Vortex Domain Walls in Ferroelectrics

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.

Mechanical manipulation for ordered topological defects

Randomly distributed topological defects created during the spontaneous symmetry breaking are the fingerprints to trace the evolution of symmetry, range of interaction, and order parameters in condensed matter systems. However, the effective mean to manipulate topological defects into ordered form is elusive due to the topological protection. Here, we establish a strategy to effectively align the topological domain networks in hexagonal manganites through a mechanical approach. It is found that the nanoindentation strain gives rise to a threefold Magnus-type force distribution, leading to a sixfold symmetric domain pattern by driving the vortex and antivortex in opposite directions. On the basis of this rationale, sizeable mono-chirality topological stripe is readily achieved by expanding the nanoindentation to scratch, directly transferring the randomly distributed topological defects into an ordered form. This discovery provides a mechanical strategy to manipulate topological protected domains not only on ferroelectrics but also on ferromagnets/antiferromagnets and ferroelastics.

Observation of Hidden Polar Phases and Flux Closure Domain Topology in Bi2WO6 Thin Films

Topological textures of ferroelectric polarizations have promise as alternative devices for future information technology. A polarization rotation inevitably deviates from the stable orientation in axial ferroelectrics, but local energy losses compromise the global symmetry, resulting in a distorted shape of the topological vortex or inhibiting the vortex. Easy planar isotropy helps to promote rotating structures and, accordingly, to facilitate access to nontrivial textures. Here, we investigate the domain structure of an epitaxial thin film of bismuth tungsten oxide (Bi₂WO₆) grown on a (001) SrTiO₃ substrate. By using angle-resolved piezoresponse force microscopy and scanning transmission electron microscopy, we find the existence of a hidden phase with ⟨100⟩-oriented ferroelectric polarizations in the middle of the four variant ⟨110⟩-oriented polarization domains, which assists in the formation of flux closure domains. The results suggest that this material is one step closer to becoming an isotropic two-dimensional polar material.

Nonabelian Ginzburg-Landau theory for ferroelectrics

The Ginzburg-Landau theory, which was introduced to phenomenologically describe the destruction of superconductivity by a magnetic field at the beginning, has brought up much more knowledge beyond the original one as a mean-field theory of thermodynamics states. There the complex order parameter plays an important role. Here we propose a macroscopic theory to describe the features of ferroelectrics by a two-component complex order parameter coupled to nonabelian gauge potentials that provide more freedom to reflect interplays between different measurables. Within this theoretical framework, some recently discovered empirical static and time-independent phenomena, such as vortex, anti-vortex, spiral orders can be obtained as solutions for different gauge potentials. It is expected to bring in a new angle of view with more elucidation than the traditional one that takes the polarization as order parameter.

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

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

Electric-field control of the nucleation and motion of isolated three-fold polar vertices

Recently various topological polar structures have been discovered in oxide thin films. Despite the increasing evidence of their switchability under electrical and/or mechanical fields, the dynamic property of isolated ones, which is usually required for applications such as data storage, is still absent. Here, we show the controlled nucleation and motion of isolated three-fold vertices under an applied electric field. At the PbTiO3/SrRuO3 interface, a two-unit-cell thick SrTiO3 layer provides electrical boundary conditions for the formation of three-fold vertices. Utilizing the SrTiO3 layer and in situ electrical testing system, we find that isolated three-fold vertices can move in a controllable and reversible manner with a velocity up to ~629 nm s-1. Microstructural evolution of the nucleation and propagation of isolated three-fold vertices is further revealed by phase-field simulations. This work demonstrates the ability to electrically manipulate isolated three-fold vertices, shedding light on the dynamic property of isolated topological polar structures.

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.

Chiral structures of electric polarization vectors quantified by X-ray resonant scattering

Resonant elastic X-ray scattering (REXS) offers a unique tool to investigate solid-state systems providing spatial knowledge from diffraction combined with electronic information through the enhanced absorption process, allowing the probing of magnetic, charge, spin, and orbital degrees of spatial order together with electronic structure. A new promising application of REXS is to elucidate the chiral structure of electrical polarization emergent in a ferroelectric oxide superlattice in which the polarization vectors in the REXS amplitude are implicitly described through an anisotropic tensor corresponding to the quadrupole moment. Here, we present a detailed theoretical framework and analysis to quantitatively analyze the experimental results of Ti L-edge REXS of a polar vortex array formed in a PbTiO₃/SrTiO₃ superlattice. Based on this theoretical framework, REXS for polar chiral structures can become a useful tool similar to x-ray resonant magnetic scattering (XRMS), enabling a comprehensive study of both electric and magnetic REXS on the chiral structures.

The polar chiral texture of the vortex or skyrmion structure in ferroelectric oxide PbTiO₃/SrTiO₃ superlattice attracts attention. Here, the authors report a theoretical framework to probe emergent chirality of electrical polarization textures.

TopoTEM: A Python Package for Quantifying and Visualizing Scanning Transmission Electron Microscopy Data of Polar Topologies

The exotic internal structure of polar topologies in multiferroic materials offers a rich landscape for materials science research. As the spatial scale of these entities is often subatomic in nature, aberration-corrected transmission electron microscopy (TEM) is the ideal characterization technique. Software to quantify and visualize the slight shifts in atomic placement within unit cells is of paramount importance due to the now routine acquisition of images at such resolution. In the previous ~decade since the commercialization of aberration-corrected TEM, many research groups have written their own code to visualize these polar entities. More recently, open-access Python packages have been developed for the purpose of TEM atomic position quantification. Building on these packages, we introduce the TEMUL Toolkit: a Python package for analysis and visualization of atomic resolution images. Here, we focus specifically on the TopoTEM module of the toolkit where we show an easy to follow, streamlined version of calculating the atomic displacements relative to the surrounding lattice and thus plotting polarization. We hope this toolkit will benefit the rapidly expanding field of topology-based nano-electronic and quantum materials research, and we invite the electron microscopy community to contribute to this open-access project.

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

Multiferroic topologies are an emerging solution for future low-power magnetic nanoelectronics due to their combined tuneable functionality and mobility. Here, we show that in addition to being magnetoelectric multiferroic at room temperature, thin-film Aurivillius phase Bi6TixFeyMnzO18 is an ideal material platform for both domain wall and vortex topology-based nanoelectronic devices. Utilizing atomic-resolution electron microscopy, we reveal the presence and structure of 180°-type charged head-to-head and tail-to-tail domain walls passing throughout the thin film. Theoretical calculations confirm the subunit cell cation site preference and charged domain wall energetics for Bi6TixFeyMnzO18. Finally, we show that polar vortex-type topologies also form at out-of-phase boundaries of stacking faults when internal strain and electrostatic energy gradients are altered. This study could pave the way for controlled polar vortex topology formation via strain engineering in other multiferroic thin films. Moreover, these results confirm that the subunit cell topological features play an important role in controlling the charge and spin state of Aurivillius phase films and other multiferroic heterostructures.

Origin of Ferroelectric Domain Wall Alignment with Surface Trenches in Ultrathin Films

Engraving trenches on the surfaces of ultrathin ferroelectric (FE) films and superlattices promises control over the orientation and direction of FE domain walls (DWs). Through exploiting the phenomenon of DW-surface trench (ST) parallel alignment, systems where DWs are known for becoming electrical conductors could now become useful nanocircuits using only standard lithographical techniques. Despite this clear application, the microscopic mechanism responsible for the alignment phenomenon has remained elusive. Using ultrathin PbTiO_{3} films as a model system, we explore this mechanism with large scale density functional theory simulations on as many as 5,136 atoms. Although we expect multiple contributing factors, we show that parallel DW-ST alignment can be well explained by this configuration giving rise to an arrangement of electric dipole moments which best restore polar continuity to the film. These moments preserve the polar texture of the pristine film, thus minimizing ST-induced depolarizing fields. Given the generality of this mechanism, we suggest that STs could be used to engineer other exotic polar textures in a variety of FE nanostructures as supported by the appearance of ST-induced polar cycloidal modulations in this Letter. Our simulations also support experimental observations of ST-induced negative strains which have been suggested to play a role in the alignment mechanism.

Atomic-Scale Tunable Flexoelectric Couplings in Oxide Multiferroics

Flexoelectricity is an effective tool in modulating the crystallographic structures and properties of oxides for multifunctional applications. However, engineering the nonuniform strain to obtain tunable flexoelectric behaviors at the atomic scale remains an ongoing challenge in conventional substrate-imposed ferroelectric films. Here, the regulatable flexoelectric behaviors are demonstrated at atomic scale in [110]-oriented BiFeO₃ thin films, which are triggered by the strain-field coupling of high-density interfacial dislocations. Using aberration-corrected scanning transmission electron microscopy, the asymmetric polarization rotation around the single dislocation is revealed, which is induced by the gradient strain fields of the single dislocation. These strain fields are highly correlated to generate huge strain gradients between neighboring dislocations, and thereby, serial flexoelectric responses are engineered as a function of dislocation spacings in thicker BiFeO₃ films. This work opens a pathway for the modulation of flexoelectric responses in ferroelectrics, which could be extended to other functional materials to create exotic phenomena.