Defect-Induced Hedgehog Polarization States in Multiferroics

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

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

Large Electromechanical Response in a Polycrystalline Alkali-Deficient (K,Na)NbO3 Thin Film on Silicon

The demand for large electromechanical performance in lead-free polycrystalline piezoelectric thin films is driven by the need for compact, high-performance microelectromechanical systems (MEMS) based devices operating at low voltages. Here we significantly enhance the electromechanical response in a polycrystalline lead-free oxide thin film by utilizing lattice-defect-induced structural inhomogeneities. Unlike prior observations in mismatched epitaxial films with limited low-frequency enhancements, we achieve large electromechanical strain in a polycrystalline (K,Na)NbO3 film integrated on silicon. This is achieved by inducing self-assembled Nb-rich planar faults with a nonstoichiometric composition. The film exhibits an effective piezoelectric coefficient of 565 pm V-1 at 1 kHz, surpassing those of lead-based counterparts. Notably, lattice defect growth is substrate-independent, and the large electromechanical response is extended to even higher frequencies in a polycrystalline film. Improved properties arise from unique lattice defect morphology and frequency-dependent relaxation behavior, offering a new route to remarkable electromechanical response in polycrystalline thin films.

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.

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.

Diverse Defects in Alkali Niobate Thin Films: Understanding at Atomic Scales and Their Implications on Properties

Defects in ferroelectric materials have many implications on the material properties which, in most cases, are detrimental. However, engineering these defects can also create opportunities for property enhancement as well as for tailoring novel functionalities. To purposely manipulate these defects, a thorough knowledge of their spatial atomic arrangement, as well as elastic and electrostatic interactions with the surrounding lattice, is highly crucial. In this work, analytical scanning transmission electron microscopy (STEM) is used to reveal a diverse range of multidimensional crystalline defects (point, line, planar, and secondary phase) in (K,Na)NbO₃ (KNN) ferroelectric thin films. The atomic-scale analyses of the defect-lattice interactions suggest strong elastic and electrostatic couplings which vary among the individual defects and correspondingly affect the electric polarization. In particular, the observed polarization orientations are correlated with lattice relaxations as well as strain gradients and can strongly impact the properties of the ferroelectric films. The knowledge and understanding obtained in this study open a new avenue for the improvement of properties as well as the discovery of defect-based functionalities in alkali niobate thin films.

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

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

Monodomain Liquid Crystals of Two-Dimensional Sheets by Boundary-Free Sheargraphy

Eliminating topological defects to achieve monodomain liquid crystals is highly significant for the fundamental studies of soft matter and building long-range ordered materials. However, liquid crystals are metastable and sensitive to external stimuli, such as flow, confinement, and electromagnetic fields, which cause their intrinsic polycrystallinity and topological defects. Here, we achieve the monodomain liquid crystals of graphene oxide over 30 cm through boundary-free sheargraphy. The obtained monodomain liquid crystals exhibit large-area uniform alignment of sheets, which has the same optical polarized angle and intensity. The monodomain liquid crystals provide bidirectionally ordered skeletons, which can be applied as lightweight thermal management materials with bidirectionally high thermal and electrical conductivity. Furthermore, we extend the controllable topology of two-dimensional colloids by introducing singularities and disclinations in monodomain liquid crystals. Topological structures with defect strength from - 2 to + 2 were realized. This work provides a facile methodology to study the structural order of soft matter at a macroscopic level, facilitating the fabrication of metamaterials with tunable and highly anisotropic architectures.

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.

Origin of giant electric-field-induced strain in faulted alkali niobate films

A large electromechanical response in ferroelectrics is highly desirable for developing high-performance sensors and actuators. Enhanced electromechanical coupling in ferroelectrics is usually obtained at morphotropic phase boundaries requiring stoichiometric control of complex compositions. Recently it was shown that giant piezoelectricity can be obtained in films with nanopillar structures. Here, we elucidate its origin in terms of atomic structure and demonstrate a different system with a greatly enhanced response. This is in non-stoichiometric potassium sodium niobate epitaxial thin films with a high density of self-assembled planar faults. A giant piezoelectric coefficient of ∼1900 picometer per volt is demonstrated at 1 kHz, which is almost double the highest ever reported effective piezoelectric response in any existing thin films. The large oxygen octahedral distortions and the coupling between the structural distortion and polarization orientation mediated by charge redistribution at the planar faults enable the giant electric-field-induced strain. Our findings demonstrate an important mechanism for realizing the unprecedentedly giant electromechanical coupling and can be extended to many other material functions by engineering lattice faults in non-stoichiometric compositions.

Maximizing the electromechanical response is crucial for developing piezoelectric devices. Here, the authors demonstrate a giant electric-field-induced strain and its origin in alkali niobate epitaxial thin films with self-assembled planar faults.

Isolated-Oxygen-Vacancy Hardening in Lead-Free Piezoelectrics

Defect engineering is a well-established approach to customize the functionalities of perovskite oxides. In demanding high-power applications of piezoelectric materials, acceptor doping serves as the state-of-the-art hardening approach, but inevitably deteriorates the electromechanical properties. Here, a new hardening effect associated with isolated oxygen vacancies for achieving well-balanced performances is proposed. Guided by theoretical design, a well-balanced performance of mechanical quality factor (Q_m ) and piezoelectric coefficient (d₃₃ ) is achieved in lead-free potassium sodium niobate ceramics, where Q_m increases by over 60% while d₃₃ remains almost unchanged. By atomic-scale Z-contrast imaging, hysteresis measurement, and quantitative piezoresponse force microscopy analysis, it is revealed that the improved Q_m results from the inhibition of both extrinsic and intrinsic losses while the unchanged d₃₃ is associated with the polarization contributions being retained. More encouragingly, the hardening effect shows exceptional stability with increasing vibration velocity, offering potential in material design for practical high-power applications such as pharmaceutical extraction and ultrasonic osteotomes.

Evolution from Lead-Based to Lead-Free Piezoelectrics: Engineering of Lattices, Domains, Boundaries, and Defects Leading to Giant Response

Piezoelectric materials are known to mankind for more than a century, with numerous advancements made in both scientific understandings and practical applications. In the last two decades, in particular, the research on piezoelectrics has largely been driven by the constantly changing technological demand, and the drive toward a sustainable society. Hence, environmental-friendly "lead-free piezoelectrics" have emerged in the anticipation of replacing lead-based counterparts with at least comparable performance. However, there are still obstacles to be overcome for realizing this objective, while the efforts in this direction already seem to culminate. Therefore, novel structural strategies need to be designed to address these issues and for further breakthrough in this field. Here, various strategies to enhance piezoelectric properties in lead-free systems with fundamental and historical context, and from atomic to macroscopic scale, are explored. The main challenges currently faced in the transition from lead-based to lead-free piezoelectrics are identified and key milestones for future research in this field are suggested. These include: i) decoding the fundamental mechanisms; ii) large temperature-stable piezoresponse; and iii) fabrication-friendly and tailorable composition. Strategic insights and general guidelines for the synergistic design of new piezoelectric materials for obtaining a large piezoelectric response are also provided.

Thickness-Dependent Polar Domain Evolution in Strained, Ultrathin PbTiO3 Films

Ferroelectric ultrathin films have great potential in electronic devices and device miniaturization with the innovation of technology. In the process of product commercialization, understanding the domain evolution and topological properties of ferroelectrics is a prerequisite for high-density storage devices. In this work, a series of ultrathin PbTiO₃ (PTO) films with varying thicknesses were deposited on cubic KTaO₃ substrates by pulsed laser deposition and were researched by Cs-corrected scanning transmission electron microscopy (STEM), reciprocal space mapping (RSM), and piezoresponse force microscopy (PFM). RSM experiments indicate the existence of a/c domains and show that the lattice constant varies continuously, which is further confirmed by atomic-scale STEM imaging. Diffraction contrast analysis clarifies that with the decrease in PTO film thickness, the critical thickness for the formation of a/c domains could be missing. When the thickness of PTO films is less than 6 nm, the domain configurations in the ultrathin PTO films are the coexistence of a/c domains and bowl-like topological structures, where the latter ones were identified as convergent and divergent types of meron. In addition, abundant 90° charged domain walls in these ultrathin PTO films were identified. PFM studies reveal clear ferroelectric properties for these ultrathin PTO films. These results may shed light on further understanding the domain evolution and topological properties in ultrathin ferroelectric PTO films.

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

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

Recent Progress on Topological Structures in Ferroic Thin Films and Heterostructures

Topological spin/polarization structures in ferroic materials continue to draw great attention as a result of their fascinating physical behaviors and promising applications in the field of high-density nonvolatile memories as well as future energy-efficient nanoelectronic and spintronic devices. Such developments have been made, in part, based on recent advances in theoretical calculations, the synthesis of high-quality thin films, and the characterization of their emergent phenomena and exotic phases. Herein, progress over the last decade in the study of topological structures in ferroic thin films and heterostructures is explored, including the observation of topological structures and control of their structures and emergent physical phenomena through epitaxial strain, layer thickness, electric, magnetic fields, etc. First, the evolution of topological spin structures (e.g., magnetic skyrmions) and associated functionalities (e.g., topological Hall effect) in magnetic thin films and heterostructures is discussed. Then, the exotic polar topologies (e.g., domain walls, closure domains, polar vortices, bubble domains, and polar skyrmions) and their emergent physical properties in ferroelectric oxide films and heterostructures are explored. Finally, a brief overview and prospectus of how the field may evolve in the coming years is provided.

Polar meron lattice in strained oxide ferroelectrics

A topological meron features a non-coplanar structure, whose order parameters in the core region are perpendicular to those near the perimeter. A meron is half of a skyrmion, and both have potential applications for information carrying and storage. Although merons and skyrmions in ferromagnetic materials can be readily obtained via inter-spin interactions, their behaviour and even existence in ferroelectric materials are still elusive. Here we observe using electron microscopy not only the atomic morphology of merons with a topological charge of 1/2, but also a periodic meron lattice in ultrathin PbTiO₃ films under tensile epitaxial strain on a SmScO₃ substrate. Phase-field simulations rationalize the formation of merons for which an epitaxial strain, as a single alterable parameter, plays a critical role in the coupling of lattice and charge. This study suggests that by engineering strain at the nanoscale it should be possible to fabricate topological polar textures, which in turn could facilitate the development of nanoscale ferroelectric devices.

Intrinsic and extrinsic effects on the electrotoroidic switching in a ferroelectric notched nanodot by a homogeneous electric field

The control of topological defects in ferroelectrics, in particular by a homogeneous electric field, has emerged as an active research direction. A polarization vortex, which is a fundamental topological defect formed in ferroelectric nanodots, has recently been demonstrated to be switchable by a homogeneous electric field through the control of the built-in electrical distribution using low-symmetry nanodots. Such electrotoroidic switching is investigated for nearly ideal systems, e.g., free-standing nanodots. However, the electrotoroidic switching may be impacted by several factors, for instance, the nanoscale effect of flexoelectricity (intrinsic effect), epitaxial strain and the frequency of the applied field (extrinsic effects). In the present study, the switching of the polarization vortex in a notched nanodot under a homogeneous electric field is investigated. The emphasis is put on a comparison between intrinsic and extrinsic effects on the vortex switching. The results show that the vortex switching takes place through alternate vortex-to-polar and polar-to-vortex transformations due to the appearance of the notch. Although the flexoelectricity breaks the symmetry of the polarization field in the notched nanodot during the polarization transformation and gives rise to an unusual behavior of the vortex core, which departs from the symmetry axis of the notched nanodot, this intrinsic effect plays a relatively insignificant role in the switching behavior of the polarization vortex. In comparison to the intrinsic effect, interestingly, the extrinsic effects strongly influence the vortex switching behavior. Specifically, the frequency of the applied electric field can alter both the shape of the toroidal hysteresis loop and the domain transformation process of the vortex switching. In addition, under substrate constraints, the magnitude of the coercive electric fields at which the vortex-to-polar and polar-to-vortex transformations occur linearly decreases with the increase of strain. The present study provides instructive information on the efficient control of a polarization vortex, which is dominated by extrinsic factors rather than intrinsic ones.

Real-time studies of ferroelectric domain switching: a review

Ferroelectric materials have been utilized in a broad range of electronic, optical, and electromechanical applications and hold the promise for the design of future high-density nonvolatile memories and multifunctional nano-devices. The applications of ferroelectric materials stem from the ability to switch polarized domains by applying an electric field, and therefore a fundamental understanding of the switching dynamics is critical for design of practical devices. In this review, we summarize the progress in the study of the microscopic process of ferroelectric domain switching using recently developed in situ transmission electron microscopy (TEM). We first briefly introduce the instrumentation, experimental procedures, imaging mechanisms, and analytical methods of the state-of-the-art in situ TEM techniques. The application of these techniques to studying a wide range of complex switching phenomena, including domain nucleation, domain wall motion, domain relaxation, domain-defect interaction, and the interplay between different types of domains, is demonstrated. The underlying physics of these dynamic processes are discussed.

Rotational polarization nanotopologies in BaTiO3/SrTiO3 superlattices

Ferroelectrics are characterized by domain structures as are other ferroics. At the nanoscale though, ferroelectrics may exhibit non-trivial or exotic polarization configurations under proper electrostatic and elastic conditions. These polar states may possess emerging properties not present in the bulk compounds and are promising for technological applications. Here, the observation of rotational polarization topologies at the nanoscale by means of aberration-corrected scanning transmission electron microscopy is reported in BaTiO₃/SrTiO₃ superlattices grown on cubic SrTiO₃(001). The transition from a highly homogeneous polarization state to the formation of rotational nanodomains has been achieved by controlling the superlattice period while maintaining compressive clamping of the superlattice to the cubic SrTiO₃ substrate. The nanodomains revealed in BaTiO₃ prove that its nominal tetragonal structure also allows rotational polar textures.

Design and Manipulation of Ferroic Domains in Complex Oxide Heterostructures

The current burst of device concepts based on nanoscale domain-control in magnetically and electrically ordered systems motivates us to review the recent development in the design of domain engineered oxide heterostructures. The improved ability to design and control advanced ferroic domain architectures came hand in hand with major advances in investigation capacity of nanoscale ferroic states. The new avenues offered by prototypical multiferroic materials, in which electric and magnetic orders coexist, are expanding beyond the canonical low-energy-consuming electrical control of a net magnetization. Domain pattern inversion, for instance, holds promises of increased functionalities. In this review, we first describe the recent development in the creation of controlled ferroelectric and multiferroic domain architectures in thin films and multilayers. We then present techniques for probing the domain state with a particular focus on non-invasive tools allowing the determination of buried ferroic states. Finally, we discuss the switching events and their domain analysis, providing critical insight into the evolution of device concepts involving multiferroic thin films and heterostructures.

Structures and electronic properties of domain walls in BiFeO3 thin films

Domain walls (DWs) in ferroelectrics are atomically sharp and can be created, erased, and reconfigured within the same physical volume of ferroelectric matrix by external electric fields. They possess a myriad of novel properties and functionalities that are absent in the bulk of the domains, and thus could become an essential element in next-generation nanodevices based on ferroelectrics. The knowledge about the structure and properties of ferroelectric DWs not only advances the fundamental understanding of ferroelectrics, but also provides guidance for the design of ferroelectric-based devices. In this article, we provide a review of structures and properties of DWs in one of the most widely studied ferroelectric systems, BiFeO₃ thin films. We correlate their conductivity and photovoltaic properties to the atomic-scale structure and dynamic behaviors of DWs.

Controllable defect driven symmetry change and domain structure evolution in BiFeO3 with enhanced tetragonality

Defect engineering has been a powerful tool to enable the creation of exotic phases and the discovery of intriguing phenomena in ferroelectric oxides. However, the accurate control of the concentration of defects remains a big challenge. In this work, ion implantation, which can provide controllable point defects, allows us to produce a controlled defect driven true super-tetragonal (T) phase with a single-domain-state in ferroelectric BiFeO3 thin films. This point-defect engineering is found to drive the phase transition from the as-grown mixed rhombohedral-like (R) and tetragonal-like (MC) phase to true tetragonal (T) symmetry and induce the stripe multi-nanodomains to a single domain state. By further increasing the injected dose of the He ion, we demonstrate an enhanced tetragonality super-tetragonal (super-T) phase with the largest c/a ratio of ∼1.3 that has ever been experimentally achieved in BiFeO3. A combination of the morphology change and domain evolution further confirms that the mixed R/MC phase structure transforms to the single-domain-state true tetragonal phase. Moreover, the re-emergence of the R phase and in-plane nanoscale multi-domains after heat treatment reveal the memory effect and reversible phase transition and domain evolution. Our findings demonstrate the reversible control of R-Mc-T-super T symmetry changes (leading to the creation of true T phase BiFeO3 with enhanced tetragonality) and multidomain-single domain structure evolution through controllable defect engineering. This work also provides a pathway to generate large tetragonality (or c/a ratio) that could be extended to other ferroelectric material systems (such as PbTiO3, BaTiO3 and HfO2) which might lead to strong polarization enhancement.

Theoretical guidelines to create and tune electric skyrmion bubbles

Researchers have long wondered whether ferroelectrics may present topological textures akin to magnetic skyrmions and chiral bubbles, the results being modest thus far. An electric equivalent of a typical magnetic skyrmion would rely on a counterpart of the Dzyaloshinskii-Moriya interaction and seems all but impossible; further, the exotic ferroelectric orders reported to date rely on specific composites and superlattices, limiting their generality and properties. Here, we propose an original approach to write topological textures in simple ferroelectrics in a customary manner. Our second-principles simulations of columnar nanodomains, in prototype material PbTiO₃, show we can harness the Bloch-type structure of the domain wall to create objects with the usual skyrmion-defining features as well as unusual ones-including isotopological and topological transitions driven by external fields and temperature-and potentially very small sizes. Our results suggest countless possibilities for creating and manipulating such electric textures, effectively inaugurating the field of topological ferroelectrics.

Control of Domain Structures in Multiferroic Thin Films through Defect Engineering

Domain walls (DWs) have become an essential component in nanodevices based on ferroic thin films. The domain configuration and DW stability, however, are strongly dependent on the boundary conditions of thin films, which make it difficult to create complex ordered patterns of DWs. Here, it is shown that novel domain structures, that are otherwise unfavorable under the natural boundary conditions, can be realized by utilizing engineered nanosized structural defects as building blocks for reconfiguring DW patterns. It is directly observed that an array of charged defects, which are located within a monolayer thickness, can be intentionally introduced by slightly changing substrate temperature during the growth of multiferroic BiFeO₃ thin films. These defects are strongly coupled to the domain structures in the pretemperature-change portion of the BiFeO₃ film and can effectively change the configuration of newly grown domains due to the interaction between the polarization and the defects. Thus, two types of domain patterns are integrated into a single film without breaking the DW periodicity. The potential use of these defects for building complex patterns of conductive DWs is also demonstrated.