Local strain inhomogeneities during electrical triggering of a metal-insulator transition revealed by X-ray microscopy.

Electrical triggering of a metal-insulator transition (MIT) often results in the formation of characteristic spatial patterns such as a metallic filament percolating through an insulating matrix or an insulating barrier splitting a conducting matrix. When MIT triggering is driven by electrothermal effects, the temperature of the filament or barrier can be substantially higher than the rest of the material. Using X-ray microdiffraction and dark-field X-ray microscopy, we show that electrothermal MIT triggering leads to the development of an inhomogeneous strain profile across the switching device, even when the material does not undergo a pronounced, discontinuous structural transition coinciding with the MIT. Diffraction measurements further reveal evidence of unique features associated with MIT triggering including lattice distortions, tilting, and twinning, which indicate structural nonuniformity of both low- and high-resistance regions inside the switching device. Such lattice deformations do not occur under equilibrium, zero-voltage conditions, highlighting the qualitative difference between states achieved through increasing temperature and applying voltage in nonlinear electrothermal materials. Electrically induced strain, lattice distortions, and twinning could have important contributions in the MIT triggering process and drive the material into nonequilibrium states, providing an unconventional pathway to explore the phase space in strongly correlated electronic systems.

Low-temperature emergent neuromorphic networks with correlated oxide devices.

Neuromorphic computing-which aims to mimic the collective and emergent behavior of the brain's neurons, synapses, axons, and dendrites-offers an intriguing, potentially disruptive solution to society's ever-growing computational needs. Although much progress has been made in designing circuit elements that mimic the behavior of neurons and synapses, challenges remain in designing networks of elements that feature a collective response behavior. We present simulations of networks of circuits and devices based on superconducting and Mott-insulating oxides that display a multiplicity of emergent states that depend on the spatial configuration of the network. Our proposed network designs are based on experimentally known ways of tuning the properties of these oxides using light ions. We show how neuronal and synaptic behavior can be achieved with arrays of superconducting Josephson junction loops, all within the same device. We also show how a multiplicity of synaptic states could be achieved by designing arrays of devices based on hydrogenated rare earth nickelates. Together, our results demonstrate a research platform that utilizes the collective macroscopic properties of quantum materials to mimic the emergent behavior found in biological systems.

Spatial Interactions in Hydrogenated Perovskite Nickelate Synaptic Networks.

A key aspect of how the brain learns and enables decision-making processes is through synaptic interactions. Electrical transmission and communication in a network of synapses are modulated by extracellular fields generated by ionic chemical gradients. Emulating such spatial interactions in synthetic networks can be of potential use for neuromorphic learning and the hardware implementation of artificial intelligence. Here, we demonstrate that in a network of hydrogen-doped perovskite nickelate devices, electric bias across a single junction can tune the coupling strength between the neighboring cells. Electrical transport measurements and spatially resolved diffraction and nanoprobe X-ray and scanning microwave impedance spectroscopic studies suggest that graded proton distribution in the inhomogeneous medium of hydrogen-doped nickelate film enables this behavior. We further demonstrate signal integration through the coupling of various junctions.

Discovery of Charge Order in the Transition Metal Dichalcogenide Fe_{x}NbS_{2}.

The Fe intercalated transition metal dichalcogenide (TMD), Fe_{1/3}NbS_{2}, exhibits remarkable resistance switching properties and highly tunable spin ordering phases due to magnetic defects. We conduct synchrotron x-ray scattering measurements on both underintercalated (x=0.32) and overintercalated (x=0.35) samples. We discover a new charge order phase in the overintercalated sample, where the excess Fe atoms lead to a zigzag antiferromagnetic order. The agreement between the charge and magnetic ordering temperatures, as well as their intensity relationship, suggests a strong magnetoelastic coupling as the mechanism for the charge ordering. Our results reveal the first example of a charge order phase among the intercalated TMD family and demonstrate the ability to stabilize charge modulation by introducing electronic correlations, where the charge order is absent in bulk 2H-NbS_{2} compared to other pristine TMDs.

Short-Range Nematic Fluctuations in Sr_{1-x}Na_{x}Fe_{2}As_{2} Superconductors.

Interactions between nematic fluctuations, magnetic order and superconductivity are central to the physics of iron-based superconductors. Here we report on in-plane transverse acoustic phonons in hole-doped Sr_{1-x}Na_{x}Fe_{2}As_{2} measured via inelastic x-ray scattering, and extract both the nematic susceptibility and the nematic correlation length. By a self-contained method of analysis, for the underdoped (x=0.36) sample, which harbors a magnetically ordered tetragonal phase, we find it hosts a short nematic correlation length ξ∼10 Å and a large nematic susceptibility χ_{nem}. The optimal-doped (x=0.55) sample exhibits weaker phonon softening effects, indicative of both reduced ξ and χ_{nem}. Our results suggest short-range nematic fluctuations may favor superconductivity, placing emphasis on the nematic correlation length for understanding the iron-based superconductors.

Local Orthorhombicity in the Magnetic C_{4} Phase of the Hole-Doped Iron-Arsenide Superconductor Sr_{1-x}Na_{x}Fe_{2}As_{2}.

We report on temperature-dependent pair distribution function measurements of Sr_{1-x}Na_{x}Fe_{2}As_{2}, an iron-based superconductor system that contains a magnetic phase with reentrant tetragonal symmetry, known as the magnetic C_{4} phase. Quantitative refinements indicate that the instantaneous local structure in the C_{4} phase comprises fluctuating orthorhombic regions with a length scale of ∼2 nm, despite the tetragonal symmetry of the average static structure. Additionally, local orthorhombic fluctuations exist on a similar length scale at temperatures well into the paramagnetic tetragonal phase. These results highlight the exceptionally large nematic susceptibility of iron-based superconductors and have significant implications for the magnetic C_{4} phase and the neighboring C_{2} and superconducting phases.

Self-assembly of nanocrystal checkerboard patterns via non-specific interactions.

Checkerboard lattices-where the resulting structure is open, porous, and highly symmetric-are difficult to create by self-assembly. Synthetic systems that adopt such structures typically rely on shape complementarity and site-specific chemical interactions that are only available to biomolecular systems (e.g., protein, DNA). Here we show the assembly of checkerboard lattices from colloidal nanocrystals that harness the effects of multiple, coupled physical forces at disparate length scales (interfacial, interparticle, and intermolecular) and that do not rely on chemical binding. Colloidal Ag nanocubes were bi-functionalized with mixtures of hydrophilic and hydrophobic surface ligands and subsequently assembled at an air-water interface. Using feedback between molecular dynamics simulations and interfacial assembly experiments, we achieve a periodic checkerboard mesostructure that represents a tiny fraction of the phase space associated with the polymer-grafted nanocrystals used in these experiments. In a broader context, this work expands our knowledge of non-specific nanocrystal interactions and presents a computation-guided strategy for designing self-assembling materials.

Low-energy quasi-circular electron correlations with charge order wavelength in Bi2Sr2CaCu2O8+δ.

Most resonant inelastic x-ray scattering (RIXS) studies of dynamic charge order correlations in the cuprates have focused on the high-symmetry directions of the copper oxide plane. However, scattering along other in-plane directions should not be ignored as it may help understand, for example, the origin of charge order correlations or the isotropic scattering resulting in strange metal behavior. Our RIXS experiments reveal dynamic charge correlations over the qx-qy scattering plane in underdoped Bi2Sr2CaCu2O8+δ. Tracking the softening of the RIXS-measured bond-stretching phonon, we show that these dynamic correlations exist at energies below approximately 70 meV and are centered around a quasi-circular manifold in the qx-qy scattering plane with radius equal to the magnitude of the charge order wave vector, qCO. This phonon-tracking procedure also allows us to rule out fluctuations of short-range directional charge order (i.e., centered around [qx = ±qCO, qy = 0] and [qx = 0, qy = ±qCO]) as the origin of the observed correlations.

Orbital reflectometry of oxide heterostructures.

The occupation of d orbitals controls the magnitude and anisotropy of the inter-atomic electron transfer in transition-metal oxides and hence exerts a key influence on their chemical bonding and physical properties. Atomic-scale modulations of the orbital occupation at surfaces and interfaces are believed to be responsible for massive variations of the magnetic and transport properties, but could not thus far be probed in a quantitative manner. Here we show that it is possible to derive quantitative, spatially resolved orbital polarization profiles from soft-X-ray reflectivity data, without resorting to model calculations. We demonstrate that the method is sensitive enough to resolve differences of ~3% in the occupation of Ni e(g) orbitals in adjacent atomic layers of a LaNiO(3)-LaAlO(3) superlattice, in good agreement with ab initio electronic-structure calculations. The possibility to quantitatively correlate theory and experiment on the atomic scale opens up many new perspectives for orbital physics in transition-metal oxides.

Imaging mesoscopic antiferromagnetic spin textures in the dilute limit from single-geometry resonant coherent x-ray diffraction.

The detection and manipulation of antiferromagnetic domains and topological antiferromagnetic textures are of central interest to solid-state physics. A fundamental step is identifying tools to probe the mesoscopic texture of an antiferromagnetic order parameter. In this work, we demonstrate that Bragg coherent diffractive imaging can be extended to study the mesoscopic texture of an antiferromagnetic order parameter using resonant magnetic x-ray scattering. We study the onset of the antiferromagnet transition in PrNiO3, focusing on a temperature regime in which the antiferromagnetic domains are dilute in the beam spot and the coherent diffraction pattern modulating the antiferromagnetic peak is greatly simplified. We demonstrate that it is possible to extract the arrangements and sizes of these domains from single diffraction patterns and show that the approach could be extended to a time-structured light source to study the motion of dilute domains or the motion of topological defects in an antiferromagnetic spin texture.

Stabilization of three-dimensional charge order through interplanar orbital hybridization in PrxY1-xBa2Cu3O6+δ.

The shape of 3d-orbitals often governs the electronic and magnetic properties of correlated transition metal oxides. In the superconducting cuprates, the planar confinement of the [Formula: see text] orbital dictates the two-dimensional nature of the unconventional superconductivity and a competing charge order. Achieving orbital-specific control of the electronic structure to allow coupling pathways across adjacent planes would enable direct assessment of the role of dimensionality in the intertwined orders. Using Cu L3 and Pr M5 resonant x-ray scattering and first-principles calculations, we report a highly correlated three-dimensional charge order in Pr-substituted YBa2Cu3O7, where the Pr f-electrons create a direct orbital bridge between CuO2 planes. With this we demonstrate that interplanar orbital engineering can be used to surgically control electronic phases in correlated oxides and other layered materials.

Perovskite neural trees.

Trees are used by animals, humans and machines to classify information and make decisions. Natural tree structures displayed by synapses of the brain involves potentiation and depression capable of branching and is essential for survival and learning. Demonstration of such features in synthetic matter is challenging due to the need to host a complex energy landscape capable of learning, memory and electrical interrogation. We report experimental realization of tree-like conductance states at room temperature in strongly correlated perovskite nickelates by modulating proton distribution under high speed electric pulses. This demonstration represents physical realization of ultrametric trees, a concept from number theory applied to the study of spin glasses in physics that inspired early neural network theory dating almost forty years ago. We apply the tree-like memory features in spiking neural networks to demonstrate high fidelity object recognition, and in future can open new directions for neuromorphic computing and artificial intelligence.

Charge ordering in superconducting copper oxides.

Charge order has recently been identified as a leading competitor of high-temperature superconductivity in moderately doped cuprates. We provide a survey of universal and materials-specific aspects of this phenomenon, with emphasis on results obtained by scattering methods. In particular, we discuss the structure, periodicity, and stability range of the charge-ordered state, its response to various external perturbations, the influence of disorder, the coexistence and competition with superconductivity, as well as collective charge dynamics. In the context of this journal issue which honors Roger Cowley's legacy, we also discuss the connection of charge ordering with lattice vibrations and the central-peak phenomenon. We end the review with an outlook on research opportunities offered by new synthesis methods and experimental platforms, including cuprate thin films and superlattices.

Correlated states in ß-Li2IrO3 driven by applied magnetic fields.

Magnetic honeycomb iridates are thought to show strongly spin-anisotropic exchange interactions which, when highly frustrated, lead to an exotic state of matter known as the Kitaev quantum spin liquid. However, in all known examples these materials magnetically order at finite temperatures, the scale of which may imply weak frustration. Here we show that the application of a relatively small magnetic field drives the three-dimensional magnet ß-Li2IrO3 from its incommensurate ground state into a quantum correlated paramagnet. Interestingly, this paramagnetic state admixes a zig-zag spin mode analogous to the zig-zag order seen in other Mott-Kitaev compounds. The rapid onset of the field-induced correlated state implies the exchange interactions are delicately balanced, leading to strong frustration and a near degeneracy of different ground states.Materials with a Kitaev spin liquid ground state are sought after as models of quantum phases but candidates so far form either zig-zag or incommensurate magnetic order. Ruiz et al. find a crossover between these states in ß-Li2IrO3 under weak magnetic fields, indicating strongly frustrated spin interactions.

Modular soft x-ray spectrometer for applications in energy sciences and quantum materials.

Over the past decade, the advances in grating-based soft X-ray spectrometers have revolutionized the soft X-ray spectroscopies in materials research. However, these novel spectrometers are mostly dedicated designs, which cannot be easily adopted for applications with diverging demands. Here we present a versatile spectrometer design concept based on the Hettrick-Underwood optical scheme that uses modular mechanical components. The spectrometer's optics chamber can be used with gratings operated in either inside or outside orders, and the detector assembly can be reconfigured accordingly. The spectrometer can be designed to have high spectral resolution, exceeding 10 000 resolving power when using small source (∼1µm) and detector pixels (∼5µm) with high line density gratings (∼3000 lines/mm), or high throughput at moderate resolution. We report two such spectrometers with slightly different design goals and optical parameters in this paper. We show that the spectrometer with high throughput and large energy window is particularly useful for studying the sustainable energy materials. We demonstrate that the extensive resonant inelastic X-ray scattering (RIXS) map of battery cathode material LiNi1/3Co1/3Mn1/3O2 can be produced in few hours using such a spectrometer. Unlike analyzing only a handful of RIXS spectra taken at selected excitation photon energies across the elemental absorption edges to determine various spectral features like the localized dd excitations and non-resonant fluorescence emissions, these features can be easily identified in the RIXS maps. Studying such RIXS maps could reveal novel transition metal redox in battery compounds that are sometimes hard to be unambiguously identified in X-ray absorption and emission spectra. We propose that this modular spectrometer design can serve as the platform for further customization to meet specific scientific demands.

Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates.

Besides superconductivity, copper-oxide high-temperature superconductors are susceptible to other types of ordering. We used scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering in the high-temperature superconductor Bi2Sr2CaCu2O(8+x). Depending on the hole concentration, the charge ordering in this system occurs with the same period as those found in Y-based or La-based cuprates and displays the analogous competition with superconductivity. These results indicate the similarity of charge organization competing with superconductivity across different families of cuprates. We observed this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 milli-electron volts) in spectroscopic measurements, indicating that it is likely related to the organization of holes in a doped Mott insulator.

Layer selective control of the lattice structure in oxide superlattices.

A combined synchrotron X-ray diffraction and transmission electron microscopy study reveals a structural phase transition controlled by the overall thickness of epitaxial nickelate-aluminate superlattices. The transition between uniform and twin-domain states is confined to the nickelate layers and leaves the aluminate layers unaffected.