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.

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.

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.

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.

Emergent chirality in a polar meron to skyrmion phase transition.

Polar skyrmions are predicted to emerge from the interplay of elastic, electrostatic and gradient energies, in contrast to the key role of the anti-symmetric Dzyalozhinskii-Moriya interaction in magnetic skyrmions. Here, we explore the reversible transition from a skyrmion state (topological charge of -1) to a two-dimensional, tetratic lattice of merons (with topological charge of -1/2) upon varying the temperature and elastic boundary conditions in [(PbTiO3)16/(SrTiO3)16]8 membranes. This topological phase transition is accompanied by a change in chirality, from zero-net chirality (in meronic phase) to net-handedness (in skyrmionic phase). We show how scanning electron diffraction provides a robust measure of the local polarization simultaneously with the strain state at sub-nm resolution, while also directly mapping the chirality of each skyrmion. Using this, we demonstrate strain as a crucial order parameter to drive isotropic-to-anisotropic structural transitions of chiral polar skyrmions to non-chiral merons, validated with X-ray reciprocal space mapping and phase-field simulations.

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.

Layered gallium sulfide optical properties from monolayer to CVD crystalline thin films.

Interest in layered van der Waals semiconductor gallium monosulfide (GaS) is growing rapidly because of its wide band gap value between those of two-dimensional transition metal dichalcogenides and of insulating layered materials such as hexagonal boron nitride. For the design of envisaged optoelectronic, photocatalytic and photonic applications of GaS, the knowledge of its dielectric function is fundamental. Here we present a combined theoretical and experimental investigation of the dielectric function of crystalline 2H-GaS from monolayer to bulk. Spectroscopic imaging ellipsometry with micron resolution measurements are corroborated by first principle calculations of the electronic structure and dielectric function. We further demonstrate and validate the applicability of the established dielectric function to the analysis of the optical response of c-axis oriented GaS layers grown by chemical vapor deposition (CVD). These optical results can guide the design of novel, to our knowledge, optoelectronic and photonic devices based on low-dimensional GaS.

Inherent Spin-Polarization Coupling in a Magnetoelectric Vortex.

Solid-state materials are currently being explored as a platform for the manipulation of spins for spintronics and quantum information science. More broadly, a wide spectrum of ferroelectric materials, spanning from inorganic oxides to polymeric systems such as PVDF, present a different approach to explore quantum phenomena in which the spins are set and manipulated with electric fields. Using dilute Fe3+-doped ferroelectric PbTiO3-SrTiO3 superlattices as a model system, we demonstrate intrinsic spin-polarization control of spin directionality in complex ferroelectric vortices and skyrmions. Electron paramagnetic resonance (EPR) spectra show that the spins in the Fe3+ ion are strongly coupled to the local polarization and preferentially aligned perpendicular to the ferroelectric polar c axis in this complex vortex structure. The effect of polarization-spin directionality is corroborated by first-principles calculations, demonstrating the variation of the spin directionality with the polar texture and offering the potential for future quantum analogues of macroscopic magnetoelectric devices.

Interlaboratory study on Sb2S3 interplay between structure, dielectric function, and amorphous-to-crystalline phase change for photonics.

Antimony sulfide, Sb2S3, is interesting as the phase-change material for applications requiring high transmission from the visible to telecom wavelengths, with its band gap tunable from 2.2 to 1.6 eV, depending on the amorphous and crystalline phase. Here we present results from an interlaboratory study on the interplay between the structural change and resulting optical contrast during the amorphous-to-crystalline transformation triggered both thermally and optically. By statistical analysis of Raman and ellipsometric spectroscopic data, we have identified two regimes of crystallization, namely 250°C ≤ T < 300°C, resulting in Type-I spherulitic crystallization yielding an optical contrast Δn ∼ 0.4, and 300 ≤ T < 350°C, yielding Type-II crystallization bended spherulitic structure with different dielectric function and optical contrast Δn ∼ 0.2 below 1.5 eV. Based on our findings, applications of on-chip reconfigurable nanophotonic phase modulators and of a reconfigurable high-refractive-index core/phase-change shell nanoantenna are designed and proposed.

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.

Electric field control of chirality.

Polar textures have attracted substantial attention in recent years as a promising analog to spin-based textures in ferromagnets. Here, using optical second-harmonic generation­based circular dichroism, we demonstrate deterministic and reversible control of chirality over mesoscale regions in ferroelectric vortices using an applied electric field. The microscopic origins of the chirality, the pathway during the switching, and the mechanism for electric field control are described theoretically via phase-field modeling and second-principles simulations, and experimentally by examination of the microscopic response of the vortices under an applied field. The emergence of chirality from the combination of nonchiral materials and subsequent control of the handedness with an electric field has far-reaching implications for new electronics based on chirality as a field-controllable order parameter.

Atomic scale crystal field mapping of polar vortices in oxide superlattices.

Polar vortices in oxide superlattices exhibit complex polarization topologies. Using a combination of electron energy loss near-edge structure analysis, crystal field multiplet theory, and first-principles calculations, we probe the electronic structure within such polar vortices in [(PbTiO3)16/(SrTiO3)16] superlattices at the atomic scale. The peaks in Ti [Formula: see text]-edge spectra shift systematically depending on the position of the Ti4+ cations within the vortices i.e., the direction and magnitude of the local dipole. First-principles computation of the local projected density of states on the Ti [Formula: see text] orbitals, together with the simulated crystal field multiplet spectra derived from first principles are in good agreement with the experiments.

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.

Siesta: Recent developments and applications.

A review of the present status, recent enhancements, and applicability of the Siesta program is presented. Since its debut in the mid-1990s, Siesta's flexibility, efficiency, and free distribution have given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of Siesta combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a real-space grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here, we describe the more recent implementations on top of that core scheme, which include full spin-orbit interaction, non-repeated and multiple-contact ballistic electron transport, density functional theory (DFT)+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as wannier90 and the second-principles modeling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering Siesta runs, and various post-processing utilities. Siesta has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low-level libraries, as well as data standards and support for them, particularly the PSeudopotential Markup Language definition and library for transferable pseudopotentials, and the interface to the ELectronic Structure Infrastructure library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments.

Author Correction: Spatially resolved steady-state negative capacitance.

In this Letter, the first name of author Bhagwati Prasad was misspelled Bhagawati. This error has been corrected online.

Theoretical guidelines to create and tune electric skyrmion bubbles.

Researchers have long wondered whether ferroelectrics may present topological textures akin to magnetic skyrmions and chiral bubbles, the results being modest thus far. An electric equivalent of a typical magnetic skyrmion would rely on a counterpart of the Dzyaloshinskii-Moriya interaction and seems all but impossible; further, the exotic ferroelectric orders reported to date rely on specific composites and superlattices, limiting their generality and properties. Here, we propose an original approach to write topological textures in simple ferroelectrics in a customary manner. Our second-principles simulations of columnar nanodomains, in prototype material PbTiO3, show we can harness the Bloch-type structure of the domain wall to create objects with the usual skyrmion-defining features as well as unusual ones-including isotopological and topological transitions driven by external fields and temperature-and potentially very small sizes. Our results suggest countless possibilities for creating and manipulating such electric textures, effectively inaugurating the field of topological ferroelectrics.

Spatially resolved steady-state negative capacitance.

Negative capacitance is a newly discovered state of ferroelectric materials that holds promise for electronics applications by exploiting a region of thermodynamic space that is normally not accessible1-14. Although existing reports of negative capacitance substantiate the importance of this phenomenon, they have focused on its macroscale manifestation. These manifestations demonstrate possible uses of steady-state negative capacitance-for example, enhancing the capacitance of a ferroelectric-dielectric heterostructure4,7,14 or improving the subthreshold swing of a transistor8-12. Yet they constitute only indirect measurements of the local state of negative capacitance in which the ferroelectric resides. Spatial mapping of this phenomenon would help its understanding at a microscopic scale and also help to achieve optimal design of devices with potential technological applications. Here we demonstrate a direct measurement of steady-state negative capacitance in a ferroelectric-dielectric heterostructure. We use electron microscopy complemented by phase-field and first-principles-based (second-principles) simulations in SrTiO3/PbTiO3 superlattices to directly determine, with atomic resolution, the local regions in the ferroelectric material where a state of negative capacitance is stabilized. Simultaneous vector mapping of atomic displacements (related to a complex pattern in the polarization field), in conjunction with reconstruction of the local electric field, identify the negative capacitance regions as those with higher energy density and larger polarizability: the domain walls where the polarization is suppressed.

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.

Giant Optical Polarization Rotation Induced by Spin-Orbit Coupling in Polarons.

We have uncovered a giant gyrotropic magneto-optical response for doped ferromagnetic manganite La_{2/3}Ca_{1/3}MnO_{3} around the near room-temperature paramagnetic-to-ferromagnetic transition. At odds with current wisdom, where this response is usually assumed to be fundamentally fixed by the electronic band structure, we point to the presence of small polarons as the driving force for this unexpected phenomenon. We explain the observed properties by the intricate interplay of mobility, Jahn-Teller effect, and spin-orbit coupling of small polarons. As magnetic polarons are ubiquitously inherent to many strongly correlated systems, our results provide an original, general pathway towards the generation of magnetic-responsive gigantic gyrotropic responses that may open novel avenues for magnetoelectric coupling beyond the conventional modulation of magnetization.