Subterahertz collective dynamics of polar vortices.

The collective dynamics of topological structures1-6 are of interest from both fundamental and applied perspectives. For example, studies of dynamical properties of magnetic vortices and skyrmions3,4 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 superlattices5,6, 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.

Clamping enables enhanced electromechanical responses in antiferroelectric thin films.

Thin-film materials with large electromechanical responses are fundamental enablers of next-generation micro-/nano-electromechanical applications. Conventional electromechanical materials (for example, ferroelectrics and relaxors), however, exhibit severely degraded responses when scaled down to submicrometre-thick films due to substrate constraints (clamping). This limitation is overcome, and substantial electromechanical responses in antiferroelectric thin films are achieved through an unconventional coupling of the field-induced antiferroelectric-to-ferroelectric phase transition and the substrate constraints. A detilting of the oxygen octahedra and lattice-volume expansion in all dimensions are observed commensurate with the phase transition using operando electron microscopy, such that the in-plane clamping further enhances the out-of-plane expansion, as rationalized using first-principles calculations. In turn, a non-traditional thickness scaling is realized wherein an electromechanical strain (1.7%) is produced from a model antiferroelectric PbZrO3 film that is just 100 nm thick. The high performance and understanding of the mechanism provide a promising pathway to develop high-performance micro-/nano-electromechanical systems.

Manipulating chiral spin transport with ferroelectric polarization.

A magnon is a collective excitation of the spin structure in a magnetic insulator and can transmit spin angular momentum with negligible dissipation. This quantum of a spin wave has always been manipulated through magnetic dipoles (that is, by breaking time-reversal symmetry). Here we report the experimental observation of chiral spin transport in multiferroic BiFeO3 and its control by reversing the ferroelectric polarization (that is, by breaking spatial inversion symmetry). The ferroelectrically controlled magnons show up to 18% modulation at room temperature. The spin torque that the magnons in BiFeO3 carry can be used to efficiently switch the magnetization of adjacent magnets, with a spin-torque efficiency comparable to the spin Hall effect in heavy metals. Utilizing such controllable magnon generation and transmission in BiFeO3, an all-oxide, energy-scalable logic is demonstrated composed of spin-orbit injection, detection and magnetoelectric control. Our observations open a new chapter of multiferroic magnons and pave another path towards low-dissipation nanoelectronics.

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.

Flexoelectric Enhancement of Strain Gradient Elasticity Across a Ferroelectric-to-Paraelectric Phase Transition.

We study the temperature dependent elastic properties of Ba0.8Sr0.2TiO3 freestanding membranes across the ferroelectric-to-paraelectric phase transition using an atomic force microscope. The bending rigidity of thin membranes can be stiffer compared to stretching due to strain gradient elasticity (SGE). We measure the Young's modulus of freestanding Ba0.8Sr0.2TiO3 drumheads in bending and stretching dominated deformation regimes on a variable temperature platform, finding a peak in the difference between the two Young's moduli obtained at the phase transition. This demonstrates a dependence of SGE on the dielectric properties of a material and alludes to a flexoelectric origin of an effective SGE.

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.

Non-volatile electric-field control of inversion symmetry.

Competition between ground states at phase boundaries can lead to significant changes in properties under stimuli, particularly when these ground states have different crystal symmetries. A key challenge is to stabilize and control the coexistence of symmetry-distinct phases. Using BiFeO3 layers confined between layers of dielectric TbScO3 as a model system, we stabilize the mixed-phase coexistence of centrosymmetric and non-centrosymmetric BiFeO3 phases at room temperature with antipolar, insulating and polar semiconducting behaviour, respectively. Application of orthogonal in-plane electric (polar) fields results in reversible non-volatile interconversion between the two phases, hence removing and introducing centrosymmetry. Counterintuitively, we find that an electric field 'erases' polarization, resulting from the anisotropy in octahedral tilts introduced by the interweaving TbScO3 layers. Consequently, this interconversion between centrosymmetric and non-centrosymmetric phases generates changes in the non-linear optical response of over three orders of magnitude, resistivity of over five orders of magnitude and control of microscopic polar order. Our work establishes a platform for cross-functional devices that take advantage of changes in optical, electrical and ferroic responses, and demonstrates octahedral tilts as an important order parameter in materials interface design.

Interplay between Point and Extended Defects and Their Effects on Jerky Domain-Wall Motion in Ferroelectric Thin Films.

Defects have a significant influence on the polarization and electromechanical properties of ferroelectric materials. Statistically, they can be seen as random pinning centers acting on an elastic manifold, slowing domain-wall propagation and raising the energy required to switch polarization. Here we show that the "dressing" of defects can lead to unprecedented control of domain-wall dynamics. We engineer defects of two different dimensionalities in ferroelectric oxide thin films-point defects externally induced via He^{2+} bombardment, and extended quasi-one-dimensional a domains formed in response to internal strains. The a domains act as extended strong pinning sites (as expected) imposing highly localized directional constraints. Surprisingly, the induced point defects in the He^{2+} bombarded samples orient and align to impose further directional pinning, screening the effect of a domains. This defect interplay produces more uniform and predictable domain-wall dynamics. Such engineered interactions between defects are crucial for advancements in ferroelectric devices.

Resonant domain-wall-enhanced tunable microwave ferroelectrics.

Ordering of ferroelectric polarization1 and its trajectory in response to an electric field2 are essential for the operation of non-volatile memories3, transducers4 and electro-optic devices5. However, for voltage control of capacitance and frequency agility in telecommunication devices, domain walls have long been thought to be a hindrance because they lead to high dielectric loss and hysteresis in the device response to an applied electric field6. To avoid these effects, tunable dielectrics are often operated under piezoelectric resonance conditions, relying on operation well above the ferroelectric Curie temperature7, where tunability is compromised. Therefore, there is an unavoidable trade-off between the requirements of high tunability and low loss in tunable dielectric devices, which leads to severe limitations on their figure of merit. Here we show that domain structure can in fact be exploited to obtain ultralow loss and exceptional frequency selectivity without piezoelectric resonance. We use intrinsically tunable materials with properties that are defined not only by their chemical composition, but also by the proximity and accessibility of thermodynamically predicted strain-induced, ferroelectric domain-wall variants8. The resulting gigahertz microwave tunability and dielectric loss are better than those of the best film devices by one to two orders of magnitude and comparable to those of bulk single crystals. The measured quality factors exceed the theoretically predicted zero-field intrinsic limit owing to domain-wall fluctuations, rather than field-induced piezoelectric oscillations, which are usually associated with resonance. Resonant frequency tuning across the entire L, S and C microwave bands (1-8 gigahertz) is achieved in an individual device-a range about 100 times larger than that of the best intrinsically tunable material. These results point to a rich phase space of possible nanometre-scale domain structures that can be used to surmount current limitations, and demonstrate a promising strategy for obtaining ultrahigh frequency agility and low-loss microwave devices.

Pure Chiral Polar Vortex Phase in PbTiO3/SrTiO3 Superlattices with Tunable Circular Dichroism.

Nontrivial polarization textures have been demonstrated in ferroelectric/dielectric superlattices, where the electrostatic, elastic, and different gradient energies compete in a delicate balance. When PbTiO3/SrTiO3 superlattices are grown on DyScO3, the coexistence of ferroelectric domains and vortex structure is observed for n = 12-20 unit cells. Here, we report an approach to achieve single-phase vortex structures in superlattices by controlling the epitaxial strain using Sr1.04Al0.12Ga0.35Ta0.50O3 substrates. The domain width follows Kittel's law with the thickness of the ferroelectric PbTiO3 layers. A phase transition from vortex to a disordered phase with temperature is characterized by the correlation length. Resonant soft X-ray diffraction circular dichroism at the titanium L-edge reveals enhanced chirality with the thickness of the ferroelectric layer. These results are supported by second-principles simulations, which demonstrate that the integrated helicity increases with n. The stabilization of chiral single-phase polar vortices in ferroelectric/dielectric superlattices can enable novel optoelectronic devices with enhanced ferroelectric-light interaction.

Tunable Artificial Relaxor Behavior in [BaTiO_{3}]_{m}/[BaZrO_{3}]_{n} Superlattices.

[BaTiO_{3}]_{m}/[BaZrO_{3}]_{n} (m, n=4-12) superlattices are used to demonstrate the fabrication and deterministic control of an artificial relaxor. X-ray diffraction and atomic-resolution imaging studies confirm the production of high-quality heterostructures. With decreasing BaTiO_{3} layer thickness, dielectric measurements reveal systematically lower dielectric-maximum temperatures, while hysteresis loops and third-harmonic nonlinearity studies suggest a transition from ferroelectriclike to relaxorlike behavior driven by tuning the random-field strength. This system provides a novel platform for studying the size effect and interaction length scale of the nanoscale-polar structures in relaxors.

Hexagonal Close-Packed Polar-Skyrmion Lattice in Ultrathin Ferroelectric PbTiO_{3} Films.

Polar skyrmions are topologically stable, swirling polarization textures with particlelike characteristics, which hold promise for next-generation, nanoscale logic and memory. However, the understanding of how to create ordered polar skyrmion lattice structures and how such structures respond to applied electric fields, temperature, and film thickness remains elusive. Here, using phase-field simulations, the evolution of polar topology and the emergence of a phase transition to a hexagonal close-packed skyrmion lattice is explored through the construction of a temperature-electric field phase diagram for ultrathin ferroelectric PbTiO_{3} films. The hexagonal-lattice skyrmion crystal can be stabilized under application of an external, out-of-plane electric field which carefully adjusts the delicate interplay of elastic, electrostatic, and gradient energies. In addition, the lattice constants of the polar skyrmion crystals are found to increase with film thickness, consistent with expectation from Kittel's law. Our studies pave the way for the development of novel ordered condensed matter phases assembled from topological polar textures and related emergent properties in nanoscale ferroelectrics.

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 0.68PbMg1/3Nb2/3O3-0.32PbTiO3 (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.

Structural Chirality of Polar Skyrmions Probed by Resonant Elastic X-Ray Scattering.

An escalating challenge in condensed-matter research is the characterization of emergent order-parameter nanostructures such as ferroelectric and ferromagnetic skyrmions. Their small length scales coupled with complex, three-dimensional polarization or spin structures makes them demanding to trace out fully. Resonant elastic x-ray scattering (REXS) has emerged as a technique to study chirality in spin textures such as skyrmions and domain walls. It has, however, been used to a considerably lesser extent to study analogous features in ferroelectrics. Here, we present a framework for modeling REXS from an arbitrary arrangement of charge quadrupole moments, which can be applied to nanostructures in materials such as ferroelectrics. With this, we demonstrate how extended reciprocal space scans using REXS with circularly polarized x rays can probe the three-dimensional structure and chirality of polar skyrmions. Measurements, bolstered by quantitative scattering calculations, show that polar skyrmions of mixed chirality coexist, and that REXS allows valuation of relative fractions of right- and left-handed skyrmions. Our quantitative analysis of the structure and chirality of polar skyrmions highlights the capability of REXS for establishing complex topological structures toward future application exploits.

Vortex Domain Walls in Ferroelectrics.

Controlling the domain formation in ferroelectric materials at the nanoscale is a fertile ground to explore emergent phenomena and their technological prospects. For example, charged ferroelectric domain walls in BiFeO3 and ErMnO3 exhibit significantly enhanced conductivity which could serve as the foundation for next-generation circuits (Estévez and Laurson, Phys. Rev. B 2015, 91, 054407). Here, we describe a concept in which polar vortices perform the same role as a ferroelectric domain wall in classical domain structures with the key difference being that the polar vortices can accommodate charged (i.e., head-to-head and tail-to-tail) domains, for example, in ferroelectric PbTiO3/dielectric SrTiO3 superlattices. Such a vortex domain wall structure can be manipulated in a reversible fashion under an external applied field.

Local Probe Comparison of Ferroelectric Switching Event Statistics in the Creep and Depinning Regimes in Pb(Zr_{0.2}Ti_{0.8})O_{3} Thin Films.

Ferroelectric materials provide a useful model system to explore the jerky, highly nonlinear dynamics of elastic interfaces in disordered media. The distribution of nanoscale switching event sizes is studied in two Pb(Zr_{0.2}Ti_{0.8})O_{3} thin films with different disorder landscapes using piezoresponse force microscopy. While the switching event statistics show the expected power-law scaling, significant variations in the value of the scaling exponent τ are seen, possibly as a consequence of the different intrinsic disorder landscapes in the samples and of further alterations under high tip bias applied during domain writing. Importantly, higher exponent values (1.98-2.87) are observed when crackling statistics are acquired only for events occurring in the creep regime. The exponents are systematically lowered when all events across both creep and depinning regimes are considered-the first time such a distinction is made in studies of ferroelectric materials. These results show that distinguishing the two regimes is of crucial importance, significantly affecting the exponent value and potentially leading to incorrect assignment of universality class.

Emergent chirality in the electric polarization texture of titanate superlattices.

Chirality is a geometrical property by which an object is not superimposable onto its mirror image, thereby imparting a handedness. Chirality determines many important properties in nature-from the strength of the weak interactions according to the electroweak theory in particle physics to the binding of enzymes with naturally occurring amino acids or sugars, reactions that are fundamental for life. In condensed matter physics, the prediction of topologically protected magnetic skyrmions and related spin textures in chiral magnets has stimulated significant research. If the magnetic dipoles were replaced by their electrical counterparts, then electrically controllable chiral devices could be designed. Complex oxide BaTiO3/SrTiO3 nanocomposites and PbTiO3/SrTiO3 superlattices are perfect candidates, since "polar vortices," in which a continuous rotation of ferroelectric polarization spontaneously forms, have been recently discovered. Using resonant soft X-ray diffraction, we report the observation of a strong circular dichroism from the interaction between circularly polarized light and the chiral electric polarization texture that emerges in PbTiO3/SrTiO3 superlattices. This hallmark of chirality is explained by a helical rotation of electric polarization that second-principles simulations predict to reside within complex 3D polarization textures comprising ordered topological line defects. The handedness of the texture can be topologically characterized by the sign of the helicity number of the chiral line defects. This coupling between the optical and novel polar properties could be exploited to encode chiral signatures into photon or electron beams for information processing.

Light-Induced Currents at Domain Walls in Multiferroic BiFeO3.

Multiferroic BiFeO3 (BFO) films with spontaneously formed periodic stripe domains can generate above-gap open circuit voltages under visible light illumination; nevertheless the underlying mechanism behind this intriguing optoelectronic response has not been understood to date. Here, we make contact-free measurements of light-induced currents in epitaxial BFO films via detecting terahertz radiation emanated by these currents, enabling a direct probe of the intrinsic charge separation mechanisms along with quantitative measurements of the current amplitudes and their directions. In the periodic stripe samples, we find that the net photocurrent is dominated by the charge separation across the domain walls, whereas in the monodomain samples the photovoltaic response arises from a bulk shift current associated with the non-centrosymmetry of the crystal. The peak current amplitude driven by the charge separation at the domain walls is found to be 2 orders of magnitude higher than the bulk shift current response, indicating the prominent role of domain walls acting as nanoscale junctions to efficiently separate photogenerated charges in the stripe domain BFO films. These findings show that domain-wall-engineered BFO thin films offer exciting prospects for ferroelectric-based optoelectronics, as well as bias-free strong terahertz emitters.