Optical creation of a supercrystal with three-dimensional nanoscale periodicity

Liquid-Crystal-Like Dynamic Transition in Ferroelectric-Dielectric Superlattices

Nanostructured ferroelectrics display exotic multidomain configurations resulting from the electrostatic and elastic boundary conditions they are subject to. While the ferroelectric domains appear frozen in experimental images, atomistic second-principles studies suggest that they may become spontaneously mobile upon heating, with the polar order melting in a liquidlike fashion. Here, we run molecular dynamics simulations of model systems (PbTiO_{3}/SrTiO_{3} superlattices) to study the unique features of this transformation. Most notably, we find that the multidomain state loses its translational and orientational orders at different temperatures, resembling the behavior of liquid crystals and yielding an intermediate hexaticlike phase. Our simulations reveal the mechanism responsible for the melting and allow us to characterize the stochastic dynamics in the hexaticlike phase: we find evidence that it is thermally activated, with domain reorientation rates that grow from tens of gigahertzs to terahertzs in a narrow temperature window.

Spontaneous Supercrystal Formation During a Strain-Engineered Metal-Insulator Transition

Mott metal-insulator transitions possess electronic, magnetic, and structural degrees of freedom promising next-generation energy-efficient electronics. A previously unknown, hierarchically ordered, and anisotropic supercrystal state is reported and its intrinsic formation characterized in-situ during a Mott transition in a Ca2RuO4 thin film. Machine learning-assisted X-ray nanodiffraction together with cryogenic electron microscopy reveal multi-scale periodic domain formation at and below the film transition temperature (TFilm ≈ 200-250 K) and a separate anisotropic spatial structure at and above TFilm. Local resistivity measurements imply an intrinsic coupling of the supercrystal orientation to the material's anisotropic conductivity. These findings add a new degree of complexity to the physical understanding of Mott transitions, opening opportunities for designing materials with tunable electronic properties.

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.

Ultralow Strain-Induced Emergent Polarization Structures in a Flexible Freestanding BaTiO3 Membrane

The engineering of ferroic orders, which involves the evolution of atomic structure and local ferroic configuration in the development of next-generation electronic devices. Until now, diverse polarization structures and topological domains are obtained in ferroelectric thin films or heterostructures, and the polarization switching and subsequent domain nucleation are found to be more conducive to building energy-efficient and multifunctional polarization structures. In this work, a continuous and periodic strain in a flexible freestanding BaTiO3 membrane to achieve a zigzag morphology is introduced. The polar head/tail boundaries and vortex/anti-vortex domains are constructed by a compressive strain as low as ≈0.5%, which is extremely lower than that used in epitaxial rigid ferroelectrics. Overall, this study c efficient polarization structures, which is of both theoretical value and practical significance for the development of next-generation flexible multifunctional devices.

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.

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.

Implementation of a laser-neutron pump-probe capability for inelastic neutron scattering

Knowledge about nonequilibrium dynamics in spin systems is of great importance to both fundamental science and technological applications. Inelastic neutron scattering (INS) is an indispensable tool to study spin excitations in complex magnetic materials. However, conventional INS spectrometers currently only perform steady-state measurements and probe averaged properties over many collision events between spin excitations in thermodynamic equilibrium, while the exact picture of re-equilibration of these excitations remains unknown. In this paper, we report on the design and implementation of a time-resolved laser-neutron pump-probe capability at hybrid spectrometer (beamline 14-B) at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory. This capability allows us to excite out-of-equilibrium magnons with a nanosecond pulsed laser source and probe the resulting dynamics using INS. Here, we discussed technical aspects to implement such a capability in a neutron beamline, including choices of suitable neutron instrumentation and material systems, laser excitation scheme, experimental configurations, and relevant firmware and software development to allow for time-synchronized pump-probe measurements. We demonstrated that the laser-induced nonequilibrium structure factor is able to be resolved by INS in a quantum magnet. The method developed in this work will provide SNS with advanced capabilities for performing out-of-equilibrium measurements, opening up an entirely new research direction to study out-of-equilibrium phenomena using neutrons.

Evidence of 3D Topological-Domain Dynamics in KTN:Li Polarization-Supercrystal Formation

We experimentally and theoretically investigate thermal domain evolution in near-transition KTN:Li. Results allow us to establish how polarization supercrystals form, a hidden 3D topological phase composed of hypervortex defects. These are the result of six converging polarization vortices, each associated to one orientation of the 3D broken inversion symmetry. We also identify rescaling soliton lattices and domain patterns that replicate on different scales. Findings shed light on volume domain self-organization into closed-flux patterns and open up new scenarios for topologically protected noise-resistant ferroelectric memory bits.

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.

Ultrafast Switching of Interfacial Thermal Conductance

Dynamical control of thermal transport at the nanoscale provides a time-domain strategy for optimizing thermal management in nanoelectronics, magnetic devices, and thermoelectric devices. However, the rate of change available for thermal switches and regulators is limited to millisecond time scales, calling for a faster modulation speed. Here, time-resolved X-ray diffraction measurements and thermal transport modeling reveal an ultrafast modulation of the interfacial thermal conductance of an FeRh/MgO heterostructure as a result of a structural phase transition driven by optical excitation. Within 90 ps after optical excitation, the interfacial thermal conductance is reduced by a factor of 5 and lasts for a few nanoseconds, in comparison to the value at the equilibrium FeRh/MgO interface. The experimental results combined with thermal transport calculations suggest that the reduced interfacial thermal conductance results from enhanced phonon scattering at the interface where the lattice experiences transient in-plane biaxial stress due to the structural phase transition of FeRh. Our results suggest that optically driven phase transitions can be utilized for ultrafast nanoscale thermal switches for device application.

Induction and Ferroelectric Switching of Flux Closure Domains in Strained PbTiO3 with Neural Network Quantum Molecular Dynamics

We have developed an extension of the Neural Network Quantum Molecular Dynamics (NNQMD) simulation method to incorporate electric-field dynamics based on Born effective charge (BEC), called NNQMD-BEC. We first validate NNQMD-BEC for the switching mechanisms of archetypal ferroelectric PbTiO3 bulk crystal and 180° domain walls (DWs). NNQMD-BEC simulations correctly describe the nucleation-and-growth mechanism during DW switching. In triaxially strained PbTiO3 with strain conditions commonly seen in many superlattice configurations, we find that flux-closure texture can be induced with application of an electric field perpendicular to the original polarization direction. Upon field reversal, the flux-closure texture switches via a pair of transient vortices as the intermediate state, indicating an energy-efficient switching pathway. Our NNQMD-BEC method provides a theoretical guidance to study electro-mechano effects with existing machine learning force fields using a simple BEC extension, which will be relevant for engineering applications such as field-controlled switching in mechanically strained ferroelectric devices.

The emergence of three-dimensional chiral domain walls in polar vortices

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.

Real-space imaging of periodic nanotextures in thin films via phasing of diffraction data

New properties and exotic quantum phenomena can form due to periodic nanotextures, including Moire patterns, ferroic domains, and topologically protected magnetization and polarization textures. Despite the availability of powerful tools to characterize the atomic crystal structure, the visualization of nanoscale strain-modulated structural motifs remains challenging. Here, we develop nondestructive real-space imaging of periodic lattice distortions in thin epitaxial films and report an emergent periodic nanotexture in a Mott insulator. Specifically, we combine iterative phase retrieval with unsupervised machine learning to invert the diffuse scattering pattern from conventional X-ray reciprocal-space maps into real-space images of crystalline displacements. Our imaging in PbTiO3/SrTiO3 superlattices exhibiting checkerboard strain modulation substantiates published phase-field model calculations. Furthermore, the imaging of biaxially strained Mott insulator Ca2RuO4 reveals a strain-induced nanotexture comprised of nanometer-thin metallic-structure wires separated by nanometer-thin Mott-insulating-structure walls, as confirmed by cryogenic scanning transmission electron microscopy (cryo-STEM). The nanotexture in Ca2RuO4 film is induced by the metal-to-insulator transition and has not been reported in bulk crystals. We expect the phasing of diffuse X-ray scattering from thin crystalline films in combination with cryo-STEM to open a powerful avenue for discovering, visualizing, and quantifying the periodic strain-modulated structures in quantum materials.

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.

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.

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.

Interface-related phenomena in epitaxial complex oxide ferroics across different thin film platforms: opportunities and challenges

Interfaces in complex oxides give rise to fascinating new physical phenomena arising from the interconnected spin, lattice, charge and orbital degrees of freedom. Most commonly, interfaces are engineered in epitaxial superlattice films. Of growing interest also are epitaxial vertically aligned nanocomposite films where interfaces form by self-assembly. These two thin film forms offer different capabilities for materials tuning and have been explored largely separately from one another. Ferroics (ferroelectric, ferromagnetic, multiferroic) are among the most fascinating phenomena to be manipulated using interface effects. Hence, in this review we compare and contrast the ferroic properties that arise in these two different film forms, highlighting exemplary materials combinations which demonstrate novel, enhanced and/or emergent ferroic functionalities. We discuss the origins of the observed functionalities and propose where knowledge can be translated from one materials form to another, to potentially produce new functionalities. Finally, for the two different film forms we present a perspective on underexplored/emerging research directions.

Anomalous Optical Properties of KTN:Li Ferroelectric Supercrystals

We report a spectroscopic investigation of potassium-lithium-tantalate-niobate (KTN:Li) across its room-temperature ferroelectric phase transition, when the sample manifests a supercrystal phase. Reflection and transmission results indicate an unexpected temperature-dependent enhancement of average index of refraction from 450 nm to 1100 nm, with no appreciable accompanying increase in absorption. Second-harmonic generation and phase-contrast imaging indicate that the enhancement is correlated to ferroelectric domains and highly localized at the supercrystal lattice sites. Implementing a two-component effective medium model, the response of each lattice site is found to be compatible with giant broadband refraction.

Light-Driven Ultrafast Polarization Manipulation in a Relaxor Ferroelectric

Relaxor ferroelectrics have been intensely studied for decades based on their unique electromechanical responses which arise from local structural heterogeneity involving polar nanoregions or domains. Here, we report first studies of the ultrafast dynamics and reconfigurability of the polarization in freestanding films of the prototypical relaxor 0.68PbMg_1/3Nb_2/3O₃-0.32PbTiO₃ (PMN-0.32PT) by probing its atomic-scale response via femtosecond-resolution, electron-scattering approaches. By combining these structural measurements with dynamic phase-field simulations, we show that femtosecond light pulses drive a change in both the magnitude and direction of the polarization vector within polar nanodomains on few-picosecond time scales. This study defines new opportunities for dynamic reconfigurable control of the polarization in nanoscale relaxor ferroelectrics.

Squishing Skyrmions: Symmetry-Guided Dynamic Transformation of Polar Topologies Under Compression

Mechanical controllability of recently discovered topological defects (e.g., skyrmions) in ferroelectric materials is of interest for the development of ultralow-power mechano-electronics that are protected against thermal noise. However, fundamental understanding is hindered by the "multiscale quantum challenge" to describe topological switching encompassing large spatiotemporal scales with quantum mechanical accuracy. Here, we overcome this challenge by developing a machine-learning-based multiscale simulation framework─a hybrid neural network quantum molecular dynamics (NNQMD) and molecular mechanics (MM) method. For nanostructures composed of SrTiO₃ and PbTiO₃, we find how the symmetry of mechanical loading essentially controls polar topological switching. We find under symmetry-breaking uniaxial compression a squishing-to-annihilation pathway versus formation of a topological composite named skyrmionium under symmetry-preserving isotropic compression. The distinct pathways are explained in terms of the underlying materials' elasticity and symmetry, as well as the Landau-Lifshitz-Kittel scaling law. Such rational control of ferroelectric topologies will likely facilitate exploration of the rich ferroelectric "topotronics" design space.

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.

Snapshots of a light-induced metastable hidden phase driven by the collapse of charge order

Nonequilibrium hidden states provide a unique window into thermally inaccessible regimes of strong coupling between microscopic degrees of freedom in quantum materials. Understanding the origin of these states allows the exploration of far-from-equilibrium thermodynamics and the development of optoelectronic devices with on-demand photoresponses. However, mapping the ultrafast formation of a long-lived hidden phase remains a longstanding challenge since the initial state is not recovered rapidly. Here, using state-of-the-art single-shot spectroscopy techniques, we present a direct ultrafast visualization of the photoinduced phase transition to both transient and long-lived hidden states in an electronic crystal, 1T-TaS₂, and demonstrate a commonality in their microscopic pathways, driven by the collapse of charge order. We present a theory of fluctuation-dominated process that helps explain the nature of the metastable state. Our results shed light on the origin of this elusive state and pave the way for the discovery of other exotic phases of matter.

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.

Exploring far-from-equilibrium ultrafast polarization control in ferroelectric oxides with excited-state neural network quantum molecular dynamics

Ferroelectric materials exhibit a rich range of complex polar topologies, but their study under far-from-equilibrium optical excitation has been largely unexplored because of the difficulty in modeling the multiple spatiotemporal scales involved quantum-mechanically. To study optical excitation at spatiotemporal scales where these topologies emerge, we have performed multiscale excited-state neural network quantum molecular dynamics simulations that integrate quantum-mechanical description of electronic excitation and billion-atom machine learning molecular dynamics to describe ultrafast polarization control in an archetypal ferroelectric oxide, lead titanate. Far-from-equilibrium quantum simulations reveal a marked photo-induced change in the electronic energy landscape and resulting cross-over from ferroelectric to octahedral tilting topological dynamics within picoseconds. The coupling and frustration of these dynamics, in turn, create topological defects in the form of polar strings. The demonstrated nexus of multiscale quantum simulation and machine learning will boost not only the emerging field of ferroelectric topotronics but also broader optoelectronic applications.

High-k perovskite gate oxide for modulation beyond 1014 cm-2

Scaling down of semiconductor devices requires high-k dielectric materials to continue lowering the operating voltage of field-effect transistors (FETs) and storing sufficient charge on a smaller area. Here, we investigate the dielectric properties of epitaxial BaHf_0.6Ti_0.4O₃ (BHTO), an alloy of perovskite oxide barium hafnate (BaHfO₃) and barium titanate (BaTiO₃). We found the dielectric constant, the breakdown field, and the leakage current to be 150, 5.0 megavolts per centimeter (MV cm^-1), and 10^-4 amperes per square centimeter at 2 MV cm^-1, respectively. The results suggest that two-dimensional (2D) carrier density of more than n_2D = 10¹⁴ per square centimeter (cm^-2) could be modulated by the BHTO gate oxide. We demonstrate an n-type accumulation mode FET and direct suppression of more than n_2D = 10¹⁴ cm^-2 via an n-type depletion-mode FET. We attribute the large dielectric constant, high breakdown field, and low leakage current of BHTO to the nanometer scale stoichiometric modulation of hafnium and titanium.

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

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

Light-induced dimension crossover dictated by excitonic correlations

In low-dimensional systems with strong electronic correlations, the application of an ultrashort laser pulse often yields novel phases that are otherwise inaccessible. The central challenge in understanding such phenomena is to determine how dimensionality and many-body correlations together govern the pathway of a non-adiabatic transition. To this end, we examine a layered compound, 1T-TiSe2, whose three-dimensional charge-density-wave (3D CDW) state also features exciton condensation due to strong electron-hole interactions. We find that photoexcitation suppresses the equilibrium 3D CDW while creating a nonequilibrium 2D CDW. Remarkably, the dimension reduction does not occur unless bound electron-hole pairs are broken. This relation suggests that excitonic correlations maintain the out-of-plane CDW coherence, settling a long-standing debate over their role in the CDW transition. Our findings demonstrate how optical manipulation of electronic interaction enables one to control the dimensionality of a broken-symmetry order, paving the way for realizing other emergent states in strongly correlated systems.

Ferroelectric incommensurate spin crystals

Ferroics, especially ferromagnets, can form complex topological spin structures such as vortices¹ and skyrmions^2,3 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 PbTiO₃/SrTiO₃, which was later shown to be a model system owing to its high depolarizing field^4-8. To date, the electric dipole equivalent of ordered magnetic spin lattices driven by the Dzyaloshinskii-Moriya interaction (DMi)^9,10 has not been experimentally observed. Here we examine a domain structure in a single PbTiO₃ epitaxial layer sandwiched between SrRuO₃ electrodes. 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^11-13. These findings further blur the border between emergent ferromagnetic and ferroelectric topologies, clearing the way for experimental realization of further electric counterparts of magnetic DMi-driven phases.

Emergent Fabry-Pérot Interference for Light-Matter Interaction in van der Waals WS2/SiP2 Heterostructures

Fabry-Pérot interference plays an important role in modulating the spectral intensity of optical response originating from light-matter interactions. Examples of such interference occurring in the substrate as the resonating cavity have been demonstrated and probed by two-dimensional layered materials. Similarly, the Fabry-Pérot interference can occur and modulate the optical response in the heterostructure; however, this remains elusive. Herein, we observe the Fabry-Pérot interference on photoluminescence (PL) and Raman spectra in monolayer WS₂/SiP₂ heterostructures by varying the thickness of bottom SiP₂ from 2 to 193 nm, which serves as the Fabry-Pérot cavity. Both the intensities of the PL spectra and the E_2g¹ Raman mode of WS₂/SiP₂ heterostructures first decrease to almost zero while displaying an interference increase at a SiP₂ thickness of 75 nm. Our findings clearly demonstrate the Fabry-Pérot interference in the optical response of heterostructures, providing crucial information to optimize the optical response and paving the way toward photodetector applications.

Inq, a Modern GPU-Accelerated Computational Framework for (Time-Dependent) Density Functional Theory

We present inq, a new implementation of density functional theory (DFT) and time-dependent DFT (TDDFT) written from scratch to work on graphic processing units (GPUs). Besides GPU support, inq makes use of modern code design features and takes advantage of newly available hardware. By designing the code around algorithms, rather than against specific implementations and numerical libraries, we aim to provide a concise and modular code. The result is a fairly complete DFT/TDDFT implementation in roughly 12 000 lines of open-source C++ code representing a modular platform for community-driven application development on emerging high-performance computing architectures.

Probing Ultrafast Dynamics of Ferroelectrics by Time-Resolved Pump-Probe Spectroscopy

Ferroelectric materials have been a key research topic owing to their wide variety of modern electronic and photonic applications. For the quick exploration of higher operating speed, smaller size, and superior efficiencies of novel ferroelectric devices, the ultrafast dynamics of ferroelectrics that directly reflect their respond time and lifetimes have drawn considerable attention. Driven by time-resolved pump-probe spectroscopy that allows for probing, controlling, and modulating dynamic processes of ferroelectrics in real-time, much research efforts have been made to understand and exploit the ultrafast dynamics of ferroelectric. Herein, the current state of ultrafast dynamic features of ferroelectrics tracked by time-resolved pump-probe spectroscopy is reviewed, which includes ferroelectrics order parameters of polarization, lattice, spin, electronic excitation, and their coupling. Several potential perspectives and possible further applications combining ultrafast pump-probe spectroscopy and ferroelectrics are also presented. This review offers a clear guidance of ultrafast dynamics of ferroelectric orders, which may promote the rapid development of next-generation devices.

Laser-Induced Cooperative Transition in Molecular Electronic Crystal

The competing and non-equilibrium phase transitions, involving dynamic tunability of cooperative electronic and magnetic states in strongly correlated materials, show great promise in quantum sensing and information technology. To date, the stabilization of transient states is still in the preliminary stage, particularly with respect to molecular electronic solids. Here, a dynamic and cooperative phase in potassium-7,7,8,8-tetracyanoquinodimethane (K-TCNQ) with the control of pulsed electromagnetic excitation is demonstrated. Simultaneous dynamic and coherent lattice perturbation with 8 ns pulsed laser (532 nm, 15 MW cm^-2 , 10 Hz) in such a molecular electronic crystal initiates a stable long-lived (over 400 days) conducting paramagnetic state (≈42 Ωcm), showing the charge-spin bistability over a broad temperature range from 2 to 360 K. Comprehensive noise spectroscopy, in situ high-pressure measurements, electron spin resonance (ESR), theoretical model, and scanning tunneling microscopy/spectroscopy (STM/STS) studies provide further evidence that such a transition is cooperative, requiring a dedicated charge-spin-lattice decoupling to activate and subsequently stabilize nonequilibrium phase. The cooperativity triggered by ultrahigh-strain-rate (above 10⁶ s^{- 1} ) pulsed excitation offers a collective control toward the generation and stabilization of strongly correlated electronic and magnetic orders in molecular electronic solids and offers unique electro-magnetic phases with technological promises.

Ultrafast Modulations and Detection of a Ferro-Rotational Charge Density Wave Using Time-Resolved Electric Quadrupole Second Harmonic Generation

We show the ferro-rotational nature of the commensurate charge density wave (CCDW) in 1T-TaS_{2} and track its dynamic modulations by temperature-dependent and time-resolved electric quadrupole rotation anisotropy-second harmonic generation (EQ RA-SHG), respectively. The ultrafast modulations manifest as the breathing and the rotation of the EQ RA-SHG patterns at three frequencies around the reported single CCDW amplitude mode frequency. A sudden shift of the triplet frequencies and a dramatic increase in the breathing and rotation magnitude further reveal a photoinduced transient CDW phase across a critical pump fluence of ∼0.5  mJ/cm^{2}.

Study on the phase transition dynamics of HfO2-based ferroelectric films under ultrafast electric pulse

Wake-up effect and fatigue in HfO₂-based ferroelectric films are closely related to the phase transition dynamics of the film subjected to ultrafast electric pulses. Here, we establish a multiphase coexistence phase field dynamics model for HfO₂-based ferroelectric films in the ultrafast time scale and study the effects of the amplitude, width and frequency of the electric pulse on the phase transition dynamics. Based on the simulation results, we obtain the analytical equation of the volume fraction of switchedc-domains under low fields as a function of pulse duration. And we found that monoclinic phase can transform into ferroelectricc-domains under high amplitude electric field (E⩾ 2.8 MV cm^-1). The electric pulse duration affects the film's retention properties. When the duration of the electric pulse is less than 1.2 ns or longer than 1.8 ns, the ferroelectricc-domains will respectively invert into other phases or increase cumulatively after removing the electric field. The frequency of cyclic pulse is related to the degree of wake up effect. The lower the pulse frequency is, the more obvious the 'wake up' effect is.

Atomic mapping of periodic dipole waves in ferroelectric oxide

A dipole wave is composed of head-to-tail connected electric dipoles in the form of sine function. Potential applications in information carrying, transporting, and processing are expected, and logic circuits based on nonlinear wave interaction are promising for dipole waves. Although similar spin waves are well known in ferromagnetic materials for their roles in some physical essence, electric dipole wave behavior and even its existence in ferroelectric materials are still elusive. Here, we observe the atomic morphology of large-scale dipole waves in PbTiO3/SrTiO3 superlattice mediated by tensile epitaxial strains on scandate substrates. The dipole waves can be expressed in the formula of y = Asin (2πx/L) + y 0, where the wave amplitude (A) and wavelength (L) correspond to 1.5 and 6.6 nm, respectively. This study suggests that by engineering strain at the nanoscale, it should be possible to fabricate unknown polar textures, which could facilitate the development of nanoscale ferroelectric devices.

In situmonitoring of epitaxial ferroelectric thin-film growth

In ferroelectric thin films, the polarization state and the domain configuration define the macroscopic ferroelectric properties such as the switching dynamics. Engineering of the ferroelectric domain configuration during synthesis is in permanent evolution and can be achieved by a range of approaches, extending from epitaxial strain tuning over electrostatic environment control to the influence of interface atomic termination. Exotic polar states are now designed in the technologically relevant ultrathin regime. The promise of energy-efficient devices based on ultrathin ferroelectric films depends on the ability to create, probe, and manipulate polar states in ever more complex epitaxial architectures. Because most ferroelectric oxides exhibit ferroelectricity during the epitaxial deposition process, the direct access to the polarization emergence and its evolution during the growth process, beyond the realm of existing structuralin situdiagnostic tools, is becoming of paramount importance. We review the recent progress in the field of monitoring polar states with an emphasis on the non-invasive probes allowing investigations of polarization during the thin film growth of ferroelectric oxides. A particular importance is given to optical second harmonic generationin situ. The ability to determine the net polarization and domain configuration of ultrathin films and multilayers during the growth of multilayers brings new insights towards a better understanding of the physics of ultrathin ferroelectrics and further control of ferroelectric-based heterostructures for devices.

Subterahertz collective dynamics of polar vortices

The collective dynamics of topological structures^1-6 are of interest from both fundamental and applied perspectives. For example, studies of dynamical properties of magnetic vortices and skyrmions^3,4 have not only deepened our understanding of many-body physics but also offered potential applications in data processing and storage⁷. Topological structures constructed from electrical polarization, rather than electron spin, have recently been realized in ferroelectric superlattices^5,6, 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. Here, 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 vortices³. 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.

Metal-ferroelectric supercrystals with periodically curved metallic layers

Simultaneous manipulation of multiple boundary conditions in nanoscale heterostructures offers a versatile route to stabilizing unusual structures and emergent phases. Here, we show that a stable supercrystal phase comprising a three-dimensional ordering of nanoscale domains with tailored periodicities can be engineered in PbTiO₃-SrRuO₃ ferroelectric-metal superlattices. A combination of laboratory and synchrotron X-ray diffraction, piezoresponse force microscopy, scanning transmission electron microscopy and phase-field simulations reveals a complex hierarchical domain structure that forms to minimize the elastic and electrostatic energy. Large local deformations of the ferroelectric lattice are accommodated by periodic lattice modulations of the metallic SrRuO₃ layers with curvatures up to 10⁷ m^-1. Our results show that multidomain ferroelectric systems can be exploited as versatile templates to induce large curvatures in correlated materials, and present a route for engineering correlated materials with modulated structural and electronic properties that can be controlled using electric fields.

Extremely Fast Optical and Nonvolatile Control of Mixed-Phase Multiferroic BiFeO3 via Instantaneous Strain Perturbation

Multiferroics-materials that exhibit coupled ferroic orders-are considered to be one of the most promising candidate material systems for next-generation spintronics, memory, low-power nanoelectronics and so on. To advance potential applications, approaches that lead to persistent and extremely fast functional property changes are in demand. Herein, it is revealed that the phase transition and the correlated ferroic orders in multiferroic BiFeO₃ (BFO) can be modulated via illumination of single short/ultrashort light pulses. Heat transport simulations and ultrafast optical pump-probe spectroscopy reveal that the transient strain induced by light pulses plays a key role in determining the persistent final states. Having identified the diffusionless phase transformation features via scanning transmission electron microscopy, sequential laser pulse illumination is further demonstrated to perform large-area phase and domain manipulation in a deterministic way. The work contributes to all-optical and rapid nonvolatile control of multiferroicity, offering different routes while designing novel optoelectronics.

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.

Multiferroic heterostructures for spintronics

For next-generation technology, magnetic systems are of interest due to the natural ability to store information and, through spin transport, propagate this information for logic functions. Controlling the magnetization state through currents has proven energy inefficient. Multiferroic thin-film heterostructures, combining ferroelectric and ferromagnetic orders, hold promise for energy efficient electronics. The electric field control of magnetic order is expected to reduce energy dissipation by 2–3 orders of magnitude relative to the current state-of-the-art. The coupling between electrical and magnetic orders in multiferroic and magnetoelectric thin-film heterostructures relies on interfacial coupling though magnetic exchange or mechanical strain and the correlation between domains in adjacent functional ferroic layers. We review the recent developments in electrical control of magnetism through artificial magnetoelectric heterostructures, domain imprint, emergent physics and device paradigms for magnetoelectric logic, neuromorphic devices, and hybrid magnetoelectric/spin-current-based applications. Finally, we conclude with a discussion of experiments that probe the crucial dynamics of the magnetoelectric switching and optical tuning of ferroelectric states towards all-optical control of magnetoelectric switching events.

Optically Induced Three-Stage Picosecond Amorphization in Low-Temperature SrTiO3

Photoexcitation can drastically modify potential energy surfaces of materials, allowing access to hidden phases. SrTiO₃ (STO) is an ideal material for photoexcitation studies due to its prevalent use in nanostructured devices and its rich range of functionality-changing lattice motions. Recently, a hidden ferroelectric phase in STO was accessed through weak terahertz excitation of polarization-inducing phonon modes. In contrast, whereas strong laser excitation was shown to induce nanostructures on STO surfaces and control nanopolarization patterns in STO-based heterostructures, the dynamic pathways underlying these optically induced structural changes remain unknown. Here nonadiabatic quantum molecular dynamics reveals picosecond amorphization in photoexcited STO at temperatures as low as 10 K. The three-stage pathway involves photoinduced charge transfer and optical phonon activation followed by nonlinear charge and lattice dynamics that ultimately lead to amorphization. This atomistic understanding could guide not only rational laser nanostructuring of STO but also broader "quantum materials on demand" technologies.

Interface and surface stabilization of the polarization in ferroelectric thin films

With an ever-increasing societal demand for energy for electronic devices and in the face of the current climate issues, the need for low-energy-consuming electronics has never been greater. Ferroelectrics are promising energy-efficient device components for digital information storage, with the functionality relying on the manipulation of their polarization in ultrathin films. Polar discontinuities at the thin film interfaces and surfaces, however, can cause loss of polarization and thus functionality. Here we show how the interface and surface influence the overall polarization of the thin film. We show that the structure of the interface and surface can be tailored toward a specific polarization direction and strength, and that great control in the engineering of ferroelectrics thin films can be achieved.

Ferroelectric perovskites present a switchable spontaneous polarization and are promising energy-efficient device components for digital information storage. Full control of the ferroelectric polarization in ultrathin films of ferroelectric perovskites needs to be achieved in order to apply this class of materials in modern devices. However, ferroelectricity itself is not well understood in this nanoscale form, where interface and surface effects become particularly relevant and where loss of net polarization is often observed. In this work, we show that the precise control of the structure of the top surface and bottom interface of the thin film is crucial toward this aim. We explore the properties of thin films of the prototypical ferroelectric lead titanate (PbTiO₃) on a metallic strontium ruthenate (SrRuO₃) buffer using a combination of computational (density functional theory) and experimental (optical second harmonic generation) methods. We find that the polarization direction and strength are influenced by chemical and electronic processes occurring at the epitaxial interface and at the surface. The polarization is particularly sensitive to adsorbates and to surface and interface defects. These results point to the possibility of controlling the polarization direction and magnitude by engineering specific interface and surface chemistries.

Stabilizing hidden room-temperature ferroelectricity via a metastable atomic distortion pattern

Nonequilibrium atomic structures can host exotic and technologically relevant properties in otherwise conventional materials. Oxygen octahedral rotation forms a fundamental atomic distortion in perovskite oxides, but only a few patterns are predominantly present at equilibrium. This has restricted the range of possible properties and functions of perovskite oxides, necessitating the utilization of nonequilibrium patterns of octahedral rotation. Here, we report that a designed metastable pattern of octahedral rotation leads to robust room-temperature ferroelectricity in CaTiO3, which is otherwise nonpolar down to 0 K. Guided by density-functional theory, we selectively stabilize the metastable pattern, distinct from the equilibrium pattern and cooperative with ferroelectricity, in heteroepitaxial films of CaTiO3. Atomic-scale imaging combined with deep neural network analysis confirms a close correlation between the metastable pattern and ferroelectricity. This work reveals a hidden but functional pattern of oxygen octahedral rotation and opens avenues for designing multifunctional materials.

Controllable skyrmion chirality in ferroelectrics

Chirality, an intrinsic handedness, is one of the most intriguing fundamental phenomena in nature. Materials composed of chiral molecules find broad applications in areas ranging from nonlinear optics and spintronics to biology and pharmaceuticals. However, chirality is usually an invariable inherent property of a given material that cannot be easily changed at will. Here, we demonstrate that ferroelectric nanodots support skyrmions the chirality of which can be controlled and switched. We devise protocols for realizing control and efficient manipulations of the different types of skyrmions. Our findings open the route for controlled chirality with potential applications in ferroelectric-based information technologies.

Domain Dynamics under Ultrafast Electric-Field Pulses

Exploring the dynamic responses of a material is of importance to both understanding its fundamental physics at high frequencies and potential device applications. Here we develop a phase-field model for predicting the dynamics of ferroelectric materials and study the dynamic responses of ferroelectric domains and domain walls subjected to an ultrafast electric-field pulse. We discover a transition of domain evolution mechanisms from pure domain growth at a relatively low field to combined nucleation and growth of domains at a high field. We derive analytical models for the two regimes which allow us to extract the effective mass and damping coefficient of ferroelectric domain walls. The exhibition of two regimes for the ferroelectric domain dynamics at low and high electric fields is expected to be a general phenomenon that would appear for ferroic domains under other ultrafast stimuli. The present Letter also offers a general framework for studying domain dynamics and obtaining fundamental properties of domain walls and thus for manipulating the dynamic functionalities of ferroelectric materials.