Observation of room-temperature polar skyrmions

ProtonationDriven Polarization Retention Failure in Nano-Columnar Lead-Free Ferroelectric Thin Films

Understanding microscopic mechanisms of polarization retention characteristics in ferroelectric thin films is of great significance for exploring unusual physical phenomena inaccessible in the bulk counterparts and for realizing thin-film-based functional electronic devices. Perovskite (K,Na)NbO3 is an excellent class of lead-free ferroelectric oxides attracting tremendous interest thanks to its potential applications to nonvolatile memory and eco-friendly energy harvester/storage. Nonetheless, in-depth investigation of ferroelectric properties of (K,Na)NbO3 films and the following developments of nano-devices are limited due to challenging thin-film fabrication associated with nonstoichiometry by volatile K and Na atoms. Herein, ferroelectric (K,Na)NbO3 films of which the atomic-level geometrical structures strongly depend on thickness-dependent strain relaxation are epitaxially grown. Nanopillar crystal structures are identified in fully relaxed (K,Na)NbO3 films to the bulk states representing a continuous reduction of switchable polarization under air environments, that is, polarization retention failures. Protonation by water dissociation is responsible for the humidity-induced retention loss in nano-columnar (K,Na)NbO3 films. The protonation-driven polarization retention failure originates from domain wall pinning by the accumulation of mobile hydrogen ions at charged domain walls for effective screening of polarization-bound charges. Conceptually, the results will be utilized for rational design to advanced energy materials such as photo-catalysts enabling ferroelectric tuning of water splitting.

Dynamical Manipulation of Polar Topologies from Acoustic Phonon Excitations

Since the recent discovery of polar topologies, a recurrent question has been how to remotely tune them. Many efforts have focused on the pumping of polar optical phonons from optical methods, but with limited success, as only switching between specific phases has been achieved so far. Additionally, the correlation between optical pulse characteristics and the resulting phase is poorly understood. Here, we propose an alternative approach and demonstrate the deterministic and dynamical tailoring of polar topologies using acoustic phonon excitations. Our second-principles simulations reveal that by pumping specific longitudinal and transverse acoustic phonons, various topological textures can be induced in materials like BaTiO3 or PbTiO3. This method leverages the strong coupling between polarization and strain in these materials, enabling predictable and dynamic control of polar patterns. Our findings open up an alternative possibility for the manipulation of polar textures, suggesting a promising research direction.

Breakdown of Volterra's Elasticity Theory of Dislocations in Polar Skyrmion Lattices

Emerging polar skyrmion crystals (SkX) have raised much interest for technological applications owing to their nontrivial topologies of electric dipoles, quasiparticle-like behaviors, and unique electrical responses. Understanding SkX defects, especially dislocations, is crucial for their unique lattice dynamics and responses; however, it still remains elusive. Here, we have not only demonstrated that a SkX dislocation exhibits an anomalously deformed core structure with over 50% elongation of skyrmions but also discovered that Volterra's elasticity theory of dislocation is broken down in SkX. Our phase-field simulation reveals that these distinct features of SkX dislocation arise from a rigid to soft quasiparticle transition of skyrmions depending on the electric field and temperature. In SkX, there exist inherent mechanics that mitigate the mismatch by both migration and deformation of skyrmions. This work provides novel insights into a new class of lattice mechanics and related functionality arising from the unique properties of quasi-particle SkX.

Polar and quasicrystal vortex observed in twisted-bilayer molybdenum disulfide

We report the observation of an electric field in twisted-bilayer molybdenum disulfide (MoS2) and elucidate its correlation with local polar domains using four-dimensional scanning transmission electron microscopy (4D-STEM) and first-principles calculations. We reveal the emergence of in-plane topological vortices within the periodic moiré patterns for both commensurate structures at small twist angles and the incommensurate quasicrystal structure that occurs at a 30° twist. The large-angle twist leads to mosaic chiral vortex patterns with tunable characteristics. A twisted quasicrystal bilayer, characterized by its 12-fold rotational symmetry, hosts complex vortex patterns and can be manipulated by picometer-scale interlayer displacement. Our findings highlight that twisting 2D bilayers is a versatile strategy for tailoring local electric polar vortices.

Quantifying the topology of magnetic skyrmions in three dimensions

Magnetic skyrmions have so far been treated as two-dimensional spin structures characterized by a topological winding number. However, in real systems with the finite thickness of the device material being larger than the magnetic exchange length, the skyrmion spin texture extends into the third dimension and cannot be assumed as homogeneous. Using soft x-ray laminography, we reconstruct with about 20-nanometer spatial (voxel) size the full three-dimensional spin texture of a skyrmion in an 800-nanometer-diameter and 95-nanometer-thin disk patterned into a 30× [iridium/cobalt/platinum] multilayered film. A quantitative analysis finds that the evolution of the radial profile of the topological skyrmion number is nonuniform across the thickness of the disk. Estimates of the micromagnetic energy densities suggest that the changes in topological profile are related to nonuniform competing energetic interactions. Our results provide a foundation for nanoscale metrology for spintronics devices using topology as a design parameter.

Non-equilibrium pathways to emergent polar supertextures

Ultrafast stimuli can stabilize metastable states of matter inaccessible by equilibrium means. Establishing the spatiotemporal link between ultrafast excitation and metastability is crucial to understand these phenomena. Here we utilize single-shot optical pump-X-ray probe measurements to capture snapshots of the emergence of a persistent polar vortex supercrystal in a heterostructure that hosts a fine balance between built-in electrostatic and elastic frustrations by design. By perturbing this balance with photoinduced charges, an initially heterogeneous mixture of polar phase disorders within a few picoseconds, leading to a state composed of disordered ferroelectric and suppressed vortex orders. On the picosecond-nanosecond timescales, transient labyrinthine fluctuations develop, accompanied by the recovery of the vortex order. On longer timescales, these fluctuations are progressively quenched by dynamical strain modulations, which drive the collective emergence of a single vortex supercrystal phase. Our results, corroborated by dynamical phase-field modelling, reveal non-equilibrium pathways following the ultrafast excitation of designer systems to persistent metastability.

On-demand nanoengineering of in-plane ferroelectric topologies

Hierarchical assemblies of ferroelectric nanodomains, so-called super-domains, can exhibit exotic morphologies that lead to distinct behaviours. Controlling these super-domains reliably is critical for realizing states with desired functional properties. Here we reveal the super-switching mechanism by using a biased atomic force microscopy tip, that is, the switching of the in-plane super-domains, of a model ferroelectric Pb0.6Sr0.4TiO3. We demonstrate that the writing process is dominated by a super-domain nucleation and stabilization process. A complex scanning-probe trajectory enables on-demand formation of intricate centre-divergent, centre-convergent and flux-closure polar structures. Correlative piezoresponse force microscopy and optical spectroscopy confirm the topological nature and tunability of the emergent structures. The precise and versatile nanolithography in a ferroic material and the stability of the generated structures, also validated by phase-field modelling, suggests potential for reliable multi-state nanodevice architectures and, thereby, an alternative route for the creation of tunable topological structures for applications in neuromorphic circuits.

Mimicking Antiferroelectrics with Ferroelectric Superlattices

Antiferroelectric oxides are promising materials for applications in high-density energy storage, solid-state cooling, and negative capacitance devices. However, the range of oxide antiferroelectrics available today is rather limited. In this work, it is demonstrated that antiferroelectric properties can be electrostatically engineered in artificially layered ferroelectric superlattices. Using a combination of synchrotron X-ray nanodiffraction, scanning transmission electron microscopy, macroscopic electrical measurements, and lateral and vertical piezoresponse force microscopy in parallel-plate capacitor geometry, a highly reversible field-induced transition is observed from a stable in-plane polarized state to a state with in-plane and out-of-plane polarized nanodomains that mimics, at the domain level, the nonpolar to polar transition of traditional antiferroelectrics, with corresponding polarization-voltage double hysteresis and comparable energy storage capacity. Furthermore, it is found that such superlattices exhibit large out-of-plane dielectric responses without involving flux-closure domain dynamics. These results demonstrate that electrostatic and strain engineering in artificially layered materials offers a promising route for the creation of synthetic antiferroelectrics.

Interplay between Point and Extended Defects and Their Effects on Jerky Domain-Wall Motion in Ferroelectric Thin Films

Defects have a significant influence on the polarization and electromechanical properties of ferroelectric materials. Statistically, they can be seen as random pinning centers acting on an elastic manifold, slowing domain-wall propagation and raising the energy required to switch polarization. Here we show that the "dressing" of defects can lead to unprecedented control of domain-wall dynamics. We engineer defects of two different dimensionalities in ferroelectric oxide thin films-point defects externally induced via He^{2+} bombardment, and extended quasi-one-dimensional a domains formed in response to internal strains. The a domains act as extended strong pinning sites (as expected) imposing highly localized directional constraints. Surprisingly, the induced point defects in the He^{2+} bombarded samples orient and align to impose further directional pinning, screening the effect of a domains. This defect interplay produces more uniform and predictable domain-wall dynamics. Such engineered interactions between defects are crucial for advancements in ferroelectric devices.

Electric Field-Manipulated Optical Chirality in Ferroelectric Vortex Domains

Manipulating optical chirality via electric fields has garnered considerable attention in the realm of both fundamental physics and practical applications. Chiral ferroelectrics, characterized by their inherent optical chirality and switchable spontaneous polarization, are emerging as a promising platform for electronic-photonic integrated circuits applications. Unlike organics with chiral carbon centers, integrating chirality into technologically mature inorganic ferroelectrics has posed a long-standing challenge. Here, the successful introduction of chirality is reported into self-assembly La-doped BiFeO3 nanoislands, which exhibit ferroelectric vortex domains. By employing synergistic experimental techniques with piezoresponse force microscopy and nonlinear optical second-harmonic generation probes, a clear correlation between chirality and polarization configuration within these ferroelectric nanoislands is established. Furthermore, the deterministic control of ferroelectric vortex domains and chirality is demonstrated by applying electric fields, enabling reversible and nonvolatile generation and elimination of optically chiral signals. These findings significantly expand the repertoire of field-controllable chiral systems and lay the groundwork for the development of innovative ferroelectric optoelectronic devices.

Liquid-Crystal-Like Dynamic Transition in Ferroelectric-Dielectric Superlattices

Nanostructured ferroelectrics display exotic multidomain configurations resulting from the electrostatic and elastic boundary conditions they are subject to. While the ferroelectric domains appear frozen in experimental images, atomistic second-principles studies suggest that they may become spontaneously mobile upon heating, with the polar order melting in a liquidlike fashion. Here, we run molecular dynamics simulations of model systems (PbTiO_{3}/SrTiO_{3} superlattices) to study the unique features of this transformation. Most notably, we find that the multidomain state loses its translational and orientational orders at different temperatures, resembling the behavior of liquid crystals and yielding an intermediate hexaticlike phase. Our simulations reveal the mechanism responsible for the melting and allow us to characterize the stochastic dynamics in the hexaticlike phase: we find evidence that it is thermally activated, with domain reorientation rates that grow from tens of gigahertzs to terahertzs in a narrow temperature window.

Antiskyrmions in Ferroelectric Barium Titanate

Typical magnetic skyrmion is a string of inverted magnetization within a ferromagnet, protected by a sleeve of a vortexlike spin texture, such that its cross-section carries an integer topological charge. Some magnets form antiskyrmions, the antiparticle strings which carry an opposite topological charge. Here we demonstrate that topologically equivalent but purely electric antiskyrmion can exist in a ferroelectric material as well. In particular, our computer experiments reveal that the archetype ferroelectric, barium titanate, can host antiskyrmions at zero field. The polarization pattern around their cores reminds ring windings of decorative knots rather than the typical magnetic antiskyrmion texture. We show that the antiskyrmion of barium titanate has just 2-3 nm in diameter, a hexagonal cross section, and an exotic topological charge with doubled magnitude and opposite sign when compared to the standard skyrmion string.

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.

Ferroelectric Order Evolution in Freestanding PbTiO3 Films Monitored by Optical Second Harmonic Generation

The demand for low-dimensional ferroelectric devices is steadily increasing, however, the thick substrates in epitaxial films impede further size miniaturization. Freestanding films offer a potential solution by eliminating substrate constraints. Nevertheless, it remains an ongoing challenge to improve the stability in thin and fragile freestanding films under strain and temperature. In this work, the structure and ferroelectric order of freestanding PbTiO3 (PTO) films are investigated under continuous variation of the strain and temperature using nondestructive optical second harmonic generation (SHG) technique. The findings reveal that there are both out-of-plane and in-plane domains with polarization along out-of-plane and in-plane directions in the orthorhombic-like freestanding PTO films, respectively. In contrast, only out-of-plane domains are observed in the tetragonal epitaxial PTO films. Remarkably, the ferroelectricity of freestanding PTO films is strengthened under small uniaxial tensile strain from 0% up to 1.66% and well-maintained under larger biaxial tensile strain up to 2.76% along the [100] direction and up to 4.46% along the [010] direction. Moreover, a high Curie temperature of 630 K is identified in 50 nm thick freestanding PTO films by wide-temperature-range SHG. These findings provide valuable understanding for the development of the next-generation electronic nanodevices with flexibility and thermostability.

Optical Control of Adaptive Nanoscale Domain Networks

Adaptive networks can sense and adjust to dynamic environments to optimize their performance. Understanding their nanoscale responses to external stimuli is essential for applications in nanodevices and neuromorphic computing. However, it is challenging to image such responses on the nanoscale with crystallographic sensitivity. Here, the evolution of nanodomain networks in (PbTiO3)n/(SrTiO3)n superlattices (SLs) is directly visualized in real space as the system adapts to ultrafast repetitive optical excitations that emulate controlled neural inputs. The adaptive response allows the system to explore a wealth of metastable states that are previously inaccessible. Their reconfiguration and competition are quantitatively measured by scanning x-ray nanodiffraction as a function of the number of applied pulses, in which crystallographic characteristics are quantitatively assessed by assorted diffraction patterns using unsupervised machine-learning methods. The corresponding domain boundaries and their connectivity are drastically altered by light, holding promise for light-programable nanocircuits in analogy to neuroplasticity. Phase-field simulations elucidate that the reconfiguration of the domain networks is a result of the interplay between photocarriers and transient lattice temperature. The demonstrated optical control scheme and the uncovered nanoscopic insights open opportunities for the remote control of adaptive nanoscale domain networks.

Giant Piezoelectric Effects of Topological Structures in Stretched Ferroelectric Membranes

Freestanding ferroelectric oxide membranes emerge as a promising platform for exploring the interplay between topological polar ordering and dipolar interactions that are continuously tunable by strain. Our investigations combining density functional theory (DFT) and deep-learning-assisted molecular dynamics simulations demonstrate that DFT-predicted strain-driven morphotropic phase boundary involving monoclinic phases manifest as diverse domain structures at room temperatures, featuring continuous distributions of dipole orientations and mobile domain walls. Detailed analysis of dynamic structures reveals that the enhanced piezoelectric response observed in stretched PbTiO_{3} membranes results from small-angle rotations of dipoles at domain walls, distinct from conventional polarization rotation mechanism and adaptive phase theory inferred from static structures. We identify a ferroelectric topological structure, termed "dipole spiral," which exhibits a giant intrinsic piezoelectric response (>320  pC/N). This helical structure, possessing a rotational zero-energy mode, unlocks new possibilities for exploring chiral phonon dynamics and dipolar Dzyaloshinskii-Moriya-like interactions.

Ferroelectric Texture of Individual Barium Titanate Nanocrystals

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

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

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

Electric-field-induced multiferroic topological solitons

Topologically protected spin whirls in ferromagnets are foreseen as the cart-horse of solitonic information technologies. Nevertheless, the future of skyrmionics may rely on antiferromagnets due to their immunity to dipolar fields, straight motion along the driving force and ultrafast dynamics. While complex topological objects were recently discovered in intrinsic antiferromagnets, mastering their nucleation, stabilization and manipulation with energy-efficient means remains an outstanding challenge. Designing topological polar states in magnetoelectric antiferromagnetic multiferroics would allow one to electrically write, detect and erase topological antiferromagnetic entities. Here we stabilize ferroelectric centre states using a radial electric field in multiferroic BiFeO3 thin films. We show that such polar textures contain flux closures of antiferromagnetic spin cycloids, with distinct antiferromagnetic entities at their cores depending on the electric field polarity. By tuning the epitaxial strain, quadrants of canted antiferromagnetic domains can also be electrically designed. These results open the path to reconfigurable topological states in multiferroic antiferromagnets.

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.

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.

Shaping single crystalline BaTiO3nanostructures by focused neon or helium ion milling

The realization of perovskite oxide nanostructures with controlled shape and dimensions remains a challenge. Here, we investigate the use of helium and neon focused ion beam (FIB) milling in an ion microscope to fabricate BaTiO3nanopillars of sub-500 nm in diameter starting from BaTiO3(001) single crystals. Irradiation of BaTiO3with He ions induces the formation of nanobubbles inside the material, eventually leading to surface swelling and blistering. Ne-FIB is shown to be suitable for milling without inducing surface swelling. The resulting structures are defect-free single crystal nanopillars, which are enveloped, on the top and lateral sidewalls, by a point defect-rich crystalline region and an outer Ne-rich amorphous layer. The amorphous layer can be selectively etched by dipping in diluted HF. The geometry and beam-induced damage of the milled nanopillars depend strongly on the patterning parameters and can be well controlled. Ne ion milling is shown to be an effective method to rapidly prototype BaTiO3crystalline nanostructures.

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.

Coexistence of Quantum-Spin-Hall and Quantum-Hall-Topological-Insulating States in Graphene/hBN on SrTiO3 Substrate

SrTiO3 (STO) substrate, a perovskite oxide material known for its high dielectric constant (ɛ), facilitates the observation of various (high-temperature) quantum phenomena. A quantum Hall topological insulating (QHTI) state, comprising two copies of QH states with antiparallel two ferromagnetic edge-spin overlap protected by the U(1) axial rotation symmetry of spin polarization, has recently been achieved in low magnetic field (B) even as high as ≈100 K in a monolayer graphene/thin hexagonal boron nitride (hBN) spacer placed on an STO substrate, thanks to the high ɛ of STO. Despite the use of the heavy STO substrate, however, proximity-induced quantum spin Hall (QSH) states in 2D TI phases, featuring a topologically protected helical edge spin phase within time-reversal-symmetry, is not confirmed. Here, with the use of a monolayer hBN spacer, it is revealed the coexistence of QSH (at B = 0T) and QHTI (at B ≠ 0) states in the same single graphene sample placed on an STO, with a crossover regime between the two at low B. It is also classified that the different symmetries of the two nontrivial helical edge spin phases in the two states lead to different interaction with electron-puddle quantum dots, caused by a local surface pocket of the STO, in the crossover regime, resulting in a spin dephasing only for the QHTI state. The results obtained using STO substrates open the doors to investigations of novel QH spin states with different symmetries and their correlations with quantum phenomena. This exploration holds value for potential applications in spintronic devices.

Polymer nanocomposite dielectrics for capacitive energy storage

Owing to their excellent discharged energy density over a broad temperature range, polymer nanocomposites offer immense potential as dielectric materials in advanced electrical and electronic systems, such as intelligent electric vehicles, smart grids and renewable energy generation. In recent years, various nanoscale approaches have been developed to induce appreciable enhancement in discharged energy density. In this Review, we discuss the state-of-the-art polymer nanocomposites with improved energy density from three key aspects: dipole activity, breakdown resistance and heat tolerance. We also describe the physical properties of polymer nanocomposite interfaces, showing how the electrical, mechanical and thermal characteristics impact energy storage performances and how they are interrelated. Further, we discuss multi-level nanotechnologies including monomer design, crosslinking, polymer blending, nanofiller incorporation and multilayer fabrication. We conclude by presenting the current challenges and future opportunities in this field.

Local-orbital ptychography for ultrahigh-resolution imaging

Technical advances paired with developments in methodology have enabled electron microscopy to reach atomic resolution. Further improving the information limit in microscopic imaging requires further improvements in methodology. Here we report a ptychographic method that describes the object as the sum of discrete atomic-orbital-like functions (for example, Gaussian functions) and the probe in terms of aberration functions. Using this method, we realize an improved information limit of microscopic imaging, reaching down to 14 pm. High-quality probes and objects contribute to superior signal-to-noise ratios at low electron doses, allowing for relaxation of the sample thickness restriction to 50 nm for dense materials. Additionally, our method has the capability to decompose the total phase into element components, revealing that the information limit is element dependent. With enhanced spatial resolution, signal-to-noise ratio and thickness threshold compared with conventional ptychography methods, our local-orbital ptychography may find applications in atomic-resolution imaging of metals, ceramics, electronic devices or beam-sensitive material.

Artificial Domain Patterning in Ultrathin Ferroelectric Films via Modifying the Surface Electrostatic Boundary Conditions

Nanoscale spatially controlled modulation of the properties of ferroelectrics via artificial domain pattering is crucial to their emerging optoelectronics applications. New patterning strategies to achieve high precision and efficiency and to link the resultant domain structures with device functionalities are being sought. Here, we present an epitaxial heterostructure of SrRuO3/PbTiO3/SrRuO3, wherein the domain configuration is delicately determined by the charge screening conditions in the SrRuO3 layer and the substrate strains. Chemical etching of the top SrRuO3 layer leads to a transition from in-plane a domains to out-of-plane c domains, accompanied by a giant (>105) modification in the second harmonic generation response. The modulation effect, coupled with the plasmonic resonance effect from SrRuO3, enables a highly flexible design of nonlinear optical devices, as demonstrated by a simulated split-ring resonator metasurface. This domain patterning strategy may be extended to more thin-film ferroelectric systems with domain stabilities amenable to electrostatic boundary conditions.

Brownian Electric Bubble Quasiparticles

Recent works on electric bubbles (including the experimental demonstration of electric skyrmions) constitute a breakthrough akin to the discovery of magnetic skyrmions some 15 years ago. So far research has focused on obtaining and visualizing these objects, which often appear to be immobile (pinned) in experiments. Thus, critical aspects of magnetic skyrmions-e.g., their quasiparticle nature, Brownian motion-remain unexplored (unproven) for electric bubbles. Here we use predictive atomistic simulations to investigate the basic dynamical properties of these objects in pinning-free model systems. We show that it is possible to find regimes where the electric bubbles can present long lifetimes (∼ns) despite being relatively small (diameter <2  nm). Additionally, we find that they can display stochastic dynamics with large and highly tunable diffusion constants. We thus establish the quasiparticle nature of electric bubbles and put them forward for the physical effects and applications (e.g., in token-based probabilistic computing) considered for magnetic skyrmions.

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.

Interlayer Coupling Controlled Ordering and Phases in Polar Vortex Superlattices

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

Emergent Three-Dimensional Electric Dipole Sinewave in Bulk Perovskite Oxides

The magnetic and electric dipoles of ferroics play a central role in their fascinating properties. In particular, topological configurations have shown promising potential for use in novel electromechanical and electronic devices. Magnetic configurations from simple collinear to complex topological are well-documented. In contrast, many complex topological features in the electric counterpart remain unexplored. Here, we report the first example of three-dimensional electric dipole sinewave topological structure in a PbZrO3-based bulk perovskite, which presents an interesting triple-hysteresis loop macroscopically. This polar configuration consists of two orthogonal sinewave electric dipole modulations decoded from a polar incommensurate phase by advanced diffraction and atomic-resolution imaging techniques. The resulting topology is unraveled to be the competition between the antiferroelectric and ferroelectric states, stabilized by the modulation of the Pb 6s2 lone pair and the antiferrodistortive effect. These findings further reinforce the similarity of the magnetic and electric topologies.

Particle-based model of liquid crystal skyrmion dynamics

Motivated by recent experimental results that reveal rich collective dynamics of thousands-to-millions of active liquid crystal skyrmions, we have developed a coarse-grained, particle-based model of the dynamics of skyrmions in a dilute regime. The basic physical mechanism of skyrmion motion is related to squirming undulations of domains with high director twist within the skyrmion cores when the electric field is turned on and off. The motion is not related to mass flow and is caused only by the reorientation dynamics of the director field. Based on the results of the "fine-grained" Frank-Oseen continuum model, we have mapped these squirming director distortions onto an effective force that acts asymmetrically upon switching the electrical field on or off. The resulting model correctly reproduces the skyrmion dynamics, including velocity reversal as a function of the frequency of a pulse width modulated driving voltage. We have also obtained approximate analytical expressions for the phenomenological model parameters encoding their dependence upon the cholesteric pitch and the strength of the electric field. This has been achieved by fitting coarse-grained skyrmion trajectories to those determined in the framework of the Frank-Oseen model.

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.

Evidence of 3D Topological-Domain Dynamics in KTN:Li Polarization-Supercrystal Formation

We experimentally and theoretically investigate thermal domain evolution in near-transition KTN:Li. Results allow us to establish how polarization supercrystals form, a hidden 3D topological phase composed of hypervortex defects. These are the result of six converging polarization vortices, each associated to one orientation of the 3D broken inversion symmetry. We also identify rescaling soliton lattices and domain patterns that replicate on different scales. Findings shed light on volume domain self-organization into closed-flux patterns and open up new scenarios for topologically protected noise-resistant ferroelectric memory bits.

A 2D ferroelectric vortex pattern in twisted BaTiO3 freestanding layers

The wealth of complex polar topologies1-10 recently found in nanoscale ferroelectrics results from a delicate balance between the intrinsic tendency of the materials to develop a homogeneous polarization and the electric and mechanical boundary conditions imposed on them. Ferroelectric-dielectric interfaces are model systems in which polarization curling originates from open circuit-like electric boundary conditions, to avoid the build-up of polarization charges through the formation of flux-closure11-14 domains that evolve into vortex-like structures at the nanoscale15-17 level. Although ferroelectricity is known to couple strongly with strain (both homogeneous18 and inhomogeneous19,20), the effect of mechanical constraints21 on thin-film nanoscale ferroelectrics has been comparatively less explored because of the relative paucity of strain patterns that can be implemented experimentally. Here we show that the stacking of freestanding ferroelectric perovskite layers with controlled twist angles provides an opportunity to tailor these topological nanostructures in a way determined by the lateral strain modulation associated with the twisting. Furthermore, we find that a peculiar pattern of polarization vortices and antivortices emerges from the flexoelectric coupling of polarization to strain gradients. This finding provides opportunities to create two-dimensional high-density vortex crystals that would enable us to explore previously unknown physical effects and functionalities.

Super-tetragonal Sr4Al2O7 as a sacrificial layer for high-integrity freestanding oxide membranes

Identifying a suitable water-soluble sacrificial layer is crucial to fabricating large-scale freestanding oxide membranes, which offer attractive functionalities and integrations with advanced semiconductor technologies. Here, we introduce a water-soluble sacrificial layer, "super-tetragonal" Sr4Al2O7 (SAOT). The low-symmetric crystal structure enables a superior capability to sustain epitaxial strain, allowing for broad tunability in lattice constants. The resultant structural coherency and defect-free interface in perovskite ABO3/SAOT heterostructures effectively restrain crack formation during the water release of freestanding oxide membranes. For a variety of nonferroelectric oxide membranes, the crack-free areas can span up to a millimeter in scale. This compelling feature, combined with the inherent high water solubility, makes SAOT a versatile and feasible sacrificial layer for producing high-quality freestanding oxide membranes, thereby boosting their potential for innovative device applications.

Field-controlled dynamics of skyrmions and monopoles

Magnetic monopoles, despite their ongoing experimental search as elementary particles, have inspired the discovery of analogous excitations in condensed matter systems. In chiral condensed matter systems, emergent monopoles are responsible for the onset of transitions between topologically distinct states and phases, such as in the case of transitions from helical and conical phase to A-phase comprising periodic arrays of skyrmions. By combining numerical modeling and optical characterizations, we describe how different geometrical configurations of skyrmions terminating at monopoles can be realized in liquid crystals and liquid crystal ferromagnets. We demonstrate how these complex structures can be effectively manipulated by external magnetic and electric fields. Furthermore, we discuss how our findings may hint at similar dynamics in other physical systems and their potential applications.

A ferroelectric fin diode for robust non-volatile memory

Among today's nonvolatile memories, ferroelectric-based capacitors, tunnel junctions and field-effect transistors (FET) are already industrially integrated and/or intensively investigated to improve their performances. Concurrently, because of the tremendous development of artificial intelligence and big-data issues, there is an urgent need to realize high-density crossbar arrays, a prerequisite for the future of memories and emerging computing algorithms. Here, a two-terminal ferroelectric fin diode (FFD) in which a ferroelectric capacitor and a fin-like semiconductor channel are combined to share both top and bottom electrodes is designed. Such a device not only shows both digital and analog memory functionalities but is also robust and universal as it works using two very different ferroelectric materials. When compared to all current nonvolatile memories, it cumulatively demonstrates an endurance up to 1010 cycles, an ON/OFF ratio of ~102, a feature size of 30 nm, an operating energy of ~20 fJ and an operation speed of 100 ns. Beyond these superior performances, the simple two-terminal structure and their self-rectifying ratio of ~ 104 permit to consider them as new electronic building blocks for designing passive crossbar arrays which are crucial for the future in-memory computing.

Dynamical Control of Topology in Polar Skyrmions via Twisted Light

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

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.

Motion and teleportation of polar bubbles in low-dimensional ferroelectrics

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

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.

High-Temperature Ferroic Glassy States in SrTiO_{3}-Based Thin Films

Disordered ferroics hold great promise for next-generation magnetoelectric devices because their lack of symmetry constraints implies negligible hysteresis with low energy costs. However, the transition temperature and the magnitude of polarization and magnetization are still too low to meet application requirements. Here, taking the prototype perovskite of SrTiO_{3} as an instance, we realize a coexisting spin and dipole reentrant glass states in SrTiO_{3} homoepitaxial films via manipulation of local symmetry. Room-temperature saturation magnetization and spontaneous polarization reach ∼ 10  emu/cm^{3} and ∼ 25  μC/cm^{2}, respectively, with high transition temperatures (101 K and 236 K for spin and dipole glass temperatures and 556 K and 1100 K for Curie temperatures, respectively). Our atomic-scale investigation points out an underlying mechanism, where the Ti/O-defective unit cells break the local translational and orbital symmetry to drive the formation of unusual slush states. This study advances our understanding of the nature of the intricate couplings of ferroic glasses. Our approach could be applied to numerous perovskite oxides for the simultaneous control of the local magnetic and polar orderings and for the exploration of the underlying physics.

The anti-symmetric and anisotropic symmetric exchange interactions between electric dipoles in hafnia

The anti-symmetric and anisotropic symmetric exchange interactions between two magnetic dipole moments - responsible for intriguing magnetic textures (e.g., magnetic skyrmions) - have been discovered since last century, while their electric analogues were either hidden for a long time or still not known. It is only recently that the anti-symmetric exchange interactions between electric dipoles was proved to exist (with materials hosting such an interaction being still rare) and the existence of anisotropic symmetric exchange interaction between electric dipoles remains ambiguous. Here, by symmetry analysis and first-principles calculations, we identify hafnia as a candidate material hosting the non-collinear dipole alignments, the analysis of which reveals the anti-symmetric and anisotropic symmetric exchange interactions between electric dipoles in this material. Our findings can hopefully deepen the current knowledge of electromagnetism in condensed matter, and imply the possibility of discovering novel states of matter (e.g., electric skyrmions) in hafnia-related materials.

Dynamic Motion of Polar Skyrmions in Oxide Heterostructures

Polar skyrmions have been widely investigated in oxide heterostructures due to their exotic properties and intriguing physical insights. However, the field-driven motion of polar skyrmions, akin to that of the magnetic counterpart, remains elusive. Herein, using phase-field simulations, we demonstrate the dynamic motion of polar skyrmions with integrated external thermal, electrical, and mechanical stimuli. External heating reduced the spontaneous polarization, while an applied electric field decreased the skyrmion size and weakened the interactions between the skyrmions. Together, the skyrmion motion barrier is significantly reduced from 40 to 2 eV under 9 V at 500 K. An applied mechanical force transformed the skyrmions into a c-domain region near the indenter center under the electric field, providing the space and driving force needed for the motion of the skyrmions. This study confirms that polar skyrmions can move like particles and provides concrete design principles for polar skyrmion-based electronic devices.