fertile environment for novel materials physics. If a polarization discontinuity arises, it can drive a redistribution of electronic carriers and changes in band structure, which often result in emergent 2D conductivity. If such a discontinuity is not tolerated, then its amelioration usually involves the formation of complex topological patterns, such as flux-closure domains, dipolar vortices, skyrmions, merons, or Hopfions. The degrees of freedom required for the development of such patterns, in which dipolar rotation is a hallmark, are readily found in multiaxial ferroelectrics. In uniaxial ferroelectrics, where only two opposite polar orientations are possible, it has been assumed that discontinuities are unavoidable when antiparallel components of polarization meet. This perception has been borne out by the appearance of charged conducting domain walls in systems such as hexagonal manganites and lithium niobate. Here, experimental and theoretical investigations on lead germanate (Pb₅ Ge₃ O₁₁ ) reveal that polar discontinuities can be obviated at head-to-head and tail-to-tail domain walls by mutual domain bifurcation along two different axes, creating a characteristic saddle-point domain wall morphology and associated novel dipolar topology, removing the need for screening charge accumulation and associated conductivity enhancement.

Electric-field control of the nucleation and motion of isolated three-fold polar vertices

Recently various topological polar structures have been discovered in oxide thin films. Despite the increasing evidence of their switchability under electrical and/or mechanical fields, the dynamic property of isolated ones, which is usually required for applications such as data storage, is still absent. Here, we show the controlled nucleation and motion of isolated three-fold vertices under an applied electric field. At the PbTiO₃/SrRuO₃ interface, a two-unit-cell thick SrTiO₃ layer provides electrical boundary conditions for the formation of three-fold vertices. Utilizing the SrTiO₃ layer and in situ electrical testing system, we find that isolated three-fold vertices can move in a controllable and reversible manner with a velocity up to ~629 nm s⁻¹. Microstructural evolution of the nucleation and propagation of isolated three-fold vertices is further revealed by phase-field simulations. This work demonstrates the ability to electrically manipulate isolated three-fold vertices, shedding light on the dynamic property of isolated topological polar structures.

Despite various known topological polar structures, the dynamic property of isolated ones is still poorly understood. Here, the authors show the controlled nucleation and ability to move of isolated three-fold vertices under an applied electric field.

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.

Strain-Driven Mixed-Phase Domain Architectures and Topological Transitions in Pb1- x Srx TiO3 Thin Films

The potential for creating hierarchical domain structures, or mixtures of energetically degenerate phases with distinct patterns that can be modified continually, in ferroelectric thin films offers a pathway to control their mesoscale structure beyond lattice-mismatch strain with a substrate. Here, it is demonstrated that varying the strontium content provides deterministic strain-driven control of hierarchical domain structures in Pb_{1- x} Sr_x TiO₃  solid-solution thin films wherein two types, c/a and a₁ /a₂ , of nanodomains can coexist. Combining phase-field simulations, epitaxial thin-film growth, detailed structural, domain, and physical-property characterization, it is observed that the system undergoes a gradual transformation (with increasing strontium content) from droplet-like a₁ /a₂  domains in a c/a domain matrix, to a connected-labyrinth geometry of c/a domains, to a disconnected labyrinth structure of the same, and, finally, to droplet-like c/a domains in an a₁ /a₂  domain matrix. A relationship between the different mixed-phase modulation patterns and its topological nature is established. Annealing the connected-labyrinth structure leads to domain coarsening forming distinctive regions of parallel c/a and a₁ /a₂  domain stripes, offering additional design flexibility. Finally, it is found that the connected-labyrinth domain patterns exhibit the highest dielectric permittivity.

Towards computational polar-topotronics: Multiscale neural-network quantum molecular dynamics simulations of polar vortex states in SrTiO3/PbTiO3 nanowires

Recent discoveries of polar topological structures (e.g., skyrmions and merons) in ferroelectric/paraelectric heterostructures have opened a new field of polar topotronics. However, how complex interplay of photoexcitation, electric field and mechanical strain controls these topological structures remains elusive. To address this challenge, we have developed a computational approach at the nexus of machine learning and first-principles simulations. Our multiscale neural-network quantum molecular dynamics molecular mechanics approach achieves orders-of-magnitude faster computation, while maintaining quantum-mechanical accuracy for atoms within the region of interest. This approach has enabled us to investigate the dynamics of vortex states formed in PbTiO3 nanowires embedded in SrTiO3. We find topological switching of these vortex states to topologically trivial, uniformly polarized states using electric field and trivial domain-wall states using shear strain. These results, along with our earlier results on optical control of polar topology, suggest an exciting new avenue toward opto-electro-mechanical control of ultrafast, ultralow-power polar topotronic devices.

Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice

Topology, an important branch of mathematics, is an ideal theoretical tool to describe topological states and phase transitions. Many topological concepts have found their physical entities in real or reciprocal spaces identified by topological invariants, which are usually defined on orientable surfaces, such as torus and sphere. It is natural to investigate the possible physical realization of more intriguing non-orientable surfaces. Herein, we show that the set of spin-induced ferroelectric polarizations in cubic perovskite oxides AMn₃Cr₄O₁₂ (A = La and Tb) reside on the topological Roman surface—a non-orientable two-dimensional manifold formed by sewing a Möbius strip edge to that of a disc. The induced polarization may travel in a loop along the non-orientable Möbius strip or orientable disc, depending on the spin evolution as controlled by an external magnetic field. Experimentally, the periodicity of polarization can be the same or twice that of the rotating magnetic field, which is consistent with the orientability of the disc and the Möbius strip, respectively. This path-dependent topological magnetoelectric effect presents a way to detect the global geometry of a surface and deepens our understanding of topology in both mathematics and physics.

A non-orientable surface can mirror reflecting the man travelling on it. Realizing such topological object is fascinating. Here, the authors discover that antiferromagnetic-induced polarization in a solid can realize a non-orientable Roman surface.

Electrostatically Driven Polarization Flop and Strain-Induced Curvature in Free-Standing Ferroelectric Superlattices

The combination of strain and electrostatic engineering in epitaxial heterostructures of ferroelectric oxides offers many possibilities for inducing new phases, complex polar topologies, and enhanced electrical properties. However, the dominant effect of substrate clamping can also limit the electromechanical response and often leaves electrostatics to play a secondary role. Releasing the mechanical constraint imposed by the substrate can not only dramatically alter the balance between elastic and electrostatic forces, enabling them to compete on par with each other, but also activates new mechanical degrees of freedom, such as the macroscopic curvature of the heterostructure. In this work, an electrostatically driven transition from a predominantly out-of-plane polarized to an in-plane polarized state is observed when a PbTiO₃ /SrTiO₃ superlattice with a SrRuO₃ bottom electrode is released from its substrate. In turn, this polarization rotation modifies the lattice parameter mismatch between the superlattice and the thin SrRuO₃ layer, causing the heterostructure to curl up into microtubes. Through a combination of synchrotron-based scanning X-ray diffraction imaging, Raman scattering, piezoresponse force microscopy, and scanning transmission electron microscopy, the crystalline structure and domain patterns of the curved superlattices are investigated, revealing a strong anisotropy in the domain structure and a complex mechanism for strain accommodation.

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.

Exploring far-from-equilibrium ultrafast polarization control in ferroelectric oxides with excited-state neural network quantum molecular dynamics

Ferroelectric materials exhibit a rich range of complex polar topologies, but their study under far-from-equilibrium optical excitation has been largely unexplored because of the difficulty in modeling the multiple spatiotemporal scales involved quantum-mechanically. To study optical excitation at spatiotemporal scales where these topologies emerge, we have performed multiscale excited-state neural network quantum molecular dynamics simulations that integrate quantum-mechanical description of electronic excitation and billion-atom machine learning molecular dynamics to describe ultrafast polarization control in an archetypal ferroelectric oxide, lead titanate. Far-from-equilibrium quantum simulations reveal a marked photo-induced change in the electronic energy landscape and resulting cross-over from ferroelectric to octahedral tilting topological dynamics within picoseconds. The coupling and frustration of these dynamics, in turn, create topological defects in the form of polar strings. The demonstrated nexus of multiscale quantum simulation and machine learning will boost not only the emerging field of ferroelectric topotronics but also broader optoelectronic applications.

Phase Diagram of a Strained Ferroelectric Nanowire

Ferroelectric materials manifest unique dielectric, ferroelastic, and piezoelectric properties. A targeted design of ferroelectrics at the nanoscale is not only of fundamental appeal but holds the highest potential for applications. Compared to two-dimensional nanostructures such as thin films and superlattices, one-dimensional ferroelectric nanowires are investigated to a much lesser extent. Here, we reveal a variety of the topological polarization states, particularly the vortex and helical chiral phases, in loaded ferroelectric nanowires, which enable us to complete the strain–temperature phase diagram of the one-dimensional ferroelectrics. These phases are of prime importance for optoelectronics and quantum communication technologies.

TopoTEM: A Python Package for Quantifying and Visualizing Scanning Transmission Electron Microscopy Data of Polar Topologies

The exotic internal structure of polar topologies in multiferroic materials offers a rich landscape for materials science research. As the spatial scale of these entities is often subatomic in nature, aberration-corrected transmission electron microscopy (TEM) is the ideal characterization technique. Software to quantify and visualize the slight shifts in atomic placement within unit cells is of paramount importance due to the now routine acquisition of images at such resolution. In the previous ~decade since the commercialization of aberration-corrected TEM, many research groups have written their own code to visualize these polar entities. More recently, open-access Python packages have been developed for the purpose of TEM atomic position quantification. Building on these packages, we introduce the TEMUL Toolkit: a Python package for analysis and visualization of atomic resolution images. Here, we focus specifically on the TopoTEM module of the toolkit where we show an easy to follow, streamlined version of calculating the atomic displacements relative to the surrounding lattice and thus plotting polarization. We hope this toolkit will benefit the rapidly expanding field of topology-based nano-electronic and quantum materials research, and we invite the electron microscopy community to contribute to this open-access project.

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.

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.

Electric field control of chirality

Polar textures have attracted substantial attention in recent years as a promising analog to spin-based textures in ferromagnets. Here, using optical second-harmonic generation–based circular dichroism, we demonstrate deterministic and reversible control of chirality over mesoscale regions in ferroelectric vortices using an applied electric field. The microscopic origins of the chirality, the pathway during the switching, and the mechanism for electric field control are described theoretically via phase-field modeling and second-principles simulations, and experimentally by examination of the microscopic response of the vortices under an applied field. The emergence of chirality from the combination of nonchiral materials and subsequent control of the handedness with an electric field has far-reaching implications for new electronics based on chirality as a field-controllable order parameter.

Strain coupling of ferroelastic domains and misfit dislocations in [101]-oriented ferroelectric PbTiO3 films

High-index perovskite ferroelectric thin films possess excellent dielectric permittivity, piezoelectric coefficient, and exotic ferroelectric switching properties. They also exhibit complications in the ferroelastic domains, misfit dislocations, and strain-relaxation behaviors. Exploring the relationship of the ferroelastic domains and misfit dislocations may be of benefit for promoting the high-quality growth of these thin films. Here, the strain field of the ferroelastic domains and misfit dislocations in [101]-oriented PbTiO₃/(La, Sr)(Al, Ta)O₃ epitaxial thin films were investigated by advanced aberration-corrected (scanning) transmission electron microscopy (TEM) combined with geometry phase analysis (GPA). Two types of misfit dislocations with projected Burgers vectors of a[001] or a[100] on the (010) plane were elucidated, whose strain fields included in-plane strain and lattice rotation coupled with the c domains above them. Besides, it was demonstrated that the coupling was kept inside the PbTiO₃ films when the film thickness was increased. Furthermore, the polarization rotation was observed in both narrow c domains and around the misfit dislocation cores, which may be attributed to the flexoelectric effect. These results are expected to provide useful information for understanding the nucleation and propagation mechanism of ferroelastic domains and for further modifying the growth of high-index ferroelectric thin films.

The strain coupling of misfit dislocations and ferroelastic domains is revealed in [101]-oriented PbTiO₃/(La, Sr)(Al, Ta)O₃ films and flexoelectric-induced polarization rotation is observed around the misfit dislocation cores.

Atomic-Scale Tunable Flexoelectric Couplings in Oxide Multiferroics

Flexoelectricity is an effective tool in modulating the crystallographic structures and properties of oxides for multifunctional applications. However, engineering the nonuniform strain to obtain tunable flexoelectric behaviors at the atomic scale remains an ongoing challenge in conventional substrate-imposed ferroelectric films. Here, the regulatable flexoelectric behaviors are demonstrated at atomic scale in [110]-oriented BiFeO₃ thin films, which are triggered by the strain-field coupling of high-density interfacial dislocations. Using aberration-corrected scanning transmission electron microscopy, the asymmetric polarization rotation around the single dislocation is revealed, which is induced by the gradient strain fields of the single dislocation. These strain fields are highly correlated to generate huge strain gradients between neighboring dislocations, and thereby, serial flexoelectric responses are engineered as a function of dislocation spacings in thicker BiFeO₃ films. This work opens a pathway for the modulation of flexoelectric responses in ferroelectrics, which could be extended to other functional materials to create exotic phenomena.

Spontaneous helielectric nematic liquid crystals: Electric analog to helimagnets

Recently, a type of ferroelectric nematic fluid has been discovered in liquid crystals in which the molecular polar nature at molecule level is amplified to macroscopic scales through a ferroelectric packing of rod-shaped molecules. Here, we report on the experimental proof of a polar chiral liquid matter state, dubbed helielectric nematic, stabilized by the local polar ordering coupled to the chiral helicity. This helielectric structure carries the polar vector rotating helically, analogous to the magnetic counterpart of helimagnet. The helielectric state can be retained down to room temperature and demonstrates gigantic dielectric and nonlinear optical responses. This matter state opens a new chapter for developing the diverse polar liquid crystal devices.

Displacement separation analysis from atomic-resolution images

Structural distortions frequently occur in materials, either periodically (ferroelectric or antiferroelectric) or in local areas (domain boundaries, surfaces/interfaces, dislocations). Measuring atomic displacements from an average lattice is of crucial importance for analyzing structural distortions and their connections to physical properties. Conventionally, the displacements are measured atom-by-atom by fitting atomic-resolution images with two-dimensional gaussian functions. Here, we exhibit an efficient method, named Displacement Separation Analysis, DSA in short, to directly separate atomic displacements from an average lattice based on Fourier space filtering. Using antiferroelectric AgNbO₃ as a model system, we demonstrate the consistence between DSA and gaussian fitting. The suppression of polarization at interfacial region of h-LuFeO₃/α-Al₂O₃ heterostructure and the emergence of modulation structure in LuFe₂O_4+x is then revealed using DSA, attesting the implication of DSA in unveiling structural distortions either locally or periodically. Inspired by the simple principle of DSA, such method can be used for any atomic-resolution images, including TEM, STM, and AFM images to exhibit the atomic displacement intuitively.

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.