Long-range Order Research Articles

Relaxor unveils geometrical frustration

For over a century, materials science has been focused on comparing magnetism and ferroelectricity, revealing similarities in order types, domains, hysteresis, and responses to external stimuli. The exceptional physical properties of magnets often originate from frustration, which can result from site disorder and lattice geometry. While disordered relaxor ferroelectrics exhibit ultra-high dielectric and piezoelectric properties and fingerprinted behavior similar to spin glasses, ferroelectric-like materials with clear geometrically frustrated states have not been previously identified. Here we introduce a new type of relaxor material, a geometrically frustrated relaxor, exemplified by a Bi2Ti2O7 single crystal with a compositionally ordered pyrochlore structure. Our findings demonstrate canonical relaxor behavior, including dielectric anomalies, dipole freezing, non-ergodicity and a lack of spontaneous phase transitions. Furthermore, we show the emergence of a unique dipole ice state upon cooling, arising from conflicting order parameters related to two mutually exclusive rigid unit modes of Bi4Oʹ tetrahedral rotations. The coexistence of these rotations does not satisfy symmetry constraints, causing geometrical frustration and suppressing the long-range order. The results provide the structural mechanism of geometrical frustration manifestation in Bi-containing pyrochlores, opening up avenues for exploring exotic ground states and advanced functionalities in dielectric materials.

Nature of Excitons and Their Ligand-Mediated Delocalization in Nickel Dihalide Charge-Transfer Insulators

The fundamental optical excitations of correlated transition-metal compounds are typically identified with multielectronic transitions localized at the transition-metal site, such as dd transitions. In this vein, intense interest has surrounded the appearance of sharp, below-band-gap optical transitions, i.e., excitons, within the magnetic phase of correlated Ni2+ van der Waals magnets. The interplay of magnetic and charge-transfer insulating ground states in Ni2+ systems raises intriguing questions on the roles of long-range magnetic order and of metal-ligand charge transfer in the exciton nature, which inspired microscopic descriptions beyond typical dd excitations. Here we study the impact of charge transfer and magnetic order on the excitation spectrum of the nickel dihalides (NiX2, X=Cl, Br, and I) using Ni-L3 edge resonant inelastic x-ray scattering (RIXS). In all compounds, we detect sharp excitations, analogous to the recently reported excitons, and assign them to spin-singlet multiplets of octahedrally coordinated Ni2+ stabilized by intra-atomic Hund’s exchange. Additionally, we demonstrate that these excitons are dispersive using momentum-resolved RIXS. Our data evidence a ligand-mediated multiplet dispersion, which is tuned by the charge-transfer gap and independent of the presence of long-range magnetic order. This reveals the mechanisms governing nonlocal interactions of on-site dd excitations with the surrounding crystal or magnetic structure, in analogy to ground-state superexchange. These measurements thus establish the roles of magnetic order, self-doped ligand holes, and intersite-coupling mechanisms for the properties of dd excitations in charge-transfer insulators. Published by the American Physical Society 2024

Optimizing high-temperature energy storage in tungsten bronze-structured ceramics via high-entropy strategy and bandgap engineering

As a vital material utilized in energy storage capacitors, dielectric ceramics have widespread applications in high-power pulse devices. However, the development of dielectric ceramics with both high energy density and efficiency at high temperatures poses a significant challenge. In this study, we employ high-entropy strategy and band gap engineering to enhance the energy storage performance in tetragonal tungsten bronze-structured dielectric ceramics. The high-entropy strategy fosters cation disorder and disrupts long-range ordering, consequently regulating relaxation behavior. Simultaneously, the reduction in grain size, elevation of conductivity activation energy, and increase in band gap collectively bolster the breakdown electric strength. This cascade effect results in outstanding energy storage performance, ultimately achieving a recoverable energy density of 8.9 J cm−3 and an efficiency of 93% in Ba0.4Sr0.3Ca0.3Nb1.7Ta0.3O6 ceramics, which also exhibit superior temperature stability across a broad temperature range up to 180 °C and excellent cycling reliability up to 105. This research presents an effective method for designing tetragonal tungsten bronze dielectric ceramics with ultra-high comprehensive energy storage performance.

Structure Evolution of 2D Covalent Organic Frameworks Unveiled by Single-Crystal X-ray Diffraction.

We report 9 crystal structures of a two-dimensional (2D) covalent organic framework (COF), including the parent Py-1P, 5 derivatives formed by chemical reactions, and 3 dynamic states by solvent exchange/loss. Structure details of these porous crystals, including stacking mode, interlayer distance, pore aperture, and incline angle, before, during, and after conversion processes in solution, were unveiled by single-crystal X-ray diffraction with resolutions up to 0.85 Å. The structure evolution is triggered by stepwise conformational transformation of the molecular building blocks in 2D COF, while their long-range ordering remained unsacrificed.

Acoustic-assisted deposition of ordered self-assembled silica opal layers on hydrophilic single crystal diamond substrates

We deposited self-assembled films of a few monolayers of silica spheres from the water-based colloid on vertically moving hydrophilic single crystal diamond substrates. The use of acoustic agitation of the water suspension with the SiO2 nanospheres significantly improved the long-range order of the films with opal structure. The study examines the evolution of the structure, specifically the size of single crystal domains, with the assistance of sound frequency (0–2500 Hz) and intensity (0–125 dB). Optimal (resonance) parameters are determined based on scanning electron microscopy and optical reflection spectroscopy of the films. The production of high-quality photonic crystals, including templates for diamond-based ordered composites and inverse opal structures, is a promising application of acoustic crystallization of opals on diamond substrates.

Universal Hyperuniform Organization in Looped Leaf Vein Networks.

The leaf vein network is a hierarchical vascular system that transports water and nutrients to the leaf cells. The thick primary veins form a branched network, while the secondary veins can develop closed loops forming a well-defined cellular structure. Through extensive analysis of a variety of distinct leaf species, we discover that the apparently disordered cellular structures of the secondary vein networks exhibit a universal hyperuniform organization and possess a hidden order on large scales. Disorder hyperuniform systems lack conventional long-range order, yet they completely suppress normalized infinite-wavelength density fluctuations like crystals. Specifically, we find that the distributions of the geometric centers associated with the vein network loops possess a vanishing static structure factor in the limit that the wave number k goes to 0, i.e., S(k)∼k^{α}, where α≈0.64±0.021, providing an example of class III hyperuniformity in biology. This hyperuniform organization leads to superior efficiency of diffusive transport, as evidenced by the much faster convergence of the time-dependent spreadability S(t) to its longtime asymptotic limit, compared to that of other uncorrelated or correlated disordered but nonhyperuniform organizations. Our results also have implications for the discovery and design of novel disordered network materials with optimal transport properties.

Lifshitz transition enabling superconducting dome around a charge-order critical point.

Superconductivity often emerges as a dome around a quantum critical point (QCP) where long-range order is suppressed to zero temperature, mostly in magnetically ordered materials. However, the emergence of superconductivity at charge-order QCPs remains shrouded in mystery, despite its relevance to high-temperature superconductors and other exotic phases of matter. Here, we present resistance measurements proving that a dome of superconductivity surrounds the putative charge-density-wave QCP in pristine samples of titanium diselenide tuned with hydrostatic pressure. In addition, our quantum oscillation measurements combined with electronic structure calculations show that superconductivity sets in precisely when large electron and hole pockets suddenly appear through an abrupt change of the Fermi surface topology, also known as a Lifshitz transition. Combined with the known repulsive interaction, this suggests that unconventional s± superconductivity is mediated by charge-density-wave fluctuations in titanium diselenide. These results highlight the importance of the electronic ground state and charge fluctuations in enabling unconventional superconductivity.

Syntheses, structures, and magnetic properties of new [Co9] cluster

A new spin-cluster compound K6BaCo9(PO4H)3(PO4)6Cl2 was synthesized by the traditional solid-phase method. The fundamental magnetic unit of the compound is a coupled [Co9] cluster, which is composed of three non-coplanar triangles. These [Co9] clusters are interconnected by phosphate groups, constructing a two-dimensional framework in the ab plane. The crystal shows the clear easy-axis anisotropy. No long-range magnetic ordering was observed down to 2 K, but there is short-range spin correlation below T = 2.45 K. The Curie-Weiss temperature is about θCW = −19.38 K for the powder sample, which indicates that the dominant exchange interaction is antiferromagnetic with strong frustration (f = |θCW|/T ≈ 10). The magnetization curve presents a likely magnetic field induced transition at μ0Hc = 1.85 T.

Ultrahigh Energy Storage Performance of BiFeO3-BaTiO3 Flexible Film Capacitor with High-Temperature Stability via Defect Design.

Nanoengineering polar oxide films have attracted great attention in energy storage due to their high energy density. However, most of them are deposited on thick and rigid substrates, which is not conducive to the integration of capacitors and applications in flexible electronics. Here, an alternative strategy using van der Waals epitaxial oxide dielectrics on ultra-thin flexible mica substrates is developed and increased the disorder within the system through high laser flux. The introduction of defects can efficiently weaken or destroy the long-range ferroelectric ordering, ultimately leading to the emergence of a large numbers of weak-coupling regions. Such polarization configuration ensures fast polarization response and significantly improves energy storage characteristics. A flexible BiFeO3-BaTiO3 (BF-BT) capacitor exhibits a total energy density of 43.5 J cm-3 and an efficiency of 66.7% and maintains good energy storage performance over a wide temperature range (20-200 °C) and under large bending deformation (bending radii ≈ 2mm). This study provides a feasible approach to improve the energy storage characteristics of dielectric oxide films and paves the way for their practical application in high-energy density capacitors.

Classification of classical spin liquids: Typology and resulting landscape

Classical spin liquids (CSL) lack long-range magnetic order and are characterized by an extensive ground-state degeneracy. We propose a classification scheme of CSLs based on the structure of the flat bands of their Hamiltonians. Depending on absence or presence of the gap from the flat band, the CSL are classified as algebraic or fragile topological, respectively. Each category is further classified: the algebraic case by the nature of the emergent Gauss's law at the gap-closing point(s), and the fragile topological case by the homotopy of the eigenvector winding around the Brillouin zone. Previously identified models of CSLs fit snugly into our scheme, on a landscape where algebraic CSLs are located at transitions between fragile topological ones. It also allows us to present new families of models illustrating this landscape, which hosts both fragile topological and algebraic CSLs, as well as transitions between them. Published by the American Physical Society 2024

Discrete trapping levels of localized states in amorphous silicon nitride

The spectrum of localized hole states (traps) in amorphous silicon nitride, a-Si3N4, is experimentally studied using the method of thermally stimulated depolarization. The experiment is compared with theoretical calculations using three models of the energy spectrum of traps: discrete spectrum (monoenergetic trap), continuous spectrum, and Gaussian trap distribution. The experiment is quantitatively described by a model of a discrete spectrum of traps with an energy of 1.15 eV and a width of no more than 0.01 eV. In the case of a continuous and Gaussian spectrum of traps, the contribution to depolarization is made by the deepest traps. The blurring of the trap energy level in a-Si3N4 due to the absence of long-range order (fluctuations in the Si–N bond length and fluctuations in the N–Si–N and Si–N–Si angles) does not exceed 0.01 eV.

Chiral multiferroicity in two-dimensional hybrid organic-inorganic perovskites.

Chiral multiferroics offer remarkable capabilities for controlling quantum devices at multiple levels. However, these materials are rare due to the competing requirements of long-range orders and strict symmetry constraints. In this study, we present experimental evidence that the coexistence of ferroelectric, magnetic orders, and crystallographic chirality is achievable in hybrid organic-inorganic perovskites [(R/S)-β-methylphenethylamine]2CuCl4. By employing Landau symmetry mode analysis, we investigate the interplay between chirality and ferroic orders and propose a novel mechanism for chirality transfer in hybrid systems. This mechanism involves the coupling of non-chiral distortions, characterized by defining a pseudo-scalar quantity, ( represents the ferroelectric displacement vector and denotes the ferro-rotational vector), which distinguishes between (R)- and (S)-chirality based on its sign. Moreover, the reversal of this descriptor's sign can be associated with coordinated transitions in ferroelectric distortions, Jahn-Teller antiferro-distortions, and Dzyaloshinskii-Moriya vectors, indicating the mediating role of crystallographic chirality in magnetoelectric correlations.

Informatics-Based Learning of Oxygen Vacancy Ordering Principles in Oxygen-Deficient Perovskites.

Ordered oxygen vacancies (OOVs) in perovskites can exhibit long-range order and may be used to direct materials properties through modifications in electronic structures and broken symmetries. Based on the various vacancy patterns observed in previously known compounds, we explore the ordering principles of oxygen-deficient perovskite oxides with ABO2.5 stoichiometry to identify other OOV variants. We performed first-principles calculations to assess the OOV stability on a data set of 50 OOV structures generated from our bespoke algorithm. The algorithm employs uniform planar vacancy patterns on (111) pseudocubic perovskite layers and the approach proves effective for generating stable OOV patterns with minimal computational loads. We find as expected that the major factors determining the stability of OOV structures include coordination preferences of transition metals and elastic penalties resulting from the assemblies of polyhedra. Cooperative rotational modes of polyhedra within the OOV structures reduce elastic instabilities by optimizing the bond valence of A- and B cations. This finding explains the observed formation of vacancy channels along low-index crystallographic directions in prototypical OOV phases. The identified ordering principles enable us to devise other stable vacancy patterns with longer periodicity for targeted property design in yet to be synthesized compounds.

Strong interlayer magnetic exchange coupling in La3Ni2O7−δ revealed by inelastic neutron scattering

After several decades of studies of high-temperature superconductivity, there is no compelling theory for the mechanism yet; however, the spin fluctuations have been widely believed to play a crucial role in forming the superconducting Cooper pairs. The recent discovery of high-temperature superconductivity near 80 K in the bilayer nickelate La3Ni2O7 under pressure provides a new platform to elucidate the origins of high-temperature superconductivity. We perform elastic and inelastic neutron scattering studies on a polycrystalline sample of La3Ni2O7−δ at ambient pressure. No magnetic order can be identified down to 10 K. The absence of long-range magnetic order in neutron diffraction measurements may be ascribed to the smallness of the magnetic moment. However, we observe a weak flat spin-fluctuation signal in the inelastic scattering spectra at ∼ 45 meV. The observed spin excitations could be interpreted as a result of strong interlayer and weak intralayer magnetic couplings for stripe-type antiferromagnetic orders. Our results provide crucial information on the spin dynamics and are thus important for understanding the superconductivity in La3Ni2O7.

Anomalous magnetic and electrical properties of disordered double perovskite alloy LaCaMnFeO6

Double perovskite alloys are of significant interest owing to their intriguing magnetic properties and potential practical applications. In this study, we provided a detailed report on the structural, electrical and magnetic features of the double perovskite LaCaMnFeO6, prepared via the conventional solid-state reaction technique. Neutron diffraction analysis showed that the sample is single-phase adopting the Pnma orthorhombic structure with random distribution of La3+/Ca2+ and Mn4+/Fe3+ ions on A- and B-sites, respectively. A long-range G-type antiferromagnetic order was formed below T N = 250 K. Magnetic measurements unveiled a cluster glassy behavior at low temperatures with a complex distribution of cluster magnetic anisotropy energy. Ferromagnetic clusters consisting of two Mn4+ and one Fe3+ were found to exist in the paramagnetic phase. The complex magnetic properties of LaCaMnFeO6 are attributed to the cation disorder effect combined with the competition between magnetic interactions. Unusual electrical behavior with a large positive magnetoresistive effect was observed and correlated to magnetic phase transitions.

Local strain heterogeneity associated with Al/Si ordering in anorthite, CaAl2Si2O8, with implications for thermodynamic mixing behavior and trace element partitioning in plagioclase feldspars

Abstract Hard Mode IR powder absorption spectroscopy has been used to characterize local strain relaxation associated with Al/Si ordering in a suite of synthetic anorthite samples with structural states that vary from a high degree of Al/Si order through a metastable incommensurate structure at intermediate states of order to long-range order with I1 symmetry. The dominant feature accompanying the changing structural states is line broadening, which has been quantified by autocorrelation analysis and is attributed to local heterogeneous strain variations on a length scale of at least 1–5 unit cells. The autocorrelation results are consistent with contributions to the line broadening as being due to order parameters for both the C1 → I1 and I1 → P1 transitions, which couple biquadratically, λQod2Qdispl2. Close correlation with enthalpy variations from previously published calorimetric data indicates that the driving force for ordering can be understood in terms of elimination of strain fields arising from accommodating more or less rigid AlO4 and SiO4 tetrahedra in the feldspar framework. The metastable incommensurate structure of anorthite is closely analogous to the stable incommensurate structure that develops at intermediate compositions in the plagioclase solid solution, confirming that the same strain relaxation mechanism dominates the properties and behavior of all structural states across the solid solution. Elimination of strain heterogeneity by ordering on the basis of I1 symmetry determines the form of non-ideal mixing shown by the solid solution at high temperatures, and changes in elastic properties may contribute to a break in the slope of partitioning of trace elements between crystals and melt.

Enhanced Electron Delocalization Induced by Ferromagnetic Sulfur doped C3N4 Triggers Selective H2O2 Production.

For the 2D metal-free carbon catalysts, the atomic coplanar architecture enables a large number of pz orbitals to overlap laterally, thus forming π-electron delocalization, and the delocalization degree of the central atom dominates the catalytic activity. Herein, designing sulfur-doped defect-rich graphitic carbon nitride (S-Nv-C3N4) materials as a model, we propose a strategy to promote localized electron polarization by enhancing the ferromagnetism of ultra-thin 2D carbon nitride nanosheets. The introduction of sulfur (S) further promotes localized ferromagnetic coupling, thereby inducing long-range ferromagnetic ordering and accelerating the electron interface transport. Meanwhile, the hybridization of sulfur atoms breaks the symmetry and integrity of the unit structure, promotes electron enrichment and stimulating electron delocalization at the active site. This optimization enhances the *OOH desorption, providing a favorable kinetic pathway for the production of hydrogen peroxide (H2O2). Consequently, S-Nv-C3N4 exhibits high selectivity (>95 %) and achieves a superb H2O2 production rate, approaching 4374.8 ppm during continuous electrolysis over 300 hour. According to theoretical calculation and in situ spectroscopy, the ortho-S configuration can provide ferromagnetic perturbation in carbon active centers, leading to the electron delocalization, which optimizes the OOH* adsorption during the catalytic process.

A sustainable deposition method for diamond-like nanocomposite coatings – Insights into the evolution of atomic structure and properties

Silicon and oxygen-doped hydrogenated amorphous carbon (a-C:H:Si:O), typically termed as diamond-like nanocomposite (DLN), is amongst the most widely adapted coating materials for advanced applications. Traditionally, these coatings are deposited by plasma-enhanced chemical vapor deposition (PECVD) using organosilicon precursors, which not only restrict coating stoichiometry but also have a high environmental footprint. Here, we report the deposition of highly dense and microscopically defect-free a-C:H:Si:O coating using magnetron sputtering as a facile and sustainable deposition method that allows a fine stoichiometry control. Furthermore, we investigate the evolution of the atomic structure and the local-atomic environment when Si, O, and H atoms are successively doped into the amorphous carbon (a-C) matrix. Diffraction and spectroscopic analyses of doped coatings indicate the absence of any long-range order and an atomic-scale composite structure. The results also establish that doping of a-C leads to improved sp3 bonding, formation of Si–O-based networks, and termination of carbon dangling bonds, resulting in increased structural stability. The densification of the coating, combined with improved sp3 character, results in hardness and modulus exceeding those of PECVD-deposited coatings. These findings present a viable potential of magnetron sputtering as a straightforward and greener alternative to traditional PECVD-based methods for producing a promising coating material.

Magnetic properties and magnetoresistance of hybrid multilayer nanostructures {[(Co40Fe40B20)34(SiO2)66]/[ZnO]}n

The structural, electrical, magnetic, magneto-optical properties and magnetoresistance of {[(Co40Fe40B20)34(SiO2)66]/[ZnO]}n multilayer structures, where n = 50 is the number of bilayers (Co40Fe40B20)34(SiO2)66 nanocomposite and ZnO have been studied. The thicknesses of (Co40Fe40B20)34(SiO2)66 nanocomposite layers as well as ZnO spacers were varied in a wide range. The samples were synthesized by ion-beam sputtering onto glass ceramic substrates. The (Co40Fe40B20)34(SiO2)66 composite have an amorphous structure and the semiconductor ZnO interlayers have a hexagonal crystalline structure with the p63mc symmetry group. The nanocomposite layers containing a ferromagnetic component far from the percolation threshold are in a superparamagnetic state. The presented in the paper data of magnetization, magneto-optical transverse Kerr effect and magnetoresistance indicates that long-range ferromagnetic order does not form down to 77 K both for references ZnO films and studied multilayers with thin and thick ZnO interlayers. An increase in the magneto-optical signal in multilayers compared to references (Co40Fe40B20)34(SiO2)66 composite films has been detected at 1.2 eV. The magnetoresistance of {[(Co40Fe40B20)34(SiO2)66]/[ZnO]}n multilayers with thick (>32 nm) ZnO interlayers is lower than in reference (Co40Fe40B20)34(SiO2)66 nanocomposite, while at thin ZnO interlayers magnetoresistance is significantly higher and reaches 12 % at temperatures of 77 К. Possible mechanisms of ferromagnetic and antiferromagnetic ordering, enhancement of the magneto-optical response and magnetoresistance in {[(Co40Fe40B20)34(SiO2)66]/[ZnO]}n multilayer nanostructures are discussed.

Symmetry and stability of orientationally ordered collective motions of self-propelled, semiflexible filaments

Ordered, collective motions commonly arise spontaneously in systems of many interacting, active units, ranging from cellular tissues and bacterial colonies to self-propelled colloids and animal flocks. Active phases are especially rich when the active units are sufficiently anisotropic to produce liquid crystalline order and thus active nematic phenomena, with important biophysical examples provided by cytoskeletal filaments including microtubules and actin. Gliding assay experiments have provided a test bed to study the collective motions of these cytoskeletal filaments and unlocked diverse collective active phases, including states with long-range orientational order. However, it is not well understood how such long-range order emerges from the interplay of passive and active aligning mechanisms. We use Brownian dynamics simulations to study the collective motions of semiflexible filaments that self-propel in quasi-two-dimensions, in order to gain insights into the aligning mechanisms at work in these gliding assay systems. We find that, without aligning torques in the microscopic model, long-range orientational order can only be achieved when the filaments are able to overlap. The symmetry (nematic or polar) of the long-range order that first emerges is shown to depend on the energy cost of filament overlap and on filament flexibility. However, our model also predicts that a long-range-ordered active nematic state is merely transient, whereas long-range polar order is the only active dynamical steady state in systems with finite filament rigidity. Published by the American Physical Society 2024