Manipulating topological transformations of polar structures through real-time observation of the dynamic polarization evolution

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.

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.

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.

Effect of Aspect Ratio of Ferroelectric Nanofilms on Polarization Vortex Stability under Uniaxial Tension or Compression

Mastering the variations in the stability of a polarization vortex is fundamental for the development of ferroelectric devices based on polarization vortex domain structures. Some phase field simulations were conducted on PbTiO3 nanofilms with an initial polarization vortex under uniaxial tension or compression to investigate the conditions of vortex instability and the effects of aspect ratio of nanofilms and temperature on them. The instability of a polarization vortex is strongly dependent on aspect ratio and temperature. The critical compressive stress increases with decreasing aspect ratio under the action of compressive stress. However, the critical tensile stress first decreases and then increases with decreasing aspect ratio, then continues to decrease. There are two inflection points in the curve. In addition, an elevated temperature makes both the critical tensile and compressive stresses decline, and will also cause the aspect ratio corresponding to the inflection point to decrease. These are very important for the design of promising nano-ferroelectric devices based on polarization vortices to improve their performance while maintaining storage density.

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.

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.

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.

A small-dataset-trained deep learning framework for identifying atoms on transmission electron microscopy images

To accurately identify atoms on noisy transmission electron microscope images, a deep learning (DL) approach is employed to estimate the map of probabilities at each pixel for being an atom with element discernment. Thanks to a delicately-designed loss function and the ability to extract features, the proposed DL networks can be trained by a small dataset created from approximately 30 experimental images, each with a size of 256 × 256 pixels². The accuracy and robustness of the network were verified by resolving the structural defects of graphene and polar structures in PbTiO₃/SrTiO₃ multilayers from both the general TEM images and their imitated images on which intensities of some pixels lost randomly. Such a network has the potential to identify atoms from very few images of beam-sensitive material and explosive images recorded in a dynamical atomic process. The idea of using a small-dataset-trained DL framework to resolve a specific problem may prove instructive for practical DL applications in various fields.

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.

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.

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.

Charged Domain Wall and Polar Vortex Topologies in a Room-Temperature Magnetoelectric Multiferroic Thin Film

Multiferroic topologies are an emerging solution for future low-power magnetic nanoelectronics due to their combined tuneable functionality and mobility. Here, we show that in addition to being magnetoelectric multiferroic at room temperature, thin-film Aurivillius phase Bi₆Ti_xFe_yMn_zO₁₈ is an ideal material platform for both domain wall and vortex topology-based nanoelectronic devices. Utilizing atomic-resolution electron microscopy, we reveal the presence and structure of 180°-type charged head-to-head and tail-to-tail domain walls passing throughout the thin film. Theoretical calculations confirm the subunit cell cation site preference and charged domain wall energetics for Bi₆Ti_xFe_yMn_zO₁₈. Finally, we show that polar vortex-type topologies also form at out-of-phase boundaries of stacking faults when internal strain and electrostatic energy gradients are altered. This study could pave the way for controlled polar vortex topology formation via strain engineering in other multiferroic thin films. Moreover, these results confirm that the subunit cell topological features play an important role in controlling the charge and spin state of Aurivillius phase films and other multiferroic heterostructures.

Interplay of domain structure and phase transitions: theory, experiment and functionality

Domain walls and phase boundaries are fundamental ingredients of ferroelectrics and strongly influence their functional properties. Although both interfaces have been studied for decades, often only a phenomenological macroscopic understanding has been established. The recent developments in experiments and theory allow to address the relevant time and length scales and revisit nucleation, phase propagation and the coupling of domains and phase transitions. This review attempts to specify regularities of domain formation and evolution at ferroelectric transitions and give an overview on unusual polar topological structures that appear as transient states and at the nanoscale. We survey the benefits, validity, and limitations of experimental tools as well as simulation methods to study phase and domain interfaces. We focus on the recent success of these tools in joint scale-bridging studies to solve long lasting puzzles in the field and give an outlook on recent trends in superlattices.

Atomic-scale fatigue mechanism of ferroelectric tunnel junctions

Ferroelectric tunnel junctions (FTJs) are promising candidates for next-generation memories due to fast read/write speeds and low-power consumptions. Here, we investigate resistance fatigue of FTJs, which is performed on Pt/BaTiO₃/Nb:SrTiO₃ devices. By direct observations of the 5–unit cell–thick BaTiO₃ barrier with high-angle annular dark-field imaging and electron energy loss spectroscopy, oxygen vacancies are found to aggregate at the Pt/BaTiO₃ interface during repetitive switching, leading to a ferroelectric dead layer preventing domain nucleation and growth. Severe oxygen deficiency also makes BaTiO₃ lattices energetically unfavorable and lastly induces a destruction of local perovskite structure of the barrier. Ferroelectric properties are thus degraded, which reduces barrier contrast between ON and OFF states and smears electroresistance characteristics of Pt/BaTiO₃/Nb:SrTiO₃ FTJs. These results reveal an atomic-scale fatigue mechanism of ultrathin ferroelectric barriers associated with the aggregation of charged defects, facilitating the design of reliable FTJs and ferroelectric nanoelectronic devices for practical applications.

Atomic scale crystal field mapping of polar vortices in oxide superlattices

Polar vortices in oxide superlattices exhibit complex polarization topologies. Using a combination of electron energy loss near-edge structure analysis, crystal field multiplet theory, and first-principles calculations, we probe the electronic structure within such polar vortices in [(PbTiO₃)₁₆/(SrTiO₃)₁₆] superlattices at the atomic scale. The peaks in Ti [Formula: see text]-edge spectra shift systematically depending on the position of the Ti⁴⁺ cations within the vortices i.e., the direction and magnitude of the local dipole. First-principles computation of the local projected density of states on the Ti [Formula: see text] orbitals, together with the simulated crystal field multiplet spectra derived from first principles are in good agreement with the experiments.

In Situ Cryogenic HAADF-STEM Observation of Spontaneous Transition of Ferroelectric Polarization Domain Structures at Low Temperatures

Precise determination of atomic structures in ferroelectric thin films and their evolution with temperature is crucial for fundamental study and design of functional materials. However, this has been impeded by the lack of techniques applicable to a thin-film geometry. Here we use cryogenic scanning transmission electron microscopy (STEM) to observe the atomic structure of a BaTiO₃ film on a (111)-SrTiO₃ substrate under varying temperatures. Our study explicitly proves a structure transition from a complex polymorphic nanodomain configuration at room temperature transitioning to a homogeneous ground-state rhombohedral structure of BaTiO₃ below ∼250 K, which was predicted by phase-field simulation. More importantly, another unexpected transition is revealed, a transition to complex nanodomains below ∼105 K caused by an altered mechanical boundary condition due to the antiferrodistortive phase transition of the SrTiO₃ substrate. This study demonstrates the power of cryogenic STEM in elucidating structure-property relationships in numerous functional materials at low temperatures.

Magnetoelectric phase transition driven by interfacial-engineered Dzyaloshinskii-Moriya interaction

Strongly correlated oxides with a broken symmetry could exhibit various phase transitions, such as superconductivity, magnetism and ferroelectricity. Construction of superlattices using these materials is effective to design crystal symmetries at atomic scale for emergent orderings and phases. Here, antiferromagnetic Ruddlesden-Popper Sr₂IrO₄ and perovskite paraelectric (ferroelectric) SrTiO₃ (BaTiO₃) are selected to epitaxially fabricate superlattices for symmetry engineering. An emergent magnetoelectric phase transition is achieved in Sr₂IrO₄/SrTiO₃ superlattices with artificially designed ferroelectricity, where an observable interfacial Dzyaloshinskii-Moriya interaction driven by non-equivalent interface is considered as the microscopic origin. By further increasing the polarization namely interfacial Dzyaloshinskii-Moriya interaction via replacing SrTiO₃ with BaTiO₃, the transition temperature can be enhanced from 46 K to 203 K, accompanying a pronounced magnetoelectric coefficient of ~495 mV/cm·Oe. This interfacial engineering of Dzyaloshinskii-Moriya interaction provides a strategy to design quantum phases and orderings in correlated electron systems.

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.

Atomic mapping of periodic dipole waves in ferroelectric oxide

A dipole wave is composed of head-to-tail connected electric dipoles in the form of sine function. Potential applications in information carrying, transporting, and processing are expected, and logic circuits based on nonlinear wave interaction are promising for dipole waves. Although similar spin waves are well known in ferromagnetic materials for their roles in some physical essence, electric dipole wave behavior and even its existence in ferroelectric materials are still elusive. Here, we observe the atomic morphology of large-scale dipole waves in PbTiO3/SrTiO3 superlattice mediated by tensile epitaxial strains on scandate substrates. The dipole waves can be expressed in the formula of y = Asin (2πx/L) + y 0, where the wave amplitude (A) and wavelength (L) correspond to 1.5 and 6.6 nm, respectively. This study suggests that by engineering strain at the nanoscale, it should be possible to fabricate unknown polar textures, which could facilitate the development of nanoscale ferroelectric devices.

Creating polar antivortex in PbTiO3/SrTiO3 superlattice

Nontrivial topological structures offer a rich playground in condensed matters and promise alternative device configurations for post-Moore electronics. While recently a number of polar topologies have been discovered in confined ferroelectric PbTiO3 within artificially engineered PbTiO3/SrTiO3 superlattices, little attention was paid to possible topological polar structures in SrTiO3. Here we successfully create previously unrealized polar antivortices within the SrTiO3 of PbTiO3/SrTiO3 superlattices, accomplished by carefully engineering their thicknesses guided by phase-field simulation. Field- and thermal-induced Kosterlitz-Thouless-like topological phase transitions have also been demonstrated, and it was discovered that the driving force for antivortex formation is electrostatic instead of elastic. This work completes an important missing link in polar topologies, expands the reaches of topological structures, and offers insight into searching and manipulating polar textures.

Direct Observation of Fractal-Dimensional Percolation in the 3D Cluster Dynamics of a Ferroelectric Supercrystal

We perform percolation analysis of crossed-polarizer transmission images in a biased nanodisordered bulk KTN:Li perovskite. Two distinct percolative transitions are identified at two electric field thresholds. The low-field transition involves a directional fractal chain of dimension D=1.65, while the high-field transition has a dimension D>2. Direct cluster imaging in the volume is achieved using high-resolution orthographic 3D projections based on giant refraction. Percolation is attributed to a full-3D domain reorientation that mediates the transition from a ferroelectric supercrystal state to a disordered domain mosaic.

Atomic-scale observations of electrical and mechanical manipulation of topological polar flux closure

Flux-closures, stable topological polar structures of nanometer size, are considered to be promising candidates as elements of future nanoelectronic and electromechanical devices. Understanding their phase transition pathways under external stimuli is therefore of vital importance for these potential applications. Here, using an atomically resolved in situ electron microscopy technique, we track the evolutions of the polarization of the flux-closure structure under both electric and stress fields with atomic resolution. We find that the flux-closure can be reversibly and controllably manipulated between the topological and ordinary ferroelectric states, enabling potential applications in electromechanical and nanoelectronic devices.

The ability to controllably manipulate complex topological polar configurations such as polar flux-closures via external stimuli may allow the construction of new electromechanical and nanoelectronic devices. Here, using atomically resolved in situ scanning transmission electron microscopy, we find that the polar flux-closures in PbTiO₃/SrTiO₃ superlattice films are mobile and can be reversibly switched to ordinary single ferroelectric c or a domains under an applied electric field or stress. Specifically, the electric field initially drives movement of a flux-closure via domain wall motion and then breaks it to form intermediate a/c striped domains, whereas mechanical stress first squeezes the core of a flux-closure toward the interface and then form a/c domains with disappearance of the core. After removal of the external stimulus, the flux-closure structure spontaneously recovers. These observations can be precisely reproduced by phase field simulations, which also reveal the evolutions of the competing energies during phase transitions. Such reversible switching between flux-closures and ordinary ferroelectric states provides a foundation for potential electromechanical and nanoelectronic applications.