Trapped O2 and the origin of voltage fade in layered Li-rich cathodes.

Oxygen redox cathodes, such as Li1.2Ni0.13Co0.13Mn0.54O2, deliver higher energy densities than those based on transition metal redox alone. However, they commonly exhibit voltage fade, a gradually diminishing discharge voltage on extended cycling. Recent research has shown that, on the first charge, oxidation of O2- ions forms O2 molecules trapped in nano-sized voids within the structure, which can be fully reduced to O2- on the subsequent discharge. Here we show that the loss of O-redox capacity on cycling and therefore voltage fade arises from a combination of a reduction in the reversibility of the O2-/O2 redox process and O2 loss. The closed voids that trap O2 grow on cycling, rendering more of the trapped O2 electrochemically inactive. The size and density of voids leads to cracking of the particles and open voids at the surfaces, releasing O2. Our findings implicate the thermodynamic driving force to form O2 as the root cause of transition metal migration, void formation and consequently voltage fade in Li-rich cathodes.

Weak signal extraction enabled by deep neural network denoising of diffraction data.

The removal or cancellation of noise has wide-spread applications in imaging and acoustics. In applications in everyday life, such as image restoration, denoising may even include generative aspects, which are unfaithful to the ground truth. For scientific use, however, denoising must reproduce the ground truth accurately. Denoising scientific data is further challenged by unknown noise profiles. In fact, such data will often include noise from multiple distinct sources, which substantially reduces the applicability of simulation-based approaches. Here we show how scientific data can be denoised by using a deep convolutional neural network such that weak signals appear with quantitative accuracy. In particular, we study X-ray diffraction and resonant X-ray scattering data recorded on crystalline materials. We demonstrate that weak signals stemming from charge ordering, insignificant in the noisy data, become visible and accurate in the denoised data. This success is enabled by supervised training of a deep neural network with pairs of measured low- and high-noise data. We additionally show that using artificial noise does not yield such quantitatively accurate results. Our approach thus illustrates a practical strategy for noise filtering that can be applied to challenging acquisition problems.

Universal Stripe Symmetry of Short-Range Charge Density Waves in Cuprate Superconductors.

The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios is challenging for the short-range CDW in bismuth-based cuprates. Here, high-resolution resonant inelastic x-ray scattering is employed to uncover the spatial symmetry of the CDW in Bi2 Sr2 - x Lax CuO6 + δ . Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes are found in reciprocal space. Based on Fourier transform analysis of real-space models, the results are interpreted as evidence of unidirectional charge stripes, hosted by mutually 90°-rotated anisotropic domains. This work paves the way for a unified symmetry and microscopic description of CDW order in cuprates.

Signature of quantum criticality in cuprates by charge density fluctuations.

The universality of the strange metal phase in many quantum materials is often attributed to the presence of a quantum critical point (QCP), a zero-temperature phase transition ruled by quantum fluctuations. In cuprates, where superconductivity hinders direct QCP observation, indirect evidence comes from the identification of fluctuations compatible with the strange metal phase. Here we show that the recently discovered charge density fluctuations (CDF) possess the right properties to be associated to a quantum phase transition. Using resonant x-ray scattering, we studied the CDF in two families of cuprate superconductors across a wide doping range (up to p = 0.22). At p* ≈ 0.19, the putative QCP, the CDF intensity peaks, and the characteristic energy Δ is minimum, marking a wedge-shaped region in the phase diagram indicative of a quantum critical behavior, albeit with anomalies. These findings strengthen the role of charge order in explaining strange metal phenomenology and provide insights into high-temperature superconductivity.

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.

Chiral phonons in quartz probed by X-rays.

The concept of chirality is of great relevance in nature, from chiral molecules such as sugar to parity transformations in particle physics. In condensed matter physics, recent studies have demonstrated chiral fermions and their relevance in emergent phenomena closely related to topology1-3. The experimental verification of chiral phonons (bosons) remains challenging, however, despite their expected strong impact on fundamental physical properties4-6. Here we show experimental proof of chiral phonons using resonant inelastic X-ray scattering with circularly polarized X-rays. Using the prototypical chiral material quartz, we demonstrate that circularly polarized X-rays, which are intrinsically chiral, couple to chiral phonons at specific positions in reciprocal space, allowing us to determine the chiral dispersion of the lattice modes. Our experimental proof of chiral phonons demonstrates a new degree of freedom in condensed matter that is both of fundamental importance and opens the door to exploration of new emergent phenomena based on chiral bosons.

Magnetic excitations beyond the single- and double-magnons.

A photon carrying one unit of angular momentum can change the spin angular momentum of a magnetic system with one unit (ΔMs = ±1) at most. This implies that a two-photon scattering process can manipulate the spin angular momentum of the magnetic system with a maximum of two units. Herein we describe a triple-magnon excitation in α-Fe2O3, which contradicts this conventional wisdom that only 1- and 2-magnon excitations are possible in a resonant inelastic X-ray scattering experiment. We observe an excitation at exactly three times the magnon energy, along with additional excitations at four and five times the magnon energy, suggesting quadruple and quintuple-magnons as well. Guided by theoretical calculations, we reveal how a two-photon scattering process can create exotic higher-rank magnons and the relevance of these quasiparticles for magnon-based applications.

Critical role of hydrogen for superconductivity in nickelates.

The newly discovered nickelate superconductors so far only exist in epitaxial thin films synthesized by a topotactic reaction with metal hydrides1. This method changes the nickelates from the perovskite to an infinite-layer structure by deintercalation of apical oxygens1-3. Such a chemical reaction may introduce hydrogen (H), influencing the physical properties of the end materials4-9. Unfortunately, H is insensitive to most characterization techniques and is difficult to detect because of its light weight. Here, in optimally Sr doped Nd0.8Sr0.2NiO2H epitaxial films, secondary-ion mass spectroscopy shows abundant H existing in the form of Nd0.8Sr0.2NiO2Hx (x ≅ 0.2-0.5). Zero resistivity is found within a very narrow H-doping window of 0.22 ≤ x ≤ 0.28, showing unequivocally the critical role of H in superconductivity. Resonant inelastic X-ray scattering demonstrates the existence of itinerant interstitial s (IIS) orbitals originating from apical oxygen deintercalation. Density functional theory calculations show that electronegative H- occupies the apical oxygen sites annihilating IIS orbitals, reducing the IIS-Ni 3d orbital hybridization. This leads the electronic structure of H-doped Nd0.8Sr0.2NiO2Hx to be more two-dimensional-like, which might be relevant for the observed superconductivity. We highlight that H is an important ingredient for superconductivity in epitaxial infinite-layer nickelates.

Resonant inelastic x-ray scattering from U3O8and UN.

Resonant inelastic x-ray scattering (RIXS) using an incident energy tuned to the uraniumN4,5absorption edges is reported from epitaxial films ofα-U3O8and UN. Theory shows that for U3O8the multiplets associated with a 5f1configuration with a ground state of2F5/2and the excited state of2F7/2are observed. However, the strong transition predicted at a transfer energy of 1.67 eV is not observed. We assume this is a consequence of the intermediate state lifetime broadening due to interaction with continuum states when the transferred energy exceeds the onset of the continuum in the presence of the core hole. This hypothesis is supported by the results obtained for the 5f-itinerant system UN, where no sharp transitions have been observed, although the broad scattering response centred at ∼1 eV is considered a signature of a predominantly 5f3configuration in this band-like semi-metallic system. These experiments and theory add important information on these materials, both of which have been investigated since the 1960s, as well as whether RIXS at the uraniumNedge can become a valuable tool for actinide research.

Correlation driven near-flat band Stoner excitations in a Kagome magnet.

Among condensed matter systems, Mott insulators exhibit diverse properties that emerge from electronic correlations. In itinerant metals, correlations are usually weak, but can also be enhanced via geometrical confinement of electrons, that manifest as 'flat' dispersionless electronic bands. In the fast developing field of topological materials, which includes Dirac and Weyl semimetals, flat bands are one of the important components that can result in unusual magnetic and transport behaviour. To date, characterisation of flat bands and their magnetism is scarce, hindering the design of novel materials. Here, we investigate the ferromagnetic Kagomé semimetal Co3Sn2S2 using resonant inelastic X-ray scattering. Remarkably, nearly non-dispersive Stoner spin excitation peaks are observed, sharply contrasting with the featureless Stoner continuum expected in conventional ferromagnetic metals. Our band structure and dynamic spin susceptibility calculations, and thermal evolution of the excitations, confirm the nearly non-dispersive Stoner excitations as unique signatures of correlations and spin-polarized electronic flat bands in Co3Sn2S2. These observations serve as a cornerstone for further exploration of band-induced symmetry-breaking orders in topological materials.

Charge density waves in infinite-layer NdNiO2 nickelates.

In materials science, much effort has been devoted to the reproduction of superconductivity in chemical compositions, analogous to cuprate superconductors since their discovery over 30 years ago. This approach was recently successful in realising superconductivity in infinite-layer nickelates1-6. Although differing from cuprates in electronic and magnetic properties, strong Coulomb interactions suggest that infinite-layer nickelates have a propensity towards various symmetry-breaking orders that populate cuprates7-10. Here we report the observation of charge density waves (CDWs) in infinite-layer NdNiO2 films using Ni L3 resonant X-ray scattering. Remarkably, CDWs form in Nd 5d and Ni 3d orbitals at the same commensurate wavevector (0.333, 0) reciprocal lattice units, with non-negligible out-of-plane dependence and an in-plane correlation length of up to ~60 Å. Spectroscopic studies reveal a strong connection between CDWs and Nd 5d-Ni 3d orbital hybridization. Upon entering the superconducting state at 20% Sr doping, the CDWs disappear. Our work demonstrates the existence of CDWs in infinite-layer nickelates with a multiorbital character distinct from cuprates, which establishes their low-energy physics.

Paramagnons and high-temperature superconductivity in a model family of cuprates.

Cuprate superconductors have the highest critical temperatures (Tc) at ambient pressure, yet a consensus on the superconducting mechanism remains to be established. Finding an empirical parameter that limits the highest reachable Tc can provide crucial insight into this outstanding problem. Here, in the first two Ruddlesden-Popper members of the model Hg-family of cuprates, which are chemically nearly identical and have the highest Tc among all cuprate families, we use inelastic photon scattering to reveal that the energy of magnetic fluctuations may play such a role. In particular, we observe the single-paramagnon spectra to be nearly identical between the two compounds, apart from an energy scale difference of ~30% which matches their difference in Tc. The empirical correlation between paramagnon energy and maximal Tc is further found to extend to other cuprate families with relatively high Tc's, hinting at a fundamental connection between them.

I21: an advanced high-resolution resonant inelastic X-ray scattering beamline at Diamond Light Source.

The I21 beamline at Diamond Light Source is dedicated to advanced resonant inelastic X-ray scattering (RIXS) for probing charge, orbital, spin and lattice excitations in materials across condensed matter physics, applied sciences and chemistry. Both the beamline and the RIXS spectrometer employ divergent variable-line-spacing gratings covering a broad energy range of 280-3000 eV. A combined energy resolution of ∼35 meV (16 meV) is readily achieved at 930 eV (530 eV) owing to the optimized optics and the mechanics. Considerable efforts have been paid to the design of the entire beamline, particularly the implementation of the collection mirrors, to maximize the X-ray photon throughput. The continuous rotation of the spectrometer over 150° under ultra high vacuum and a cryogenic manipulator with six degrees of freedom allow accurate mappings of low-energy excitations from solid state materials in momentum space. Most importantly, the facility features a unique combination of the high energy resolution and the high photon throughput vital for advanced RIXS applications. Together with its stability and user friendliness, I21 has become one of the most sought after RIXS beamlines in the world.

Charge order lock-in by electron-phonon coupling in La1.675Eu0.2Sr0.125CuO4.

Charge order is universal to all hole-doped cuprates. Yet, the driving interactions remain an unsolved problem. Electron-electron interaction is widely believed to be essential, whereas the role of electron-phonon interaction is unclear. We report an ultrahigh-resolution resonant inelastic x-ray scattering (RIXS) study of the in-plane bond-stretching phonon mode in stripe-ordered cuprate La1.675Eu0.2Sr0.125CuO4 Phonon softening and lifetime shortening are found around the charge ordering wave vector. In addition to these self-energy effects, the electron-phonon coupling is probed by its proportionality to the RIXS cross section. We find an enhancement of the electron-phonon coupling around the charge-stripe ordering wave vector upon cooling into the low-temperature tetragonal structure phase. These results suggest that, in addition to electronic correlations, electron-phonon coupling contributes substantially to the emergence of long-range charge-stripe order in cuprates.

Evolution of spin excitations from bulk to monolayer FeSe.

In ultrathin films of FeSe grown on SrTiO3 (FeSe/STO), the superconducting transition temperature Tc is increased by almost an order of magnitude, raising questions on the pairing mechanism. As in other superconductors, antiferromagnetic spin fluctuations have been proposed to mediate SC making it essential to study the evolution of the spin dynamics of FeSe from the bulk to the ultrathin limit. Here, we investigate the spin excitations in bulk and monolayer FeSe/STO using resonant inelastic x-ray scattering (RIXS) and quantum Monte Carlo (QMC) calculations. Despite the absence of long-range magnetic order, bulk FeSe displays dispersive magnetic excitations reminiscent of other Fe-pnictides. Conversely, the spin excitations in FeSe/STO are gapped, dispersionless, and significantly hardened relative to its bulk counterpart. By comparing our RIXS results with simulations of a bilayer Hubbard model, we connect the evolution of the spin excitations to the Fermiology of the two systems revealing a remarkable reconfiguration of spin excitations in FeSe/STO, essential to understand the role of spin fluctuations in the pairing mechanism.

Covalency does not suppress O2 formation in 4d and 5d Li-rich O-redox cathodes.

Layered Li-rich transition metal oxides undergo O-redox, involving the oxidation of the O2- ions charge compensated by extraction of Li+ ions. Recent results have shown that for 3d transition metal oxides the oxidized O2- forms molecular O2 trapped in the bulk particles. Other forms of oxidised O2- such as O22- or (O-O)n- with long bonds have been proposed, based especially on work on 4 and 5d transition metal oxides, where TM-O bonding is more covalent. Here, we show, using high resolution RIXS that molecular O2 is formed in the bulk particles on O2‒ oxidation in the archetypal Li-rich ruthenates and iridate compounds, Li2RuO3, Li2Ru0.5Sn0.5O3 and Li2Ir0.5Sn0.5O3. The results indicate that O-redox occurs across 3, 4, and 5d transition metal oxides, forming O2, i.e. the greater covalency of the 4d and 5d compounds still favours O2. RIXS and XAS data for Li2IrO3 are consistent with a charge compensation mechanism associated primarily with Ir redox up to and beyond the 5+ oxidation state, with no evidence of O-O dimerization.

Unraveling the Orbital Physics in a Canonical Orbital System KCuF_{3}.

We explore the existence of the collective orbital excitations, orbitons, in the canonical orbital system KCuF_{3} using the Cu L_{3}-edge resonant inelastic x-ray scattering. We show that the nondispersive high-energy peaks result from the Cu^{2+} dd orbital excitations. These high-energy modes display good agreement with the ab initio quantum chemistry calculation, indicating that the dd excitations are highly localized. At the same time, the low-energy excitations present clear dispersion. They match extremely well with the two-spinon continuum following the comparison with Müller ansatz calculations. The localized dd excitations and the observation of the strongly dispersive magnetic excitations suggest that the orbiton dispersion is below the resolution detection limit. Our results can reconcile with the strong local Jahn-Teller effect in KCuF_{3}, which predominantly drives orbital ordering.

Coherent many-body exciton in van der Waals antiferromagnet NiPS3.

An exciton is the bosonic quasiparticle of electron-hole pairs bound by the Coulomb interaction1. Bose-Einstein condensation of this exciton state has long been the subject of speculation in various model systems2,3, and examples have been found more recently in optical lattices and two-dimensional materials4-9. Unlike these conventional excitons formed from extended Bloch states4-9, excitonic bound states from intrinsically many-body localized states are rare. Here we show that a spin-orbit-entangled exciton state appears below the Néel temperature of 150 kelvin in NiPS3, an antiferromagnetic van der Waals material. It arises intrinsically from the archetypal many-body states of the Zhang-Rice singlet10,11, and reaches a coherent state assisted by the antiferromagnetic order. Using configuration-interaction theory, we determine the origin of the coherent excitonic excitation to be a transition from a Zhang-Rice triplet to a Zhang-Rice singlet. We combine three spectroscopic tools-resonant inelastic X-ray scattering, photoluminescence and optical absorption-to characterize the exciton and to demonstrate an extremely narrow excitonic linewidth below 50 kelvin. The discovery of the spin-orbit-entangled exciton in antiferromagnetic NiPS3 introduces van der Waals magnets as a platform to study coherent many-body excitons.

Multiorbital charge-density wave excitations and concomitant phonon anomalies in Bi2Sr2LaCuO6+δ.

Charge-density waves (CDWs) are ubiquitous in underdoped cuprate superconductors. As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3d and O-2p orbital character owing to the strong hybridization of these orbitals near the Fermi level. Here, we investigate underdoped Bi2Sr1.4La0.6CuO6+δ using resonant inelastic X-ray scattering (RIXS) and find that a short-range CDW exists at both Cu and O sublattices in the copper-oxide (CuO2) planes with a comparable periodicity and correlation length. Furthermore, we uncover bond-stretching and bond-buckling phonon anomalies concomitant to the CDWs. Comparing to slightly overdoped Bi2Sr1.8La0.2CuO6+δ, where neither CDWs nor phonon anomalies appear, we highlight that a sharp intensity anomaly is induced in the proximity of the CDW wavevector (QCDW) for the bond-buckling phonon, in concert with the diffused intensity enhancement of the bond-stretching phonon at wavevectors much greater than QCDW Our results provide a comprehensive picture of the quasistatic CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates.