Enhanced Piezoelectric Response at Nanoscale Vortex Structures in Ferroelectrics
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42 ENGINEERING↗
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Reversible long-range domain wall motion in an improper ferroelectric
Reversible ferroelectric domain wall movements beyond the 10 nm range associated with Rayleigh behavior are usually restricted to specific defect-engineered systems. Here, we demonstrate that such long-range movements naturally occur in the improper ferroelectric ErMnO 3 during electric-field-cycling. We study the electric-field-driven motion of domain walls, showing that they readily return to their initial position after having traveled distances exceeding 250 nm. By applying switching spectroscopy band-excitation piezoresponse force microscopy, we track the domain wall movement with nanometric spatial precision and analyze the local switching behavior. Phase field simulations show that the reversible long-range motion is intrinsic to the hexagonal manganites, linking it to their improper ferroelectricity and topologically protected structural vortex lines, which serve as anchor point for the ferroelectric domain walls. Our results give new insight into the local dynamics of domain walls in improper ferroelectrics and demonstrate the possibility to reversibly displace domain walls over much larger distances than commonly expected for ferroelectric systems in their pristine state, ensuring predictable device behavior for applications such as tunable capacitors or sensors.
Zahn, Manuel [Norwegian Univ. of Science and Techn↗
Ferroelectric incommensurate spin crystals
Ferroics, especially ferromagnets, can form complextopological spin structures such as vortices and skyrmions when subjected to particular electrical and mechanical boundary conditions. Simple vortex-like, electric-dipole-based topological structures have been observed in dedicated ferroelectric systems, especially ferroelectric-insulator superlattices such as PbTiO 3 /SrTiO 3 , which was later shown to be a model system owing to its high depolarizing field. To date, the electric dipole equivalent of ordered magnetic spin lattices driven by the Dzyaloshinskii-Moriya interaction (DMi) has not been experimentally observed. Here we examine a domain structure in a single PbTiO 3 epitaxial layer sandwiched between SrRuO 3 electrodes. In this work, we observe periodic clockwise and anticlockwise ferroelectric vortices that are modulated by a second ordering along their toroidal core. The resulting topology, supported by calculations, is a labyrinth-like pattern with two orthogonal periodic modulations that form an incommensurate polar crystal that provides a ferroelectric analogue to the recently discovered incommensurate spin crystals in ferromagnetic materials. These findings further blur the border between emergent ferromagnetic and ferroelectrictopologies, clearing the way for experimental realization of further electric counterparts of magnetic DMi-driven phases.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Transferring orbital angular momentum to an electron beam reveals toroidal and chiral order
Orbital angular momentum (OAM) and torque transfer play central roles in a wide range of magnetic textures and devices including skyrmions and spin-torque electronics. Analogous topological structures are now also being explored in ferroelectrics, including polarization vortex arrays in ferroelectric/dielectric superlattices. Unlike magnetic toroidal order, electric toroidal order does not couple directly to linear external fields. Instead, we find that the presence of an electric toroidal moment in a ferrorotational phase transfers measurable torque and OAM to a localized electron beam in the ballistic limit. We record these torque transfers from a high-energy electron beam using a momentum-resolved detector. This approach provides a high-sensitivity method to detect polarization fields and their more complex order parameters and topologies. In addition to toroidal order, we also demonstrate high-precision measurements of vorticity and chirality for polar vortexlike phases.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Confinement‐Driven Inverse Domain Scaling in Polycrystalline ErMnO 3
Abstract The research on topological phenomena in ferroelectric materials has revolutionized the way people understand polar order. Intriguing examples are polar skyrmions, vortex/anti‐vortex structures, and ferroelectric incommensurabilties, which promote emergent physical properties ranging from electric‐field‐controllable chirality to negative capacitance effects. Here, the impact of topologically protected vortices on the domain formation in improper ferroelectric ErMnO 3 polycrystals is studied, demonstrating inverted domain scaling behavior compared to classical ferroelectrics. It is observed that as the grain size increases, smaller domains are formed. Phase field simulations reveal that elastic strain fields drive the annihilation of vortex/anti‐vortex pairs within the grains and individual vortices at the grain boundaries. The inversion of the domain scaling behavior has far‐reaching implications, providing fundamentally new opportunities for topology‐based domain engineering and the tuning of the electromechanical and dielectric performance of ferroelectrics in general.
36 MATERIALS SCIENCE↗
Revealing the three-dimensional arrangement of polar topology in nanoparticles
In the early 2000s, low dimensional ferroelectric systems were predicted to have topologically nontrivial polar structures, such as vortices or skyrmions, depending on mechanical or electrical boundary conditions. A few variants of these structures have been experimentally observed in thin film model systems, where they are engineered by balancing electrostatic charge and elastic distortion energies. However, the measurement and classification of topological textures for general ferroelectric nanostructures have remained elusive, as it requires mapping the local polarization at the atomic scale in three dimensions. Here we unveil topological polar structures in ferroelectric BaTiO3 nanoparticles via atomic electron tomography, which enables us to reconstruct the full three-dimensional arrangement of cation atoms at an individual atom level. Our three-dimensional polarization maps reveal clear topological orderings, along with evidence of size-dependent topological transitions from a single vortex structure to multiple vortices, consistent with theoretical predictions. The discovery of the predicted topological polar ordering in nanoscale ferroelectrics, independent of epitaxial strain, widens the research perspective and offers potential for practical applications utilizing contact-free switchable toroidal moments.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Structural and Improper Ferroelectric Properties of TbInO 3 Single Crystal Grown by Laser Floating Zone
The honeycomb TbInO 3 has attracted wide research attention due to its fascinating physical properties. However, TbInO 3 single crystal was difficult to grow owing to the high melting point and serious volatilization of indium during the crystal growth. In this study, the volatilization of the indium element was effectively suppressed by controlling the growth atmosphere and pressure. The excess ratio of indium oxide was determined, and pure hexagonal TbInO 3 crystal was obtained by the laser floating zone method. Systematic studies on the crystal structure and optical and ferroelectric properties were carried out. The structure distortion resulted in the improper geometric ferroelectric revealed by single crystal diffraction and Raman spectrum measurements. The topological vortex domains and P-E hysteresis loop demonstrated the presence of ferroelectricity. TbInO 3 crystal has great potential application in vortex memory.
36 MATERIALS SCIENCE↗
Imaging and structure analysis of ferroelectric domains, domain walls, and vortices by scanning electron diffraction
Direct electron detectors in scanning transmission electron microscopy give unprecedented possibilities for structure analysis at the nanoscale. In electronic and quantum materials, this new capability gives access to, for example, emergent chiral structures and symmetry-breaking distortions that underpin functional properties. Quantifying nanoscale structural features with statistical significance, however, is complicated by the subtleties of dynamic diffraction and coexisting contrast mechanisms, which often results in a low signal-to-noise ratio and the superposition of multiple signals that are challenging to deconvolute. Here we apply scanning electron diffraction to explore local polar distortions in the uniaxial ferroelectric Er(Mn,Ti)O 3 . Using a custom-designed convolutional autoencoder with bespoke regularization, we demonstrate that subtle variations in the scattering signatures of ferroelectric domains, domain walls, and vortex textures can readily be disentangled with statistical significance and separated from extrinsic contributions due to, e.g., variations in specimen thickness or bending. The work demonstrates a pathway to quantitatively measure symmetry-breaking distortions across large areas, mapping structural changes at interfaces and topological structures with nanoscale spatial resolution.
36 MATERIALS SCIENCE↗
Probing ferroelectric domain structures and their switching dynamics in SrBi2Ta2O9 by in-situ electric biasing in transmission electron microscopy
Abstract Lead-free SrBi 2 Ta 2 O 9 (SBT) has been a promising ferroelectric material for various applications such as electronics and data storage due to its outstanding ferroelectric properties including high fatigue endurance and low leakage current. However, the atomic-scale domain structure and switching dynamics of ferroelectric SBT remain elusive. This study reveals that spontaneous polarization arises from canted bismuth-cation displacements, forming 90° and Ising-type 180° domain walls. Interestingly, topological pairs of ferroelectric vortex and antivortex connect ferroelectric boundaries where three domain walls converge. In situ electrical biasing transmission electron microscopy (TEM) reveals the dominance of 180° switching over 90°, where oxygen octahedral connectivity is protected by ferroelastic energy in the 90° domain wall. Consequently, all 180° domain walls and (anti)vortices are removed, leaving only 90° domain walls in the electrically poled states. Chemical deterioration along domain walls highlights vulnerability of SBT to ferroelectric fatigue. This study provides insight into crucial aspects for practical applications of SBT.
36 MATERIALS SCIENCE↗
Emergent topological polarization textures in relaxor ferroelectrics
Relaxor ferroelectrics underpin high-performance actuators and sensors, yet the nature of polar heterogeneities driving their broadband dielectric response remains debated. Using a unified, multimodal structural refinement framework— simultaneously fitting complementary X-ray and neutron total scattering, X-ray absorption spectra, and diffuse scattering—we reconstruct 3D mesoscale polarization maps in the classic relaxor system PbMg 1/3 Nb 2/3 O 3 –PbTiO 3 . We uncover self-organized swirling polarization textures with half-skyrmion (meron) vortices, challenging models of independent polar nanoregions. These textures, characterized by smooth changes in the polarization direction, originate from overlapping volumes in which the projections of locally correlated polarization vectors onto each volume’s long axis share the same sign. Vortex cores correlate strongly with local charge and strain gradients imposed by compositional heterogeneities. In this work, our results suggest that chemical disorder, acting via depolarizing and strain fields, stabilizes topological vortex textures of the polarization field, offering a route for engineering new dielectric and ferroelectric functionalities.
Eremenko, Maksim [National Institute of Standards ↗
Strain effects on stability of topological ferroelectric polar configurations in (PbTiO3) n /(SrTiO3) n superlattices
The (PbTiO3)n/(SrTiO3)n (PTO/STO) superlattice system has been shown to exhibit interesting topological phases (e.g., vortices and skyrmions) in addition to normal ferroelectric domain states. Existing studies are mostly focused on the dependence of topological polar distributions and properties of PTO/STO superlattice on its periodicity. Here, we study the strain effect on the topological phase transitions and ferroelectric domain structures employing phase-field simulations. We summarized in an isotropic strain (in-plane misfit strain along the x direction is equal to that along the y direction) periodicity phase diagram displaying the stability regions of different polar topological states, including normal ferroelectric twins, vortices, skyrmions, and mixtures of vortices and twins. We also analyzed the polarization configurations under anisotropic in-plane strains (in-plane misfit strain along the x direction is not equal to that along the y direction) and demonstrated that the strain anisotropy can be used to tune the directions of vortex arrays along either the [100] pc or [010] pc directions or labyrinth vortex arrays. This work offers guidance to manipulating polar structures in the PTO/STO superlattices via strain engineering.
Physics↗
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.
3D ordering↗
Critical Role of Sc Substitution in Modulating Ferroelectricity in Multiferroic LuFeO 3
Understanding how individual dopants or substitutional atoms interact with host lattices enables us to manipulate, control, and improve the functionality of materials. However, because of the intimate coupling among various degrees of freedom in multiferroics, the atomic-scale influence of individual foreign atoms has remained elusive. Here, we unravel the critical roles of individual Sc substitutional atoms in modulating ferroelectricity at the atomic scale of typical multiferroics, Lu 1–x Sc x FeO 3 , by combining advanced microscopy and theoretical studies. Atomic variations in polar displacement of intriguing topological vortex domains stabilized by Sc substitution are directly correlated with Sc atom-mediated local chemical and electronic fluctuations. The local FeO 5 trimerization magnitude and Lu/Sc–O hybridization strength are found to be significantly reinforced by Sc, clarifying the origin of the strong dependence of improper ferroelectricity on Sc content. We find that this study could pave the way for correlating dopant-regulated atomic-scale local structures with global properties to engineer emergent functionalities of numerous chemically doped functional materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Manipulating Ferroelectric Topological Polar Structures with Twisted Light
Abstract The dynamic control of non‐equilibrium states represents a central challenge in condensed matter physics. While intense terahertz fields drive metal‐insulator transitions and ferroelectricity via soft phonon modes, recent theory suggests that twisted light with orbital angular momentum (OAM) offers a distinct route to manipulate ferroelectric order and stabilize topological excitations including skyrmions, vortices, and Hopfions. Control of ferroelectric polarization in quasi‐2D CsBiNb 2 O 7 (CBNO) is demonstrated using non‐resonant twisted ultra‐violet (UV) light (375 nm, 800 THz). Combining in situ X‐ray Bragg coherent diffractive imaging (BCDI), twisted optical Raman spectroscopy, and density functional theory (DFT), three‐dimensional (3D) ionic displacements, strain fields, and polarization changes are resolved in single crystals. Operando measurements reveal light‐induced strain hysteresis under twisted light–a hallmark of nonlinear, history‐dependent ferroelastic switching driven by OAM. Discrete, irreversible domain transitions emerge as the topological charge ℓ is cycled, stabilizing non‐trivial domain textures including vortex‐antivortex pairs, Bloch/anti‐Bloch points, and merons. These persist after OAM removal, indicating a memory effect. Competing mechanisms are discussed, including multiphoton absorption, strain‐mediated polarization switching, and defect‐wall interactions. The findings establish structured light as a tool for deterministic, reversible control of ferroic states, enabling optically reconfigurable non‐volatile devices.
Chemistry↗
The emergence of three-dimensional chiral domain walls in polar vortices
Abstract Chirality or handedness of a material can be used as an order parameter to uncover the emergent electronic properties for quantum information science. Conventionally, chirality is found in naturally occurring biomolecules and magnetic materials. Chirality can be engineered in a topological polar vortex ferroelectric/dielectric system via atomic-scale symmetry-breaking operations. We use four-dimensional scanning transmission electron microscopy (4D-STEM) to map out the topology-driven three-dimensional domain walls, where the handedness of two neighbor topological domains change or remain the same. The nature of the domain walls is governed by the interplay of the local perpendicular (lateral) and parallel (axial) polarization with respect to the tubular vortex structures. Unique symmetry-breaking operations and the finite nature of domain walls result in a triple point formation at the junction of chiral and achiral domain walls. The unconventional nature of the domain walls with triple point pairs may result in unique electrostatic and magnetic properties potentially useful for quantum sensing applications.
36 MATERIALS SCIENCE↗
Atomic Scale Crystal Field Mapping of Polar Vortices in Oxide Superlattices
Polar vortices in oxide superlattices can be utilized as potential candidates for data storage applications due to their unique polarization topologies. The structure and dipole arrangement in polar vortices has been studied via X-ray scattering techniques, (scanning) transmission electron microscopy ((S)/TEM) and computational calculations. However, the fundamental correlation between the atomic structure and the electronic structure (which is manifested in the chemical bonding) has heretofore not been explored. Further, The hybridization between nominally empty $\textit{d}$ orbitals on the B-site with the occupied O 2$\textit{p}$ orbitals favors the condensation of a polar (ferroelectric) state in $\textit{AB}$O 3 perovskite oxides. The complex, continuously rotating local polarization texture of the vortices, in turn, can result in especially intricate $\textit{d}$- orbital interactions. Soft X-ray spectroscopy can probe these interactions at the transition metal $\textit{L}$-edge, but these techniques do not have the spatial resolution to resolve variations within one vortex (~5 nm region). Electron energy loss spectroscopy (EELS) in the STEM mode uses inelastically scattered electrons to probe the core-shell excitations (empty density of states) of transition metals at atomic resolution.
74 ATOMIC AND MOLECULAR PHYSICS↗
Subterahertz collective dynamics of polar vortices
The collective dynamics of topological structures are of interest from both fundamental and applied perspectives. For example, studies of dynamical properties of magnetic vortices and skyrmions have not only deepened our understanding of many-body physics but also offered potential applications in data processing and storage. Topological structures constructed from electrical polarization, rather than electron spin, have recently been realized in ferroelectric superlattices, and these are promising for ultrafast electric-field control of topological orders. However, little is known about the dynamics underlying the functionality of such complex extended nanostructures. In this study, using terahertz-field excitation and femtosecond X-ray diffraction measurements, we observe ultrafast collective polarization dynamics that are unique to polar vortices, with orders-of-magnitude higher frequencies and smaller lateral size than those of experimentally realized magnetic vortices. A previously unseen tunable mode, hereafter referred to as a vortexon, emerges in the form of transient arrays of nanoscale circular patterns of atomic displacements, which reverse their vorticity on picosecond timescales. Its frequency is considerably reduced (softened) at a critical strain, indicating a condensation (freezing) of structural dynamics. We use first-principles-based atomistic calculations and phase-field modelling to reveal the microscopic atomic arrangements and corroborate the frequencies of the vortex modes. The discovery of subterahertz collective dynamics in polar vortices opens opportunities for electric-field-driven data processing in topological structures with ultrahigh speed and density.
36 MATERIALS SCIENCE↗
Nanoscale strain wave generation by a piezoelectric grating from polar vortices
Nanostructures formed by spontaneously broken symmetry have provided new ways to manipulate quantum states. Specifically, topological structures with periodic spatial ordering, such as polar vortices and skyrmions, can be ideal hosts for creating engineered responses in both spatial and frequency domains. So far, however, only a few examples of such hierarchical engineering have been reported in the literature. Here we demonstrate that the spatially modulated piezoelectric response of a polar vortex structure can create strain waves with a characteristic nanoscale wavefront. Using time-resolved pump–probe resonant X-ray scattering and diffraction measurements, coupled with dynamical phase-field simulations, we show that the piezoelectric modulation of the spontaneously formed polar vortex crystal functions as an acoustic diffraction grating. This system converts incoming laterally uniform strain waves into outgoing waves with a characteristic sub-terahertz frequency, driven by an intrinsic excitation of the polar vortex crystal. Moreover, our phase-field simulations suggest that the dynamic mechanical displacements exhibiting vortex textures are generated from both space- and time-varying piezoelectric responses. Our findings illustrate a new method for generating nanoscale strain waves with unique spatial textures by tuning the hierarchical order of polar topologies to engineer new collective modes, allowing for a wide range of control through the topological lattice.
ferroelectrics↗