Subterahertz collective dynamics of polar vortices

Continuously Tuning Negative Capacitance via Field-Driven Polar Skyrmions in Ferroelectric Trilayer Wrinkled Films

Polar topological structures have emerged as a frontier in research due to their significant potential in nanoscale electronic devices. The periodic and ordered arrangement, as well as the dynamic control mechanisms, are essential for their practical applications. Here, we present theoretical phase-field simulations that reveal the periodic and ordered arrangement of skyrmions and in-plane vortices within (SrTiO3)10/(PbTiO3)10/(SrTiO3)10 checkerboard-patterned wrinkled trilayer films. Each skyrmion wall exhibits a stable negative capacitance that significantly enhances the effective dielectric permittivity. The negative capacitance results from polarization reversal at the domain walls under small electric field perturbations, closely linked to the depolarization field. The direction of the external electric field can determine the location of the negative capacitance region, which is not strictly confined to the original domain walls but exhibits a shift. These topologically protected structures undergo reversible phase transitions from skyrmion and vortex states to a uniform ferroelectric state under the influence of electric fields and strain, accompanied by highly tunable permittivity. This interplay between topological structures and dielectric characteristics in flexible ferroelectric films offers the opportunity to simultaneously manipulate both topological and dielectric properties through external stimuli, thereby broadening the design possibilities for flexible electronic materials.

Polar topology in self-assembled PbTiO3 ferroelectric nano-islands

The topological domains in ferroelectrics have garnered significant attention for their potential applications in nanoelectronics. However, current research is predominantly limited to rhombohedral BiFeO3 materials. To validate the universality of topological domains in non-rhombohedral ferroelectrics, it is crucial to explore the existence and characteristics of topological states in alternative material systems. In this work we successfully construct topological polar structures in PbTiO3 nano-islands with a tetragonal structure. Furthermore, the topological structures can be well manipulated by electric field and mechanical stress, making them switchable between center-divergent structure and center-converging types. Phase-field simulations revealed that the aggregation and redistribution of free charges play a decisive role in the formation and manipulation of topological states. These findings not only verify the feasibility of constructing topological domains in universal ferroelectrics, but also validate the multiple manipulability of these topological domains, displaying their significant potential in high-density nonvolatile memory devices.

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.

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.

Hidden domain boundary dynamics toward crystalline perfection

A central paradigm of nonequilibrium physics concerns the dynamics of heterogeneity and disorder, impacting processes ranging from the behavior of glasses to the emergent functionality of active matter. Understanding these complex mesoscopic systems requires probing the microscopic trajectories associated with irreversible processes, the role of fluctuations and entropy growth, and the timescales on which nonequilibrium responses are ultimately maintained. Approaches that illuminate these processes in model systems may enable a more general understanding of other heterogeneous nonequilibrium phenomena, and potentially define ultimate speed and energy cost limits for information processing technologies. Here, we apply ultrafast single-shot X-ray photon correlation spectroscopy to resolve the nonequilibrium, heterogeneous, and irreversible mesoscale dynamics during a light-induced phase transition in a (PbTiO3)16/(SrTiO3)16 superlattice. Such ferroelectric superlattice systems are a useful platform to study phase transitions and topological dynamics due to their high degree of tunability. This provides an approach for capturing the nucleation of the light-induced phase, the formation of transient mesoscale defects at the boundaries of the nuclei, and the eventual annihilation of these defects, even in systems with complex polarization topologies. We identify a nonequilibrium correlation response spanning >10 orders of magnitude in timescales, with multistep behavior similar to the plateaus observed in supercooled liquids and glasses. We further show how the observed time-dependent long-time correlations can be understood in terms of stochastic and non-Markovian dynamics of domain walls, encoded in waiting-time distributions with power-law tails. This work defines possibilities for probing the nonequilibrium and correlated dynamics of disordered and heterogeneous media.

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.

Anisotropic Ferroelectricity in Polar Vortices

The exotic polarization configurations of topologically protected dipolar textures have opened new avenues for realizing novel phenomena absent in traditional ferroelectric systems. While multiple recent studies have revealed a diverse array of emergent properties in such polar topologies, the details of their atomic and mesoscale structures remain incomplete. Through atomic- and meso-scale imaging techniques, the emergence of a macroscopic ferroelectric polarization along both principal axes of the vortex lattice while performing phase-field modeling to probe the atomic scale origins of these distinct polarization components is demonstrated. Additionally, due to the anisotropic epitaxial strain, the polarization switching behavior perpendicular and parallel to the vortices is highly anisotropic, with switching along the vortex axes occurring over numerous decades in field-pulse width. This slow switching process allows for the deterministic control of the polarization state, enabling a non-volatile, multi-state memory with excellent distinguishability and long retention times.

Polar vortex hidden in twisted bilayers of paraelectric SrTiO3

Polar topologies, such as vortex and skyrmion, have attracted significant interest due to their unique physical properties and promising applications in high-density memory devices. To date, all known polar vortices are present in or induced by ferroelectric materials. In this study, we find polar vortex arrays in paraelectric SrTiO3. Using multislice electron ptychography, the evolution of vorticity along the vortex axis is revealed in twisted bilayers of SrTiO3 with deep-sub-angstrom resolution and one picometer accuracy. The surprising finding of polar vortices in a paraelectric crystal opens up opportunities for polarization physics and corresponding new devices.

Highly Responsive Polar Vortices in All-Ferroelectric Heterostructures

The discovery of polar vortices and skyrmions in ferroelectric-dielectric superlattices [such as (PbTiO3)n/(SrTiO3)n] has ushered in an era of novel dipolar topologies and corresponding emergent phenomena. The key to creating such emergent features has generally been considered to be related to counterpoising strongly polar and non-polar materials thus creating the appropriate boundary conditions. This limits the utility these materials can have, however, by rendering (effectively) half of the structure unresponsive to applied stimuli. Here, using advanced thin-film deposition and an array of characterization and simulation approaches, polar vortices are realized in all-ferroelectric trilayers, multilayers, and superlattices built from the fundamental building block of (PbTiO3)n/(PbxSr1- xTiO3)n wherein in-plane ferroelectric polarization in the PbxSr1- xTiO3 provides the appropriate boundary conditions. These superlattices exhibit substantially enhanced electromechanical and ferroelectric responses in the out-of-plane direction that arise from the ability of the polarization in both layers to rotate to the out-of-plane direction under field. In the in-plane direction, the layers are found to be strongly coupled during switching and when heterostructured with ferroelectric-dielectric building blocks, it is possible to produce multistate switching. This approach expands the realm of systems supporting emergent dipolar texture formation and does so with entirely ferroelectric materials thus greatly improving their responses.

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.

Dynamical Manipulation of Polar Topologies from Acoustic Phonon Excitations

Since the recent discovery of polar topologies, a recurrent question has been how to remotely tune them. Many efforts have focused on the pumping of polar optical phonons from optical methods, but with limited success, as only switching between specific phases has been achieved so far. Additionally, the correlation between optical pulse characteristics and the resulting phase is poorly understood. Here, we propose an alternative approach and demonstrate the deterministic and dynamical tailoring of polar topologies using acoustic phonon excitations. Our second-principles simulations reveal that by pumping specific longitudinal and transverse acoustic phonons, various topological textures can be induced in materials like BaTiO3 or PbTiO3. This method leverages the strong coupling between polarization and strain in these materials, enabling predictable and dynamic control of polar patterns. Our findings open up an alternative possibility for the manipulation of polar textures, suggesting a promising research direction.

Non-equilibrium pathways to emergent polar supertextures

Ultrafast stimuli can stabilize metastable states of matter inaccessible by equilibrium means. Establishing the spatiotemporal link between ultrafast excitation and metastability is crucial to understand these phenomena. Here we utilize single-shot optical pump-X-ray probe measurements to capture snapshots of the emergence of a persistent polar vortex supercrystal in a heterostructure that hosts a fine balance between built-in electrostatic and elastic frustrations by design. By perturbing this balance with photoinduced charges, an initially heterogeneous mixture of polar phase disorders within a few picoseconds, leading to a state composed of disordered ferroelectric and suppressed vortex orders. On the picosecond-nanosecond timescales, transient labyrinthine fluctuations develop, accompanied by the recovery of the vortex order. On longer timescales, these fluctuations are progressively quenched by dynamical strain modulations, which drive the collective emergence of a single vortex supercrystal phase. Our results, corroborated by dynamical phase-field modelling, reveal non-equilibrium pathways following the ultrafast excitation of designer systems to persistent metastability.

Intrinsic dipole Hall effect in twisted MoTe2: magnetoelectricity and contact-free signatures of topological transitions

We discover an intrinsic dipole Hall effect in a variety of magnetic insulating states at integer fillings of twisted MoTe2 moiré superlattice, including topologically trivial and nontrivial ferro-, antiferro-, and ferri-magnetic configurations. The dipole Hall current, in linear response to in-plane electric field, generates an in-plane orbital magnetization M∥ along the field, through which an AC field can drive magnetization oscillation up to THz range. Upon the continuous topological phase transitions from trivial to quantum anomalous Hall states in both ferromagnetic and antiferromagnetic configurations, the dipole Hall current and M∥ have an abrupt sign change, enabling contact-free detection of the transitions through the magnetic stray field. In configurations where the linear response is forbidden by symmetry, the dipole Hall current and M∥ appear as a crossed nonlinear response to both in-plane and out-of-plane electric fields. These magnetoelectric phenomena showcase fascinating functionalities of insulators from the interplay between magnetism, topology, and electrical polarization.

Dynamics of Polar Vortex Crystallization

Vortex crystals are commonly observed in ultrathin ferroelectrics. However, a clear physical picture of origin of this topological state is currently lacking. Here, we show that vortex crystallization in ultrathin Pb(Zr_{0.4},Ti_{0.6})O_{3} films stems from the softening of a phonon mode and can be described as a Z_{2}×SU(1) symmetry-breaking transition. This result sheds light on the topology of the polar vortex patterns and bridges polar vortices with smectic phases, spin spirals, and other modulated states. Finally, we predict a resonant switching of the vortex tube orientation driven by midinfrared laser light which could enable new technologies.

Optical Control of Adaptive Nanoscale Domain Networks

Adaptive networks can sense and adjust to dynamic environments to optimize their performance. Understanding their nanoscale responses to external stimuli is essential for applications in nanodevices and neuromorphic computing. However, it is challenging to image such responses on the nanoscale with crystallographic sensitivity. Here, the evolution of nanodomain networks in (PbTiO3)n/(SrTiO3)n superlattices (SLs) is directly visualized in real space as the system adapts to ultrafast repetitive optical excitations that emulate controlled neural inputs. The adaptive response allows the system to explore a wealth of metastable states that are previously inaccessible. Their reconfiguration and competition are quantitatively measured by scanning x-ray nanodiffraction as a function of the number of applied pulses, in which crystallographic characteristics are quantitatively assessed by assorted diffraction patterns using unsupervised machine-learning methods. The corresponding domain boundaries and their connectivity are drastically altered by light, holding promise for light-programable nanocircuits in analogy to neuroplasticity. Phase-field simulations elucidate that the reconfiguration of the domain networks is a result of the interplay between photocarriers and transient lattice temperature. The demonstrated optical control scheme and the uncovered nanoscopic insights open opportunities for the remote control of adaptive nanoscale domain networks.

A comparative review of time-resolved x-ray and electron scattering to probe structural dynamics

The structure of molecules, particularly the dynamic changes in structure, plays an essential role in understanding physical and chemical phenomena. Time-resolved (TR) scattering techniques serve as crucial experimental tools for studying structural dynamics, offering direct sensitivity to molecular structures through scattering signals. Over the past decade, the advent of x-ray free-electron lasers (XFELs) and mega-electron-volt ultrafast electron diffraction (MeV-UED) facilities has ushered TR scattering experiments into a new era, garnering significant attention. In this review, we delve into the basic principles of TR scattering experiments, especially focusing on those that employ x-rays and electrons. We highlight the variations in experimental conditions when employing x-rays vs electrons and discuss their complementarity. Additionally, cutting-edge XFELs and MeV-UED facilities for TR x-ray and electron scattering experiments and the experiments performed at those facilities are reviewed. As new facilities are constructed and existing ones undergo upgrades, the landscape for TR x-ray and electron scattering experiments is poised for further expansion. Through this review, we aim to facilitate the effective utilization of these emerging opportunities, assisting researchers in delving deeper into the intricate dynamics of molecular structures.

Artificial Domain Patterning in Ultrathin Ferroelectric Films via Modifying the Surface Electrostatic Boundary Conditions

Nanoscale spatially controlled modulation of the properties of ferroelectrics via artificial domain pattering is crucial to their emerging optoelectronics applications. New patterning strategies to achieve high precision and efficiency and to link the resultant domain structures with device functionalities are being sought. Here, we present an epitaxial heterostructure of SrRuO3/PbTiO3/SrRuO3, wherein the domain configuration is delicately determined by the charge screening conditions in the SrRuO3 layer and the substrate strains. Chemical etching of the top SrRuO3 layer leads to a transition from in-plane a domains to out-of-plane c domains, accompanied by a giant (>105) modification in the second harmonic generation response. The modulation effect, coupled with the plasmonic resonance effect from SrRuO3, enables a highly flexible design of nonlinear optical devices, as demonstrated by a simulated split-ring resonator metasurface. This domain patterning strategy may be extended to more thin-film ferroelectric systems with domain stabilities amenable to electrostatic boundary conditions.

Unconventional Superconducting Diode Effects via Antisymmetry and Antisymmetry Breaking

Symmetry breaking plays a pivotal role in unlocking intriguing properties and functionalities in material systems. For example, the breaking of spatial and temporal symmetries leads to a fascinating phenomenon: the superconducting diode effect. However, generating and precisely controlling the superconducting diode effect pose significant challenges. Here, we take a novel route with the deliberate manipulation of magnetic charge potentials to realize unconventional superconducting flux-quantum diode effects. We achieve this through suitably tailored nanoengineered arrays of nanobar magnets on top of a superconducting thin film. We demonstrate the vital roles of inversion antisymmetry and its breaking in evoking unconventional superconducting effects, namely a magnetically symmetric diode effect and an odd-parity magnetotransport effect. These effects are nonvolatilely controllable through in situ magnetization switching of the nanobar magnets. Our findings promote the use of antisymmetry (breaking) for initiating unconventional superconducting properties, paving the way for exciting prospects and innovative functionalities in superconducting electronics.

Brownian Electric Bubble Quasiparticles

Recent works on electric bubbles (including the experimental demonstration of electric skyrmions) constitute a breakthrough akin to the discovery of magnetic skyrmions some 15 years ago. So far research has focused on obtaining and visualizing these objects, which often appear to be immobile (pinned) in experiments. Thus, critical aspects of magnetic skyrmions-e.g., their quasiparticle nature, Brownian motion-remain unexplored (unproven) for electric bubbles. Here we use predictive atomistic simulations to investigate the basic dynamical properties of these objects in pinning-free model systems. We show that it is possible to find regimes where the electric bubbles can present long lifetimes (∼ns) despite being relatively small (diameter <2  nm). Additionally, we find that they can display stochastic dynamics with large and highly tunable diffusion constants. We thus establish the quasiparticle nature of electric bubbles and put them forward for the physical effects and applications (e.g., in token-based probabilistic computing) considered for magnetic skyrmions.

Giant electric field-induced second harmonic generation in polar skyrmions

Electric field-induced second harmonic generation allows electrically controlling nonlinear light-matter interactions crucial for emerging integrated photonics applications. Despite its wide presence in materials, the figures-of-merit of electric field-induced second harmonic generation are yet to be elevated to enable novel device functionalities. Here, we show that the polar skyrmions, a topological phase spontaneously formed in PbTiO3/SrTiO3 ferroelectric superlattices, exhibit a high comprehensive electric field-induced second harmonic generation performance. The second-order nonlinear susceptibility and modulation depth, measured under non-resonant 800 nm excitation, reach ~54.2 pm V-1 and ~664% V-1, respectively, and high response bandwidth (higher than 10 MHz), wide operating temperature range (up to ~400 K) and good fatigue resistance (>1010 cycles) are also demonstrated. Through combined in-situ experiments and phase-field simulations, we establish the microscopic links between the exotic polarization configuration and field-induced transition paths of the skyrmions and their electric field-induced second harmonic generation response. Our study not only presents a highly competitive thin-film material ready for constructing on-chip devices, but opens up new avenues of utilizing topological polar structures in the fields of photonics and optoelectronics.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Terahertz radiation by quantum interference of excitons in a one-dimensional Mott insulator

Nearly monocyclic terahertz waves are used for investigating elementary excitations and for controlling electronic states in solids. They are usually generated via second-order optical nonlinearity by injecting a femtosecond laser pulse into a nonlinear optical crystal. In this framework, however, it is difficult to control phase and frequency of terahertz waves. Here, we show that in a one-dimensional Mott insulator of a nickel-bromine chain compound a terahertz wave is generated with high efficiency via strong electron modulations due to quantum interference between odd-parity and even-parity excitons produced by two-color femtosecond pulses. Using this method, one can control all of the phase, frequency, and amplitude of terahertz waves by adjusting the creation-time difference of two excitons with attosecond accuracy. This approach enables to evaluate the phase-relaxation time of excitons under strong electron correlations in Mott insulators. Moreover, phase- and frequency-controlled terahertz pulses are beneficial for coherent electronic-state controls with nearly monocyclic terahertz waves.

Polar Solomon rings in ferroelectric nanocrystals

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

A universal route to efficient non-linear response via Thomson scattering in linear solids

Non-linear materials are cornerstones of modern optics and electronics. Strong dependence on the intrinsic properties of particular materials, however, inhibits the at-will extension of demanding non-linear effects, especially those second-order ones, to widely adopted centrosymmetric materials (for example, silicon) and technologically important burgeoning spectral domains (for example, terahertz frequencies). Here we introduce a universal route to efficient non-linear responses enabled by exciting non-linear Thomson scattering, a fundamental process in electrodynamics that was known to occur only in relativistic electrons in metamaterial composed of linear materials. Such a mechanism modulates the trajectory of charges, either intrinsically or extrinsically provided in solids, at twice the driving frequency, allowing second-harmonic generation at terahertz frequencies on crystalline silicon with extremely large non-linear susceptibility in our proof-of-concept experiments. By offering a substantially material- and frequency-independent platform, our approach opens new possibilities in the fields of on-demand non-linear optics, terahertz sources, strong field light-solid interactions and integrated photonic circuits.

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.

Generation of 13.9-mJ Terahertz Radiation from Lithium Niobate Materials

Extremely strong-field terahertz (THz) radiation in free space has compelling applications in nonequilibrium condensed matter state regulation, all-optical THz electron acceleration and manipulation, THz biological effects, etc. However, these practical applications are constrained by the absence of high-intensity, high-efficiency, high-beam-quality, and stable solid-state THz light sources. Here, the generation of single-cycle 13.9-mJ extreme THz pulses from cryogenically cooled lithium niobate crystals and a 1.2% energy conversion efficiency from 800 nm to THz are demonstrated experimentally using the tilted pulse-front technique driven by a home-built 30-fs, 1.2-Joule Ti:sapphire laser amplifier. The focused peak electric field strength is estimated to be 7.5 MV cm^-1 . A record of 1.1-mJ THz single-pulse energy at a 450 mJ pump at room temperature is produced and observed that the self-phase modulation of the optical pump can induce THz saturation behavior from the crystals in the substantially nonlinear pump regime. This study lays the foundation for the generation of sub-Joule THz radiation from lithium niobate crystals and will inspire more innovations in extreme THz science and applications.

Emergent Ferroelectric Switching Behavior from Polar Vortex Lattice

Topologically protected polar textures have provided a rich playground for the exploration of novel, emergent phenomena. Recent discoveries indicate that ferroelectric vortices and skyrmions not only host properties markedly different from traditional ferroelectrics, but also that these properties can be harnessed for unique memory devices. Using a combination of capacitor-based capacitance measurements and computational models, it is demonstrated that polar vortices in dielectric-ferroelectric-dielectric trilayers exhibit classical ferroelectric bi-stability together with the existence of low-field metastable polarization states. This behavior is directly tied to the in-plane vortex ordering, and it is shown that it can be used as a new method of non-destructive readout-out of the poled state.

Ultrafast strong-field terahertz nonlinear nanometasurfaces

Strong-field terahertz (THz)-matter interaction permits the investigation of nonequilibrium behaviors in the nonperturbative zone. However, the unavailability of a high-field free-space THz source with high repetition rates, excellent beam quality, and high stability hinders its development. In this work, we obtain the nonlinear modulation dynamics of a "THz-nano" metasurface on silicon substrates using a time-resolved strong-field THz-pump THz-probe (TPTP) with a thousand orders local field enhancement through confining THz waves into nano-gaps (15 nm, λ/33,000). By switching the THz field strength, we successfully realize a self-modulation ∼50 GHz frequency shift, which is further verified via the TPTP ultrafast time-resolution technique. The phenomenon is attributed to the impact ionization (IMI) of the silicon substrate under the excitation of extremely confined strong THz fields in nano-gaps. Both strong-field induced intervalley scattering (IVS) and IMI effects of photodoped silicon occurring in nano-gaps and large-area substrates were also observed by 800 nm optical injection of carriers. These aforementioned findings provide a robust research platform for the realization of ultrafast time resolution nanoscale strong-field THz-matter interaction and new ideas for nonextreme laboratories to realize extreme THz science, applications, and THz nonlinear modulation device development.

Thermodynamics of Light-Induced Nanoscale Polar Structures in Ferroelectric Superlattices

We study the thermodynamics of nanoscale polar structures in PbTiO₃/SrTiO₃ ferroelectric superlattices induced by above-bandgap optical excitation using a phase-field model explicitly considering both structural and electronic processes. We demonstrate that the light-excited carriers provide the charge compensation of polarization bound charges and the lattice thermal energy, both of which are key to the thermodynamic stabilization of a previously observed supercrystal, a three-dimensionally periodic nanostructure, within a window of substrate strains, while different mechanical and electrical boundary conditions can stabilize a number of other nanoscale polar structures by balancing the competing short-range exchange interactions responsible for the domain wall energy and long-range electrostatic and elastic interactions. The insights into the light-induced formation and richness of nanoscale structures from this work offer theoretical guidance for exploring and manipulating the thermodynamic stability of nanoscale polar structures employing a combination of thermal, mechanical, and electrical stimuli as well as light.

Polarization Switching and Correlated Phase Transitions in Fluorite-Structure ZrO2 Nanocrystals

Unconventional ferroelectricity in fluorite-structure oxides enables tremendous opportunities in nanoelectronics owing to their superior scalability and silicon compatibility. However, their polarization order and switching process remain elusive due to the challenges of visualizing oxygen ions in nanocrystalline films. In this work, the oxygen shifting during polarization switching and correlated polar-nonpolar phase transitions are directly captured among multiple metastable phases in freestanding ZrO₂ thin films by low-dose integrated differential phase-contrast scanning transmission electron microscopy (iDPC-STEM). Bidirectional transitions between antiferroelectric and ferroelectric orders and interfacial polarization relaxation are clarified at unit-cell scale. Meanwhile, polarization switching is strongly correlated with Zr-O displacement in reversible martensitic transformation between monoclinic and orthorhombic phases and two-step tetrahedral-to-orthorhombic phase transition. These findings provide atomic insights into the transition pathways between metastable polymorphs and unravel the evolution of polarization orders in (anti)ferroelectric fluorite oxides.

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.

Dynamics of Polar Skyrmion Bubbles under Electric Fields

Room-temperature polar skyrmions, which have been recently discovered in oxide superlattice, have received considerable attention for their potential applications in nanoelectronics owing to their nanometer size, emergent chirality, and negative capacitance. For practical applications, their manipulation using external stimuli is a prerequisite. Herein, we study the dynamics of individual polar skyrmions at the nanoscale via in situ scanning transmission electron microscopy. By monitoring the electric-field-driven creation, annihilation, shrinkage, and expansion of topological structures in real space, we demonstrate the reversible transformation among skyrmion bubbles, elongated skyrmions, and monodomains. The underlying mechanism and interactions are discussed in conjunction with phase-field simulations. The electrical manipulation of nanoscale polar skyrmions allows the tuning of their dielectric permittivity at the atomic scale, and the detailed knowledge of their phase transition behaviors provides fundamentals for their applications in nanoelectronics.

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.

Ferroelectric/paraelectric superlattices for energy storage

The polarization response of antiferroelectrics to electric fields is such that the materials can store large energy densities, which makes them promising candidates for energy storage applications in pulsed-power technologies. However, relatively few materials of this kind are known. Here, we consider ferroelectric/paraelectric superlattices as artificial electrostatically engineered antiferroelectrics. Specifically, using high-throughput second-principles calculations, we engineer PbTiO₃/SrTiO₃ superlattices to optimize their energy storage performance at room temperature (to maximize density and release efficiency) with respect to different design variables (layer thicknesses, epitaxial conditions, and stiffness of the dielectric layer). We obtain results competitive with the state-of-the-art antiferroelectric capacitors and reveal the mechanisms responsible for the optimal properties.

Thin-Film Ferroelectrics

Over the last 30 years, the study of ferroelectric oxides has been revolutionized by the implementation of epitaxial-thin-film-based studies, which have driven many advances in the understanding of ferroelectric physics and the realization of novel polar structures and functionalities. New questions have motivated the development of advanced synthesis, characterization, and simulations of epitaxial thin films and, in turn, have provided new insights and applications across the micro-, meso-, and macroscopic length scales. This review traces the evolution of ferroelectric thin-film research through the early days developing understanding of the roles of size and strain on ferroelectrics to the present day, where such understanding is used to create complex hierarchical domain structures, novel polar topologies, and controlled chemical and defect profiles. The extension of epitaxial techniques, coupled with advances in high-throughput simulations, now stands to accelerate the discovery and study of new ferroelectric materials. Coming hand-in-hand with these new materials is new understanding and control of ferroelectric functionalities. Today, researchers are actively working to apply these lessons in a number of applications, including novel memory and logic architectures, as well as a host of energy conversion devices.

Spintronic terahertz emission with manipulated polarization (STEMP)

Highly efficient generation and arbitrary manipulation of spin-polarized terahertz (THz) radiation will enable chiral lightwave driven quantum nonequilibrium state regulation, induce new electronic structures, consequently provide a powerful experimental tool for investigation of nonlinear THz optics and extreme THz science and applications. THz circular dichromic spectroscopy, ultrafast electron bunch manipulation, as well as THz imaging, sensing, and telecommunication, also need chiral THz waves. Here we review optical generation of circularly-polarized THz radiation but focus on recently emerged polarization tunable spintronic THz emission techniques, which possess many advantages of ultra-broadband, high efficiency, low cost, easy for integration and so on. We believe that chiral THz sources based on the combination of electron spin, ultrafast optical techniques and material structure engineering will accelerate the development of THz science and 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.

Optical generation of strong-field terahertz radiation and its application in nonlinear terahertz metasurfaces

Extremely nonlinear terahertz (THz)-matter interactions and applications have positioned themselves as the next frontier in quantum information, nonlinear optics, and particle acceleration. However, the absence of free-space highly intense THz sources and the diffraction limit, which prevents THz waves from being concentrated to the nanoscale scale, are inhibiting the growth of extreme THz. To address this difficulty, suitably extremely concentrated THz sources are being produced, while (non-)resonant artificial metastructures are being widely used to enhance local fields, resulting in deep-subwavelength (<λ/103) confinement of highly enhanced THz fields in micro-/nano-gaps. We discuss solid-state stable sources of intense THz radiation generated by femtosecond lasers in this Review, with a special emphasis on the lithium niobate-based tilted pulse front approach and the nonlinear THz metasurfaces allowed by it. Finally, we forecast the field's future directions in extreme THz research.