Engineering polar vortex from topologically trivial domain architecture

Inverse Size-Scaling Ferroelectricity in Centrosymmetric Insulating Perovskite Oxide DyScO3

The breaking of inversion symmetry dictates the emergence of electric polarization, whose topological states in superlattices and bulks have received tremendous attention for their intriguing physics brought for novel device design. However, as for substrate oxides such as LaAlO3, KTaO3, RScO3 (R = rare earth element), their centrosymmetric trivial attributes make their functionality poorly explored. Here, the discovery of nanoscale thickness gradient-induced nonpolar-to-polar phase transition in band insulator DyScO3 is reported by using atomic resolution transmission electron microscopy. As the free-standing specimen reduces to a critical thickness ≈5 nm, its inversion symmetry is spontaneously broken by surface charge transfer, which gives rise to asymmetric Dy atomic displacements and ferrodistortive octahedral order, as substantiated by the first-principles calculations. Apart from the observation of migratable polar vortex structures, the switchable electric polarization by applied electric field is demonstrated by the piezoresponse force microscopy experiments. Given the decisive role of critical size in generating ferroelectricity, a concept of "inverse size-scaling ferroelectric" is proposed to define a class of such materials. Distinct from the proper and improper ferroelectrics, the findings offer a new platform to explore novel low-dimensional ferroelectrics and device applications in the future.

Reversible Manipulation of Polar Topologies in Oxide Ferroelectrics via Electric Fields

Polar topologies show great potentials in memories and other nano-micro devices. To integrate with silicon conducting circuits, it is vital to understand the dynamic evolution and the transformation of different domain configurations under external stimulus. Here in situ transmission electron microscopy is performed and the electrically controlled creation and annihilation of large-scale polar flux-closure array from typical c/a domains in PbTiO3/SrTiO3 bilayers is directly observed. It is found that the transformation is reversible after removal of external electric fields. Increasing external electric fields on (PbTiO3/SrTiO3)5 multilayered films, it is further found that the flux-closure domains are nucleated and propagated via the steps of first the formation of new c domains and then connection with neighboring c domains. The transition from a/c domains to flux-closure arrays under electric fields is collaborated with evaluating energy variations by phase-field simulations in which the electrostatic energy plays an important role. These results demonstrate the polar topologies can be reversibly manipulated by external stimuli, which sheds light on further understanding the dynamics behavior of polar topologies and helps for future nanoelectric applications.

Origin of Chiral Phase Transition of Polar Vortex in Ferroelectric/Dielectric Superlattices

Chiral vortices and their phase transition in ferroelectric/dielectric heterostructures have drawn significant attention in the field of condensed matter. However, the dynamical origin of the chiral phase transition from achiral to chiral polar vortices has remained elusive. Here, we develop a phase-field perturbation model and discover the softening of out-of-plane vibration mode of polar vortices in [(PbTiO3)m/(SrTiO3)m]n superlattices at a critical epitaxial strain or temperature. The softening of the mode leads to the appearance of the axial polarization at vortex cores, resulting in chiral phase transition. It is found that the local negative permittivity plays a crucial role in the enhanced oscillation of axial polarization near the phase transition. Our findings not only reveal the origin of the chiral phase transition of polar vortices but also provide considerable new insight into the dynamics of topological structures and topological phase transitions in ferroelectric systems.

Polar Vortices in Relaxor Ferroelectric Ceramics for High-Efficiency Capacitive Energy Storage

Polar vortices are predominantly observed within the confined ferroelectric films and the ferroelectric/paraelectric superlattices. This raises the intriguing question of whether polar vortices can form within relaxor ferroelectric ceramics and subsequently contribute to their energy storage performances. Here, we incorporate 10 mol % CaSnO3 into the 0.7NaNbO3-0.3Sr0.7Bi0.2TiO3 matrix, yielding a coexistence of phases: 48.8% orthorhombic P21/ma, 49.1% tetragonal P4bm, and 2.1% tetragonal P42/mnm SnO2, which is confirmed by the combination of X-ray diffraction and transmission electron microscopy. The ceramic features a pronounced core-shell structure with the shell region rich in stripe nanoscale domains of the P21/ma phase and the core region consisting of polar nanoregions deficient in the P21/ma phase, forming polar vortices. Consequently, the ceramic achieves an impressive recoverable energy storage density of 6.83 J cm-3 and an exceptional efficiency of 95.7% at a high breakdown strength of 750 kV cm-1, along with superior stability in frequency, temperature, and cycling. These results not only offer a viable approach for developing high-performance energy storage ceramics through the controlled formation of polar vortices but also offer the potential for direct electric-field control of polar vortices for high-speed data processing and storage.

Synthesizing ordered polar patterns in nonpolar SrTiO3 nanofilms via wrinkle-induced flexoelectricity

Ordered polar structures in oxide nanofilms play a pivotal role in the development of nanoelectronic applications. Hitherto, ordered polar structures have been restricted to a limited number of ferroelectric materials, and there is no effective scheme to induce and manipulate ordered polar patterns in centrosymmetric nonpolar nanofilms due to the absence of spontaneous symmetry breaking. Here, we circumvent these limitations by utilizing the wrinkle-induced strain gradient modulation associated with flexoelectricity as a general means of inducing and manipulating ordered polar patterns in nonpolar nanofilms. Leveraging the surface instability caused by strain mismatch between oxide nanofilms and pre-strained compliant substrate, we successfully fabricate striped SrTiO3 wrinkles, where well-ordered strain gradients and corresponding periodic polar patterns are readily achieved. Through in-situ piezoresponse force microscopy experiments, we show that the generated polar patterns can be manipulated by varying strain boundaries. Furthermore, the atomistic resolution images and first-principles calculations reveal that such wrinkle-induced ordered polar patterns primarily emerge from the flexoelectric coupling between the local polarization and strain gradients. These findings provide implications for manipulating polar structures by strain gradient and flexoelectric engineering, which in turn enable the realization of nontrivial polar structures in a broader range of materials.

Ultrahigh-Density Polar Vortex Lattice in Square-Shaped Moiré Bilayers of Lead Chalcogenides

Nanoscale exotic polar topological structures, such as vortices and skyrmions, hold promise for next-generation electronic devices, yet their spontaneous formation in 2D van der Waals (vdW) materials remains quite challenging. Herein, we demonstrate from first-principles that ultrahigh-density polar vortices emerge in the square moiré bilayer formed by twisting two layers of centrosymmetric PbS with the D4h point group. The emerged ferroelectricity arises from the inherent complex strain associated with the twisted structures, and the resulting electron polarization is much greater than that obtained in sliding ferroelectricity. Notably, the engineered strain patterns are characterized by peculiar inhomogeneous in-plane fields with a checkerboard distribution of uniaxial tension. This nanoscale nonuniform strain produces an ultrahigh-density vortex polarization lattice. The results from our study not only reveals a new mechanism for electric polarization and polar topologies in moiré bilayers but also provides opportunities for designing 2D ultrahigh-density electric devices.

Quasi-2D and 3D phase-field simulation studies of polar vortex domain structures for high-density domain engineering

Phase-field simulations were performed on the polar vortex array structure appearing in the SrTiO3/PbTiO3/SrTiO3 heterostructure to investigate the Kittel law relationship (w ∝ d1/2) between the vortex array period (w) and the PbTiO3 ferroelectric layer thickness (d). Quasi-two-dimensional simulation results show that the equilibrium period can be determined from the relationship between the size of the simulation box and the total free energy density and that the obtained period obeys the Kittel law. However, three-dimensional simulation results show that the polar vortex arrays are not homogeneous in the direction perpendicular to the vortex plane. In the pure vortex state, no obvious correlation exists between the simulation size and energy because of the dislocations caused by the vortex period mismatch. However, in the mixed state with ferroelectric a1/a2, the vortex domains exhibit equilibrium periods that satisfy the Kittel law relationship because of the confinement effect caused by phase separation. Further study of the confined vortex domains in these mixed states and the vortex domains of finite size due to mismatched dislocations are expected to enable domain engineering of higher domain densities.

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.

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.

Ferroelectric Texture of Individual Barium Titanate Nanocrystals

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

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

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

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

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

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.

Reversible Phase Transition between Vortex Lattice and Hexagonal Polar Skyrmion Crystals

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

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

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

Ferroelectric solitons crafted in epitaxial bismuth ferrite superlattices

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

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

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

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

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

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

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

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

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

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

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