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

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

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

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.

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.

Spatially reconfigurable antiferromagnetic states in topologically rich free-standing nanomembranes

Antiferromagnets hosting real-space topological textures are promising platforms to model fundamental ultrafast phenomena and explore spintronics. However, they have only been epitaxially fabricated on specific symmetry-matched substrates, thereby preserving their intrinsic magneto-crystalline order. This curtails their integration with dissimilar supports, restricting the scope of fundamental and applied investigations. Here we circumvent this limitation by designing detachable crystalline antiferromagnetic nanomembranes of α-Fe2O3. First, we show-via transmission-based antiferromagnetic vector mapping-that flat nanomembranes host a spin-reorientation transition and rich topological phenomenology. Second, we exploit their extreme flexibility to demonstrate the reconfiguration of antiferromagnetic states across three-dimensional membrane folds resulting from flexure-induced strains. Finally, we combine these developments using a controlled manipulator to realize the strain-driven non-thermal generation of topological textures at room temperature. The integration of such free-standing antiferromagnetic layers with flat/curved nanostructures could enable spin texture designs via magnetoelastic/geometric effects in the quasi-static and dynamical regimes, opening new explorations into curvilinear antiferromagnetism and unconventional computing.

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.

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.

Sr4Al2O7: A New Sacrificial Layer with High Water Dissolution Rate for the Synthesis of Freestanding Oxide Membranes

Freestanding perovskite oxide membranes have drawn great attention recently since they offer exceptional structural tunability and stacking ability, providing new opportunities in fundamental research and potential device applications in silicon-based semiconductor technology. Among different types of sacrificial layers, the (Ca, Sr, Ba)3Al2O6 compounds are most widely used since they can be dissolved in water and prepare high-quality perovskite oxide membranes with clean and sharp surfaces and interfaces; However, the typical transfer process takes a long time (up to hours) in obtaining millimeter-size freestanding membranes, let alone realize wafer-scale samples with high yield. Here, a new member of the SrO-Al2O3 family, Sr4Al2O7 is introduced, and its high dissolution rate, ≈10 times higher than that of Sr3Al2O6 is demonstrated. The high-dissolution-rate of Sr4Al2O7 is most likely related to the more discrete Al-O networks and higher concentration of water-soluble Sr-O species in this compound. This work significantly facilitates the preparation of freestanding membranes and sheds light on the integration of multifunctional perovskite oxides in practical electronic devices.

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.

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.

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.

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.

Resurrected and Tunable Conductivity and Ferromagnetism in the Secondary Growth La0.7Ca0.3MnO3 on Transferred SrTiO3 Membranes

To avoid the epitaxy dilemma in various thin films, such as complex oxide, silicon, organic, metal/alloy, etc., their stacking at an atomic level and secondary growth are highly desired to maximize the functionality of a promising electronic device. The ceramic nature of complex oxides and the demand for accurate and long-range-ordered stoichiometry face severe challenges. Here, the transport and magnetic properties of the La0.7Ca0.3MnO3 (LCMO) secondary growth on single-crystal freestanding SrTiO3 (STO) membranes are demonstrated. It has been experimentally found that on an only 10 nm thick STO membrane, the LCMO can offer a bulk-like Curie temperature (TC) of 253 K and negative magnetoresistance of -64%, with a weak dependence on the thickness. The resurrected conductivity and ferromagnetism in LCMO confirm the advantages of secondary growth, which benefits from the excellent flexibility and transferability. Additionally, this study explores the integration strategy of complex oxides with other functional materials.

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.

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.

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.

Two-Dimensional Oxide Crystals for Device Applications: Challenges and Opportunities

Atomically thin two-dimensional (2D) oxide crystals have garnered considerable attention because of their remarkable physical properties and potential for versatile applications. In recent years, significant advancements have been made in the design, preparation, and application of ultrathin 2D oxides, providing many opportunities for new-generation advanced technologies. This review focuses on the controllable preparation of 2D oxide crystals and their applications in electronic and optoelectronic devices. Based on their bonding nature, the various types of 2D oxide crystals are first summarized, including both layered and nonlayered crystals, as well as their current top-down and bottom-up synthetic approaches. Subsequently, in terms of the unique physical and electrical properties of 2D oxides, recent advances in device applications are emphasized, including photodetectors, field-effect transistors, dielectric layers, magnetic and ferroelectric devices, memories, and gas sensors. Finally, conclusions and future prospects of 2D oxide crystals are presented. It is hoped that this review will provide comprehensive and insightful guidance for the development of 2D oxide crystals and their device applications.

Electrode Effect on Ferroelectricity in Free-Standing Membranes of PbZr0.2Ti0.8O3

We report the effects of screening capacity, surface roughness, and interfacial epitaxy of the bottom electrodes on the polarization switching, domain wall (DW) roughness, and ferroelectric Curie temperature (TC) of PbZr0.2Ti0.8O3 (PZT)-based free-standing membranes. Singe crystalline 10-50 nm (001) PZT and PZT/La0.67Sr0.33MnO3 (LSMO) membranes are prepared on Au, correlated oxide LSMO, and two-dimensional (2D) semiconductor MoS2 base layers. Switching the polarization of PZT yields nonvolatile current modulation in the MoS2 channel at room temperature, with an on/off ratio of up to 2 × 105 and no apparent decay for more than 3 days. Piezoresponse force microscopy studies show that the coercive field Ec for the PZT membranes varies from 0.75 to 3.0 MV cm-1 on different base layers and exhibits strong polarization asymmetry. The PZT/LSMO membranes exhibit significantly smaller Ec, with the samples transferred on LSMO showing symmetric Ec of about -0.26/+0.28 MV cm-1, smaller than that of epitaxial PZT films. The DW roughness exponent ζ points to 2D random bond disorder dominated DW roughening (ζ = 0.31) at room temperature. Upon thermal quench at progressively higher temperatures, ζ values for PZT membranes on Au and LSMO approach the theoretical value for 1D random bond disorder (ζ = 2/3), while samples on MoS2 exhibits thermal roughening (ζ = 1/2). The PZT membranes on Au, LSMO, and MoS2 show TC of about 763 ± 12, 725 ± 25, and 588 ± 12 °C, respectively, well exceeding the bulk value. Our study reveals the complex interplay between the electrostatic and mechanical boundary conditions in determining ferroelectricity in free-standing PZT membranes, providing important material parameters for the functional design of PZT-based flexible nanoelectronics.

Quantum criticality at cryogenic melting of polar bubble lattices

Quantum fluctuations (QFs) caused by zero-point phonon vibrations (ZPPVs) are known to prevent the occurrence of polar phases in bulk incipient ferroelectrics down to 0 K. On the other hand, little is known about the effects of QFs on the recently discovered topological patterns in ferroelectric nanostructures. Here, by using an atomistic effective Hamiltonian within classical Monte Carlo (CMC) and path integral quantum Monte Carlo (PI-QMC), we unveil how QFs affect the topology of several dipolar phases in ultrathin Pb(Zr0.4Ti0.6)O3 (PZT) films. In particular, our PI-QMC simulations show that the ZPPVs do not suppress polar patterns but rather stabilize the labyrinth, bimeron and bubble phases within a wider range of bias field magnitudes. Moreover, we reveal that quantum fluctuations induce a quantum critical point (QCP) separating a hexagonal bubble lattice from a liquid-like state characterized by spontaneous motion, creation and annihilation of polar bubbles at cryogenic temperatures. Finally, we show that the discovered quantum melting is associated with anomalous physical response, as, e.g., demonstrated by a negative longitudinal piezoelectric coefficient.

Ultralow Tip-Force Driven Sizable-Area Domain Manipulation through Transverse Flexoelectricity

Deterministic control of ferroelectric domain is critical in the ferroelectric functional electronics. Ferroelectric polarization can be manipulated mechanically with a nano-tip through flexoelectricity. However, it usually occurs in a very localized area in ultrathin films, with possible permanent surface damage caused by a large tip-force. Here it is demonstrated that the deliberate engineering of transverse flexoelectricity offers a powerful tool for improving the mechanical domain switching. Sizable-area domain switching under an ultralow tip-force can be realized in suspended van der Waals ferroelectrics with the surface intact, due to the enhanced transverse flexoelectric field. The film thickness range for domain switching in suspended ferroelectrics is significantly improved by an order of magnitude to hundreds of nanometers, being far beyond the limited range of the substrate-supported ones. The experimental results and phase-field simulations further reveal the crucial role of the transverse flexoelectricity in the domain manipulation. This large-scale mechanical manipulation of ferroelectric domain provides opportunities for the flexoelectricity-based domain controls in emerging low-dimensional ferroelectrics and related devices.

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.

Spontaneous periodic polarization wave in helielectric fluids

By analogy with spin waves in ferromagnetic systems, the polarization (or dipole) wave is the electric counterpart that remains elusive. Here, we discover that the helielectricity, i.e. a polarization field with helicoidal helices that corresponds to a quasi-layered chiral nematic environment, causes a spontaneous formation of large-scale polarization waves in the form of the sinusoidal function. Both experimental and theoretical analyses reveal that the polarization ordering over a threshold polarization strength violates the inherent periodicity of the polarization helices, thus penalizing the compression energy. It drives a second-order structural transition to a periodically modulated polarization wave state. The roles of chirality and confinement condition are discussed.

Ferroelectric solitons crafted in epitaxial bismuth ferrite superlattices

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

Polar Solomon rings in ferroelectric nanocrystals

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

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

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

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

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

Spherical ferroelectric solitons

Spherical ferroelectric domains, such as electrical bubbles, polar skyrmion bubbles and hopfions, share a single and unique feature-their homogeneously polarized cores are surrounded by a vortex ring of polarization whose outer shells form a spherical domain boundary. The resulting polar texture, typical of three-dimensional topological solitons, has an entirely new local symmetry characterized by a high polarization and strain gradients. Consequently, spherical domains represent a different material system of their own with emergent properties drastically different from that of their surrounding medium. Examples of new functionalities inherent to spherical domains include chirality, optical response, negative capacitance and giant electromechanical response. These characteristics, particularly given that the domains naturally have an ultrafine scale, offer new opportunities in high-density and low-energy nanoelectronic technologies. This Perspective gives an insight into the complex polar structure and physical origin of these spherical domains, which facilitates the understanding and development of spherical domains for device applications.

Tuning Piezoelectricity via Thermal Annealing at a Freestanding Ferroelectric Membrane

Tuning the ferroelectric domain structure by a combination of elastic and electrostatic engineering provides an effective route for enhanced piezoelectricity. However, for epitaxial thin films, the clamping effect imposed by the substrate does not allow aftergrowth tuning and also limits the electromechanical response. In contrast, freestanding membranes, which are free of substrate constraints, enable the tuning of a subtle balance between elastic and electrostatic energies, giving new platforms for enhanced and tunable functionalities. Here, highly tunable piezoelectricity is demonstrated in freestanding PbTiO₃ membranes, by varying the ferroelectric domain structures from c-dominated to c/a and a domains via aftergrowth thermal treatment. Significantly, the piezoelectric coefficient of the c/a domain structure is enhanced by a factor of 2.5 compared with typical c domain PbTiO₃. This work presents a new strategy to manipulate the piezoelectricity in ferroelectric membranes, highlighting their great potential for nano actuators, transducers, sensors and other NEMS device applications.

Extreme Enhanced Curie Temperature and Perpendicular Exchange Bias in Freestanding Ferromagnetic Superlattices

Most recently, the freestanding of an epitaxial single-crystal oxide has been greatly developed to its fundamental concerns and the possibility of integration with metal, two-dimensional, and organic materials for more promising functionalities. In an artificial ferromagnetic oxide heterostructure and superlattice, the release of the substrate constraint can induce a reasonable transformation of the magnetic structure because the change of the lattice field occurs. In this study, we have comprehensively investigated the evolution of magnetic properties of (La_0.7Ca_0.3MnO₃/SrRuO₃)_n [(LCMO/SRO)_n] ferromagnetic superlattices while they are epitaxially on SrTiO₃ and freestanding. It is found that the Curie temperature and the perpendicular exchange bias of the freestanding superlattices exhibit extreme sensitivity to the interface number and the thickness of LCMO and SRO, which can maximumly reach ∼293 K and ∼1150 Oe. These enhanced and bulk-beyond magnetic behaviors originate from the interfacial magnetic transition from ferromagnetic to antiferromagnetic via the charge reconstruction with the assistance of strain. Our study provides not only a reference for designing a high-performance flexible ferromagnetic architectural superlattice but also a deep understanding of the interfacial effect in freestanding ferromagnetic heterostructures benefiting flexible spintronics.

Polar meron-antimeron networks in strained and twisted bilayers

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

Switchable Polar Nanotexture in Nanolaminates HfO2 -ZrO2 for Ultrafast Logic-in-Memory Operations

Nontrivial topological polar textures in ferroelectric materials, including vortices, skyrmions, and others, have the potential to develop ultrafast, high-density, reliable multilevel memory storage and conceptually innovative processing units, even beyond the limit of binary storage of 180° aligned polar materials. However, the realization of switchable polar textures at room temperature in ferroelectric materials integrated directly into silicon using a straightforward large area fabrication technique and effectively utilizing it to design multilevel programable memory and processing units has not yet been demonstrated. Here, utilizing vector piezoresponse force and conductive atomic force microscopy, microscopic evidence of the electric field switchable polar nanotexture is provided at room temperature in HfO₂ -ZrO₂ nanolaminates grown directly onto silicon using an atomic layer deposition technique. Additionally, a two-terminal Au/nanolaminates/Si ferroelectric tunnel junction is designed, which shows ultrafast (≈83 ns) nonvolatile multilevel current switching with high on/off ratio (>10⁶ ), long-term durability (>4000 s), and giant tunnel electroresistance (10⁸ %). Furthermore, 14 Boolean logic operations are tested utilizing a single device as a proof-of-concept for reconfigurable logic-in-memory processing. The results offer a potential approach to "processing with polar textures" and addressing the challenges of developing high-performance multilevel in-memory processing technology by virtue of its fundamentally distinct mechanism of operation.

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.

Synthesis of Oxide Interface-Based Two-Dimensional Electron Gas on Si

Two-dimensional electron gas (2DEG) at the interface of amorphous Al₂O₃/SrTiO₃ (aAO/STO) heterostructures has received considerable attention owing to its convenience of fabrication and relatively high mobility. The integration of these 2DEG heterostructures on a silicon wafer is highly desired for electronic applications but remains challanging up to date. Here, conductive aAO/STO heterostructures have been synthesized on a silicon wafer via a growth-and-transfer method. A scanning transmission electron microscopy image shows flat and close contact between STO membranes and a Si wafer. Electron energy loss spectroscopic measurements reveal the interfacial Ti valence state evolution, which identifies the formation of 2D charge carriers confined at the interface of aAO/STO. This work provides a feasible strategy for the integration of 2DEG on a silicon wafer and other desired substrates for potential functional and flexible electronic devices.

Observation of Moiré Patterns in Twisted Stacks of Bilayer Perovskite Oxide Nanomembranes with Various Lattice Symmetries

The design and fabrication of novel quantum devices in which exotic phenomena arise from moiré physics have sparked a new race of conceptualization and creation of artificial lattice structures. This interest is further extended to the research on thin-film transition metal oxides, with the goal of synthesizing twisted layers of perovskite oxides concurrently revealing moiré landscapes. By utilizing a sacrificial-layer-based approach, we show that such high-quality twisted bilayer oxide nanomembrane structures can be achieved. We observe atomic-scale distinct moiré patterns directly formed with different twist angles, and the symmetry-inequivalent nanomembranes can be stacked together to constitute new complex moiré configurations. This study paves the way to the construction of higher-order artificial oxide heterostructures based on different materials/symmetries and provides the materials foundation for investigating moiré-related electronic effects in an expanded selection of twisted oxide thin films.

Enhanced polarization and abnormal flexural deformation in bent freestanding perovskite oxides

Recent realizations of ultrathin freestanding perovskite oxides offer a unique platform to probe novel properties in two-dimensional oxides. Here, we observe a giant flexoelectric response in freestanding BiFeO₃ and SrTiO₃ in their bent state arising from strain gradients up to 3.5 × 10⁷ m^-1, suggesting a promising approach for realizing ultra-large polarizations. Additionally, a substantial change in membrane thickness is discovered in bent freestanding BiFeO₃, which implies an unusual bending-expansion/shrinkage effect in the ferroelectric membrane that has never been seen before in crystalline materials. Our theoretical model reveals that this unprecedented flexural deformation within the membrane is attributable to a flexoelectricity-piezoelectricity interplay. The finding unveils intriguing nanoscale electromechanical properties and provides guidance for their practical applications in flexible nanoelectromechanical systems.

Freestanding complex-oxide membranes

Complex oxides show a vast range of functional responses, unparalleled within the inorganic solids realm, making them promising materials for applications as varied as next-generation field-effect transistors, spintronic devices, electro-optic modulators, pyroelectric detectors, or oxygen reduction catalysts. Their stability in ambient conditions, chemical versatility, and large susceptibility to minute structural and electronic modifications make them ideal subjects of study to discover emergent phenomena and to generate novel functionalities for next-generation devices. Recent advances in the synthesis of single-crystal, freestanding complex oxide membranes provide an unprecedented opportunity to study these materials in a nearly-ideal system (e.g. free of mechanical/thermal interaction with substrates) as well as expanding the range of tools for tweaking their order parameters (i.e. (anti-)ferromagnetic, (anti-)ferroelectric, ferroelastic), and increasing the possibility of achieving novel heterointegration approaches (including interfacing dissimilar materials) by avoiding the chemical, structural, or thermal constraints in synthesis processes. Here, we review the recent developments in the fabrication and characterization of complex-oxide membranes and discuss their potential for unraveling novel physicochemical phenomena at the nanoscale and for further exploiting their functionalities in technologically relevant devices.