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At least 145 records · Page 8

Interfacial Electrochemistry of Catalyst-Coordinated Graphene Nanoribbons

The immobilization of molecular electrocatalysts on conductive electrodes is an appealing strategy for enhancing their overall activity relative to those of analogous molecular compounds. Here, in this study, we report on the interfacial electrochemistry of self-assembled two-dimensional nanosheets of graphene nanoribbons (GNR-2DNS) and analogs containing a Rh-based hydrogen evolution reaction (HER) catalyst (RhGNR-2DNS) immobilized on conductive electrodes. Proton-coupled electron transfer (PCET) taking place at N-centers of the nanoribbons was utilized as an indirect reporter of the interfacial electric fields experienced by the monolayer nanosheet located within the electric double layer. The experimental Pourbaix diagrams were compared with a theoretical model, which derives the experimental Pourbaix slopes as a function of parameter f, a fraction of the interfacial potential drop experienced by the redox-active group. Interestingly, our study revealed that GNR-2DNS was strongly coupled to glassy carbon electrodes (f = 1), while RhGNR-2DNS was not (f = 0.15). We further investigated the HER mechanism by RhGNR-2DNS using electrochemical and X-ray absorption spectroelectrochemical methods and compared it to homogeneous molecular model compounds. RhGNR-2DNS was found to be an active HER electrocatalyst over a broader set of aqueous pH conditions than its molecular analogs. We find that the improved HER performance in the immobilized catalyst arises due to two factors. First, redox-active bipyrimidine-based ligands were shown to dramatically alter the activity of Rh sites by increasing the electron density at the active Rh center and providing RhGNR-2DNS with improved catalysis. Second, catalyst immobilization was found to prevent catalyst aggregation that was found to occur for the molecular analog in the basic pH. Overall, this study provides valuable insights into the mechanism by which catalyst immobilization can affect the overall electrocatalytic performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Emergent properties of magnons coupled to microwave photons (Final Technical Report)

Studying the emergent properties of hybrid quantum material platforms holds great promise for advancing quantum technologies and transforming our ability to control quantum mechanical interactions. A key development in recent years is the recognition that magnons – the elementary quanta of spin waves – can serve as fundamental building blocks in quantum systems. Understanding the mechanisms behind the generation and control of hybrid quasiparticles based on magnons could pave the way for engineering new materials for quantum coherent processing and quantum computing. This research project focused on the precise control of light-matter interactions in magnetic hybrid systems and nanostructures, where light is carried by microwave photons and matter by magnons in engineered magnetic metamaterials. Furthermore, we investigated hybridized magnon interactions in magnetic nanostructures and devices. To this end, the project has developed new measurement techniques and systematically studied novel material systems for efficient magnon-photon coupling. A key focus was uncovering the fundamental mechanisms governing magnon-photon and magnon-phonon interactions – critical for utilizing magnons as coherent information transducers between carriers. Specifically, this research addressed: 1. Investigate the dispersion and collective properties of magnon hybrid systems in new material systems. 2. Develop magnonic hybrids with non-zero wavevectors and achieve effective control of magnon-polariton properties through engineered magnonic behaviors. 3. Determine how spin-orbit torques interact with electromagnetic fields in the strong coupling regime. This work generated new insights into the physics of magnonic hybrid systems and their emergent properties by broadening the range of material platforms and measurement techniques used to study magnon-photon and magnon-magnon coupling. The findings deepen our understanding of magnon-polaritons and lay the groundwork for novel spintronic devices with potential applications in quantum information science.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Oscillate and renormalize: Fast phonons reshape the Kondo effect in flat-band systems

Here, we examine the interplay between electron correlations and phonons in an Anderson-Holstein impurity model with an Einstein phonon. When the phonons are slow compared to charge fluctuations (frequency 𝜔 0 ≪ 𝑈/2, the onsite Coulomb scale 𝑈/2), we demonstrate analytically that the expected phonon-mediated reduction of interactions is completely suppressed, even in the strong-coupling regime. This suppression arises from the oscillator's inability to respond to rapid charge fluctuations, manifested as a compensation effect between the polaronic cloud and the excited-state phonons associated with valence fluctuations. We identify a frozen mixed valence phase, above a threshold dimensionless electron-phonon coupling 𝛼* when the phonons are slow, where the static phonon cloud locks the impurity into specific valence configurations, potentially explaining the puzzling coexistence of mixed valence behavior and insulating properties in materials like rust. Conversely, when the phonon is fast (𝜔 0 ≳ 𝑈/2), the system exhibits conventional polaronic behavior with renormalized onsite interactions effectively 𝑈 eff due to phonon-mediated attraction, with additional satellite features in the local spectral function due to phonon excitations. Using numerical renormalization group calculations, a fully dynamic renormalization technique, we confirm these behaviors in both regimes. These findings have important implications for strongly correlated systems where phonon energy scales may be comparable to the Coulomb scale, such as in twisted bilayer graphene, necessitating careful consideration of interaction renormalizations in theoretical models.

Anderson impurity model↗

Cation-π Bonding in Actinides: UO x + (Benzene) ( x = 0, 1, 2) Complexes Studied with Threshold Photodissociation Spectroscopy and Theory

Cation-π complexes of the form UO x + (benzene) (x = 0, 1, 2) are produced by laser vaporization and cooled in a supersonic molecular beam. These ions are mass selected and studied with UV–visible laser photodissociation spectroscopy. Each of these complexes photodissociates by elimination of the benzene ligand. Above an energetic threshold, the absorption and photodissociation are continuous, indicating a high density of strongly coupled electronic states. The thresholds for the dissociation of each of these three complexes are measured and assigned as their respective bond dissociation energies. The bond energies determined [U + –(benzene): 42.5 ± 0.3 kcal/mol; UO + –(benzene): 41.0 ± 0.3 kcal/mol; UO 2 + –(benzene): 39.7 ± 0.3 kcal/mol] are comparable to those of transition metal ion-benzene complexes. Computational studies at the DFT/B3LYP level complement the experiments, predicting dissociation energies in reasonably good agreement with the experiments. Experiments and theory agree that the U+(benzene) complex is more strongly bound than its corresponding oxide ions. This new thermochemistry on actinide cation-π bonding should stimulate higher-level computational studies on these systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Coupling of Infrared Active Colloidal Quantum Dots and Amorphous Selenium for Fast and Sensitive Photodetection

Colloidal quantum dot (CQD) based infrared (IR) photodetectors offer facile wavelength tunability in the IR and low-cost fabrication. However, owing to their large surface areas, CQDs intrinsically have significant surface traps critically affecting the speed of CQD photodetectors, typically mediated through tedious surface passivation efforts. In this report, an alternative strategy involving coupling of near-IR photoactive lead sulfide CQDs with a thermally evaporated amorphous selenium (a-Se) hole transport layer is proposed. By separating the detector into a photon absorbing CQD region and a charge transport a-Se region, the study takes advantage of the extremely low noise, predominantly hole-only transport process in a-Se. Here, a high 3 dB bandwidth of 2.5 MHz and a competitive specific detectivity of 2.5 × 10 11 Jones at room temperature are demonstrated at 980 nm. This report serves as a first demonstration of strong coupling between an IR active CQD absorber and a-Se, which paves the path to obtain fast and highly photoresponsive IR photodetection in the future.

36 MATERIALS SCIENCE↗

An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization

We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.

Burkovska, Olena [ORNL] (ORCID:0000000163101130)↗

Near-threshold states in coupled D D * − D * D * scattering from lattice QCD

The first determination of doubly charmed isospin-0 coupled-channel D D * − D * D * scattering amplitudes from lattice quantum chromodynamics (QCD) is presented. The finite-volume spectrum is computed for three lattice volumes with a light-quark mass corresponding to m π ≈ 391 MeV and is used to extract the scattering amplitudes in J P = 1 + via the Lüscher quantization condition. By analytically continuing the scattering amplitudes to complex energies, a T c c pole corresponding to a virtual bound state is found below D D * threshold. We also find a second pole, T c c ′ , corresponding to a resonance pole below the kinematically closed D * D * channel, to which it has a strong coupling. A nonzero coupling is robustly found between the S -wave D D * and D * D * channels producing a clear cusp in the D D * amplitude at the D * D * threshold energy. This suggests that the experimental T c c ′ should be observable in D D * and D * D * final states at ongoing experiments. Published by the American Physical Society 2025

Whyte, Travis (ORCID:000000027661301X)↗

Apparent 𝑤 <−1 and a Lower 𝑆 8 from Dark Axion and Dark Baryons Interactions

We show that a simple coupling between dark energy and dark matter can simultaneously address two distinct hints at new physics coming from cosmological observations. The first is the recent evidence from the DESI project and supernovae observations that the dark energy equation of state w is evolving over cosmic time from an earlier value that is <-1 to a present-day value >-1. The second observation is the so-called S8 tension, describing the suppression of the growth of matter overdensities compared to that expected in the ΛCDM model. Here, we propose a stable, technically natural particle physics implementation of this idea, in which dark matter consists of dark baryons in a strongly coupled hidden sector, and the dark energy field is the associated dark axion. The time variation of the dark matter mass results in an effective dark energy equation of state that exhibits a phantom crossing behavior consistent with recent results. It also results in a slight delay in matter-radiation equality, which suppresses the overall growth of density perturbations.

Axions↗

Disentangling the Impacts of Microtopography and Shrub Distribution on Snow Depth in a Subarctic Watershed: Toward a Predictive Understanding of Snow Spatial Variability

Snow plays a critical role in carbon cycling, vegetation dynamics, and permafrost hydrology at high latitudes by influencing surface energy exchange. Predicting snow distribution patterns is essential for understanding the evolution of Arctic ecosystems, yet scaling process-level knowledge to landscape predictions remains challenging. Here, we analyze snow depth (2019 and 2022), terrain elevation, and vegetation height from a watershed on the Seward Peninsula, Alaska, to examine how topography and shrubs shape snow redistribution across spatial scales. We find that snow depth is strongly coupled to terrain at scales below ∼60 m but becomes increasingly decoupled at larger scales. The topographic model of snow depth variation, which transforms terrain data to align with these scale-dependent snow patterns, is well correlated with local snow depth variations (linear fit R 2 > 0.5 for 85% of 100-m patches). A machine learning reconstruction of shrub canopy snow trapping reveals a simple exponential relationship between canopy structure and snow accumulation ( R 2 = 0.59), highlighting the combined influence of topography and vegetation on snow distribution. Together, these empirical relationships capture much of the observed snow variability in the watershed ( R 2 = 0.49, root mean square error (RMSE) = 30 cm), though systematic limitations persist in areas of strong scour and at coarser scales where wind-terrain interactions are more complex. These findings provide a framework for more efficient snow depth prediction and offer insights to improve snow-vegetation feedback representation in Earth System Models.

54 ENVIRONMENTAL SCIENCES↗

Mechanical Resonant Sensing of Spin Texture Dynamics in a 2D Antiferromagnet

Abstract The coupling between the spin degrees of freedom and macroscopic mechanical motions, including striction, shearing, and rotation, has attracted wide interest with applications in actuation, transduction, and information processing. Experiments so far have established the mechanical responses to the long‐range ordered or isolated single spin states. However, it remains elusive whether mechanical motions can couple to a different type of magnetic structure, the non‐collinear spin textures, which exhibit nanoscale spatial variations of spin (domain walls, skyrmions,etc.) and are promising candidates to realize high‐speed computing devices. Here, collective spin texture dynamics is detected with nanoelectromechanical resonators fabricated from 2D antiferromagnetic (AFM) MnPS 3 with 10 −9 strain sensitivity. By examining radio frequency mechanical oscillations under magnetic fields, new magnetic transitions are identified with sharp dips in resonant frequency. They are attributed to collective AFM domain wall motions as supported by the analytical modeling of magnetostriction and large‐scale spin‐dynamics simulations. Additionally, an abnormally large modulation in the mechanical nonlinearity at the transition field infers a fluid‐like response due to ultrafast domain motion. The work establishes a strong coupling between spin texture and mechanical dynamics, laying the foundation for electromechanical manipulation of spin texture and developing quantum hybrid devices.

Chemistry↗

Conformationally Adaptable Extractant Flexes Strong Lanthanide Reverse-Size Selectivity

Chemical selectivity is traditionally understood in the context of rigid molecular scaffolds with precisely defined local coordination and chemical environments that ultimately facilitate a given transformation of interest. By contrast, nature leverages dynamic structures and strong coupling to enable specific interactions with target species in otherwise complex media. Taking inspiration from nature, we demonstrate unconventional selectivity in the solvent extraction of light over heavy lanthanides using a conformationally flexible ligand called octadecyl acyclopa (ODA). This novel ligand forms pseudocyclic molecular complexes with lanthanide ions at organic/aqueous interfaces, revealed by vibrational sum frequency generation spectroscopy. These complexes are extracted into the organic phase, where femtosecond structural dynamics are probed by two-dimensional infrared spectroscopy and ab initio molecular dynamics simulations to mechanistically frame the macroscopic selectivity trends. We find larger-than-expected structural fluctuations and bond lengths for heavy Ln–ODA complexes that arise from an inability of ODA to contort around the smaller ions to satisfy all would-be bonding interactions, despite forming some individually strong bonds. This finding contrasts with the binding of ODA with lighter lanthanides where, despite individually weaker bonds, collective interactions manifest that minimize structural fluctuations and give rise to enhanced thermodynamic stability. Furthermore, these results point to a new paradigm where conformational dynamics and cumulative bonding interactions can be used to facilitate unconventional chemical transformations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Bootstrap embedding for interacting electrons in phonon coherent-state mean field

Here, we develop a Fermi–Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron–phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard–Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

Islam, Shariful [North Carolina State University, ↗

Strain‐Driven Stabilization of a Room‐Temperature Chiral Multiferroic with Coupled Ferroaxial and Ferroelectric Order

Noncollinear ferroic materials are sought after as testbeds to explore the intimate connections between topology and symmetry, which result in electronic, optical, and magnetic functionalities not observed in collinear ferroic materials. For example, ferroaxial materials have rotational structural distortions that break mirror symmetry and induce chirality. When ferroaxial order is coupled with ferroelectricity arising from a broken inversion symmetry, it offers the prospect of electric-field-control of the ferroaxial distortions and opens up new tunable functionalities. However, chiral multiferroics, especially ones stable at room temperature, are rare. A strain-stabilized, room-temperature chiral multiferroic phase in single crystals of BaTiS 3 is reported here. Using first-principles calculations, the stabilization of this multiferroic phase having P6 3 space group for biaxial tensile strains exceeding 1.5% applied on the basal ab-plane of the room temperature P6 3 cm phase of BaTiS 3 is predicted. The chiral multiferroic phase is characterized by rotational distortions of TiS 6 octahedra around the long c-axis and polar displacement of Ti atoms along the c-axis. Furthermore, the ferroaxial and ferroelectric distortions and their domains in P6 3 -BaTiS 3 are directly resolved using atomic resolution scanning transmission electron microscopy. Landau-based phenomenological modeling predicts a strong coupling between the ferroelectric and the ferroaxial order making P6 3 -BaTiS 3 an attractive test bed for achieving electric-field-control of chirality.

Chalcogenide↗

Deciphering and Manipulating Low Dimensional Magnetism

This program investigates the electronic structure and collective quantum phenomena of correlated magnetic materials using advanced angle-resolved photoemission spectroscopy (ARPES) and complementary probes, with a focus on three interrelated material families: (i) the semiconducting van der Waals magnet Cr₂Ge₂Te₆, (ii) metallic Fe-based van der Waals magnets including Fe₃GeTe₂ Fe₃GaTe₂, and Fe5GeTe₂, and (iii) kagome magnets such as FeGe, FeSn, and CsV₃Sb₅/CsCr₃Sb₅. In Cr₂Ge₂Te₆, our work established how spin excitations develop across a dimensional crossover as spins establish correlation to form long range order, providing a clean platform to isolate correlation effects. In metallic Fe-based magnets, we uncovered the dichotomy between flat and dispersive bands, revealed momentum-dependent electronic reconstructions tied to magnetic order, and demonstrated reversible, non-volatile electronic switching near room temperature, highlighting the strong coupling among spin, charge, and lattice degrees of freedom in metallic ferromagnets. In kagome magnets, we identified charge density wave formation, symmetry breaking, flat-band renormalization, and field-induced momentum-dependent electronic anisotropy, elucidating how geometric frustration and electronic correlations conspire to generate emergent quantum states. Collectively, these results establish a unified microscopic framework for understanding correlation-driven electronic reconstruction, symmetry breaking, and collective order across semiconducting and metallic magnetic systems, advancing DOE mission goals in quantum materials discovery and control.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Bottomonium properties in the quark-gluon plasma from a lattice-QCD informed 𝑇-matrix approach

Recent computations of bottomonium correlation functions with extended sources in lattice-discretized quantum chromodynamics (lQCD) provide new insights into heavy-quark dynamics at distance scales which are of the order of the inverse temperature. We analyze these results employing the thermodynamic 𝑇-matrix framework, in a continued effort to interpret lQCD data for quarkonium correlation functions in a nonperturbative and self-consistently solved quantum-many-body approach to a strongly coupled quark-gluon plasma (QGP). Its key inputs are the in-medium driving kernel (potential) of the scattering equation and an interference function which implements 3-body effects in the quarkonium coupling to the thermal medium. A simultaneous description of lQCD results for the bottomonium correlators with extended operators and the previously analyzed Wilson line correlators only requires minor refinements of the potential but calls for stronger interference effects at larger separation of the bottom quark and antiquark. We then analyze the poles of the self-consistent 𝑇 matrices on the real axis to assess the survival of the various bound states. Here, we estimate the pertinent temperatures where the poles disappear for the various bottomonium states and discuss the relation to the corresponding peaks in the bottomonium spectral functions. We also recalculate the spatial diffusion coefficient of the QGP and find it to be similar to that in our previous study.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quarkonium Spectroscopy in the Quark-Gluon Plasma

The properties of bound states are fundamental to hadronic spectroscopy and play a central role in the transition from hadronic matter to a quark-gluon plasma (QGP). In a strongly coupled QGP (sQGP), the interplay of temperature, binding energy, and large collisional widths of the partons poses formidable challenges in evaluating the in-medium properties of hadronic states and their eventual melting. In particular, the existence of heavy quarkonia in the QGP is a long-standing problem that is hard to solve by considering their spectral properties on the real-energy axis. Here, we address this problem by analyzing in-medium thermodynamic quarkonium 𝑇 matrices in the complex energy plane. We first validate this method in vacuum, where the 𝑇-matrix poles of observed states are readily identified. When deploying this approach to recent self-consistently calculated 𝑇 matrices in the QGP, we find that poles in the complex energy plane can persist to surprisingly large temperatures, depending on the strength of the in-medium interactions. While the masses and widths of the pole positions are precisely defined, the notion of a binding energy is not due to the absence of thresholds caused by the (large) widths of the underlying quark or anti-quark spectral functions. Our method thus provides a new and definitive quantum-mechanical criterion to determine the melting temperature of hadronic states in the sQGP while increasing the accuracy in the theoretical determination of transport parameters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Colossal Strain Tuning of Ferroelectric Transitions in KNbO 3 Thin Films

Strong coupling between polarization ( P ) and strain (ɛ) in ferroelectric complex oxides offers unique opportunities to dramatically tune their properties. Here colossal strain tuning of ferroelectricity in epitaxial KNbO 3 thin films grown by sub‐oxide molecular beam epitaxy is demonstrated. While bulk KNbO 3 exhibits three ferroelectric transitions and a Curie temperature ( T c ) of ≈676 K, phase‐field modeling predicts that a biaxial strain of as little as −0.6% pushes its T c > 975 K, its decomposition temperature in air, and for −1.4% strain, to T c > 1325 K, its melting point. Furthermore, a strain of −1.5% can stabilize a single phase throughout the entire temperature range of its stability. A combination of temperature‐dependent second harmonic generation measurements, synchrotron‐based X‐ray reciprocal space mapping, ferroelectric measurements, and transmission electron microscopy reveal a single tetragonal phase from 10 K to 975 K, an enhancement of ≈46% in the tetragonal phase remanent polarization ( P r ), and a ≈200% enhancement in its optical second harmonic generation coefficients over bulk values. These properties in a lead‐free system, but with properties comparable or superior to lead‐based systems, make it an attractive candidate for applications ranging from high‐temperature ferroelectric memory to cryogenic temperature quantum computing.

36 MATERIALS SCIENCE↗

Highly Responsive Polar Vortices in All‐Ferroelectric Heterostructures

Abstract The discovery of polar vortices and skyrmions in ferroelectric‐dielectric superlattices [such as (PbTiO 3 ) n /(SrTiO 3 ) n ] has ushered in an era of novel dipolar topologies and corresponding emergent phenomena. The key to creating such emergent features has generally been considered to be related to counterpoising strongly polar and non‐polar materials thus creating the appropriate boundary conditions. This limits the utility these materials can have, however, by rendering (effectively) half of the structure unresponsive to applied stimuli. Here, using advanced thin‐film deposition and an array of characterization and simulation approaches, polar vortices are realized in all‐ferroelectric trilayers, multilayers, and superlattices built from the fundamental building block of (PbTiO 3 ) n /(Pb x Sr 1− x TiO 3 ) n wherein in‐plane ferroelectric polarization in the Pb x Sr 1− x TiO 3 provides the appropriate boundary conditions. These superlattices exhibit substantially enhanced electromechanical and ferroelectric responses in the out‐of‐plane direction that arise from the ability of the polarization in both layers to rotate to the out‐of‐plane direction under field. In the in‐plane direction, the layers are found to be strongly coupled during switching and when heterostructured with ferroelectric‐dielectric building blocks, it is possible to produce multistate switching. This approach expands the realm of systems supporting emergent dipolar texture formation and does so with entirely ferroelectric materials thus greatly improving their responses.

Kavle, Pravin↗