Search

High-temperature cuprates superconductors are characterised by the complex interplay between superconductivity (SC) and charge density wave (CDW) in the context of intertwined competing orders. In contrast to abundant studies for hole-doped cuprates, the exact nature of CDW and its relationship to SC was much less explored in electron-doped counterparts. Here, we performed resonant inelastic x-ray scattering (RIXS) experiments to investigate the relationship between CDW and SC in electron-doped La$_{2-x}$Ce$_x$CuO$_4$. The short-range CDW order with a correlation length $\sim35$~\AA~was found in a wide range of temperature and doping concentration. Near the optimal doping, the CDW order is weakened inside the SC phase, implying an intimate relationship between the two orders. This interplay has been commonly reported in hole-doped La-based cuprates near the optimal doping. We reconciled the diverging behaviour of CDW across the superconducting phase in various cuprate materials by introducing the CDW correlation length as a key parameter. Our study paves the way for establishing a unified picture to describe the phenomenology of CDW and its relationship with SC in the cuprate family., Comment: 24 pages 5 figures; Supplementary Materials available upon request

Strongly-correlated transition-metal oxides are widely known for their various exotic phenomena. This is exemplified by rare-earth nickelates such as LaNiO$_{3}$, which possess intimate interconnections between their electronic, spin, and lattice degrees of freedom. Their properties can be further enhanced by pairing them in hybrid heterostructures, which can lead to hidden phases and emergent phenomena. An important example is the LaNiO$_{3}$/LaTiO$_{3}$ superlattice, where an interlayer electron transfer has been observed from LaTiO$_{3}$ into LaNiO$_{3}$ and is predicted to result in a high-spin state. However, macroscopic emergence of magnetic order has so far not been observed. Here, by using muon spin rotation, x-ray absorption, and resonant inelastic x-ray scattering, we present direct evidence of an emergent antiferromagnetic order with high magnon energy and exchange interactions at the LaNiO$_{3}$/LaTiO$_{3}$ interface. As the magnetism is purely interfacial, a single LaNiO$_{3}$/LaTiO$_{3}$ interface can essentially behave as an atomically thin quasi-two-dimensional antiferromagnet, potentially allowing its technological utilisation in advanced spintronic devices. Furthermore, its strong quasi-two-dimensional magnetic correlations and orbitally-polarized planar ligand holes make its electronic and magnetic configurations resemble the precursor states of superconducting cuprates and nickelates, but with an S $\rightarrow$ 1 spin state instead., Comment: 41 pages, 13 figures

The striking discovery of high-temperature superconductivity (HTSC) of 80 K in a bilayer nickelate La$_3$Ni$_2$O$_7$ under a moderately high pressure of about 14 GPa ignited a new wave of studying HTSC in nickelates. The properties of the parental phase at ambient pressure may contain key information on basic interactions therein and bosons that may mediate pairing giving birth to superconductivity. Moreover, the bilayer structure of La$_3$Ni$_2$O$_7$ may suggest a distinct minimal model in comparison to cuprate superconductors. Here using X-ray absorption spectroscopy and resonant inelastic X-ray scattering, we studied La$_3$Ni$_2$O$_7$ at ambient pressure, and found that Ni 3$d_{x^2-y^2}$, Ni 3$d_{z^2}$, and ligand oxygen 2$p$ orbitals dominate the low-energy physics with a small charge-transfer energy. Remarkably, well-defined optical-like magnetic excitations were found to soften into a quasi-static spin-density-wave ordering, evidencing the strong electronic correlations and rich magnetic properties. Based on a Heisenberg spin model, we found that the inter-layer effective magnetic superexchange interaction is much larger than the intra-layer ones, and proposed two viable magnetic structures. Our results set the foundation for further exploration of La$_3$Ni$_2$O$_7$ superconductor.

A comparative resonant inelastic x-ray scattering (RIXS) study of three well-known Kitaev materials is presented: $\alpha$-Li$_2$IrO$_3$, Na$_2$IrO$_3$, and $\alpha$-RuCl$_3$. Despite similar low-energy physics, these materials show distinct electronic properties, such as the large difference in the size of the charge gap. The RIXS spectra of the spin-orbit exciton for these materials show remarkably similar three-peak features, including sharp low energy peak (peak A) as well as transitions between $j_{\text{eff}}=1/2$ and $j_{\text{eff}}=3/2$ states. Comparison of experimental spectra with cluster calculations reveals that the observed three-peak structure reflects the significant role that non-local physics plays in the electronic structure of these materials. In particular, the low-energy peak A arises from a holon-doublon pair rather than a conventional particle-hole exciton as proposed earlier. Our study suggests that while spin-orbit assisted Mott insulator is still the best description for these materials, electron itinerancy cannot be ignored when formulating low-energy Hamiltonian of these materials.

Recent improvements in the energy resolution of resonant inelastic x-ray scattering experiments (RIXS) at the Cu-L$_3$ edge have enabled the study of lattice, spin, and charge excitations. Here, we report on the detection of a low intensity signal at 140meV, twice the energy of the bond-stretching (BS) phonon mode, in the cuprate superconductor $\textrm{Bi}_2\textrm{Sr}_2\textrm{Ca}\textrm{Cu}_2\textrm{O}_{8+x}$ (Bi-2212). Ultra-high resolution polarimetric RIXS measurements allow us to resolve the outgoing polarization of the signal and identify this feature as a two-phonon excitation. Further, we study the connection between the two-phonon mode and the BS one-phonon mode by constructing a joint density of states toy model that reproduces the key features of the data.

Charge density waves (CDW) have been reported in NdNiO$_2$ and LaNiO$_2$ thin films grown on SrTiO$_3$ substrates using Ni-$L_3$ resonant x-ray scattering in Refs. [1-3]. In their comment [arXiv:2306.15086] on these reports, Pelliciari et al. found no evidence for a CDW in a NdNiO$_2$ film by performing fixed-momentum energy-dependent measurements. Instead, they observed a nearby non-resonant scattering peak, attributed to the (101) substrate reflection, made accessible at Ni-$L_3$ due to third harmonic light contamination. Here we present fixed-momentum energy-dependent resonant inelastic x-ray scattering measurements across Ni-$L_3$ on NdNiO$_2$, used in the preceding study [1]. We see intrinsic Ni-$L_3$ energy profiles at all measured \textbf{Q} values, including a strong resonance effect at $\mathbf{Q}_\mathrm{CDW} = (-1/3, 0, 0.316)$ reciprocal lattice units. Attempts to measure the (101) substrate peak using third harmonic light at Ni-$L_3$ at I21, Diamond were unfruitful. Our results clearly demonstrate the electronic origin of the scattering peak published in Ref. [1] and lack of a detectable structural component in the peak.

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 topology. The experimental verification of chiral phonons (bosons) remains challenging, however, despite their expected strong impact on fundamental physical properties. 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 novel emergent phenomena based on chiral bosons, Comment: 5

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 has been challenging for the short-range CDW in bismuth-based cuprates. Here, we employed high-resolution resonant inelastic x-ray scattering to uncover the spatial symmetry of the CDW in Bi$_2$Sr$_{2-x}$La$_{x}$CuO$_{6+\delta}$. Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes were found in reciprocal space. Based on Fourier transform analysis of real-space models, we interpret the results as evidence of unidirectional charge stripes, hosted by mutually 90$^\circ$-rotated anisotropic domains. Our work paves the way for a unified symmetry and microscopic description of CDW order in cuprates., Comment: 9 pages, 3 figures and Supplementary Information; Under peer review

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 Kagom\'{e} semimetal Co$_3$Sn$_2$S$_2$ 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 Co$_3$Sn$_2$S$_2$. These observations serve as a cornerstone for further exploration of band-induced symmetry-breaking orders in topological materials., Comment: 15 pages, 4 figures, and Supplementary Information

Identifying quantum critical points (QCPs) and their associated fluctuations may hold the key to unraveling the unusual electronic phenomena observed in cuprate superconductors. Recently, signatures of quantum fluctuations associated with charge order (CO) have been inferred from the anomalous enhancement of CO excitations that accompany the reduction of the CO order parameter in the superconducting state. To gain more insight about the interplay between CO and superconductivity, here we investigate the doping dependence of this phenomenon throughout the Bi-2212 cuprate phase diagram using resonant inelastic x-ray scattering (RIXS) at the Cu L3- edge. As doping increases, the CO wavevector decreases, saturating at a commensurate value of 0.25 r.l.u. beyond a characteristic doping pc, where the correlation length becomes shorter than the apparent periodicity (4a0). Such behavior is indicative of the fluctuating nature of the CO; and the proliferation of CO excitations in the superconducting state also appears strongest at pc, consistent with expected behavior at a CO QCP. Intriguingly, pc appears to be near optimal doping, where the superconducting transition temperature Tc is maximal., Comment: This is a submitted version of the manuscript. The revised manuscript is now published on Physical Review B

Removal or cancellation of noise has wide-spread applications for imaging and acoustics. In every-day-life applications, denoising may even include generative aspects, which are unfaithful to the ground truth. For scientific use, however, denoising must reproduce the ground truth accurately. Here, we show how data can be denoised via a deep convolutional neural network such that weak signals appear with quantitative accuracy. In particular, we study X-ray diffraction 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 demonstrate 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., Comment: 14 pages, 10 figures; extended study, additional supplementary information, results unchanged

In materials science, much effort has been devoted to reproduce superconductivity in chemical compositions analogous to cuprate superconductors since their discovery over thirty years ago. This approach was recently successful in realising superconductivity in infinite-layer nickelates. Although differing from cuprates in electronic and magnetic properties, strong Coulomb interactions suggest infinite-layer nickelates have a propensity to various symmetry-breaking orders that populate the cuprates. Here we report the observation of charge density waves (CDWs) in infinite-layer NdNiO$_2$ films using Ni-$L_3$ resonant x-ray scattering. Remarkably, CDWs form in Nd 5$d$ and Ni 3$d$ orbitals at the same commensurate wavevector $(0.333, 0)\;r.l.u.$, with non-negligible out-of-plane dependence, and an in-plane correlation length up to $\sim$ 60 Angstrom. Spectroscopic studies reveal a strong connection between CDWs and the Nd 5$d$ - Ni 3$d$ orbital hybridisation. 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 multi-orbital character distinct from cuprates, which establishes their low-energy physics., Comment: 9 pages, 4 figures, and Supplementary Information

Resonant inelastic x-ray scattering (RIXS) is an evolving tool for investigating spin dynamics of strongly correlated materials, which complements inelastic neutron scattering. Both techniques have found that non-spin-conserving (NSC) excitations in quasi-1D isotropic quantum antiferromagnets are confined to the two-spinon phase space. Outside this phase space, only spin-conserving (SC) four-spinon excitations have been detected using O $K$-edge RIXS. Here, we investigate SrCuO$_2$ and find four-spinon excitations outside the two-spinon phase space at both O $K$- and Cu $L_3$-edges. Using the Kramers-Heisenberg formalism, we demonstrate that the four-spinon excitations arise from both SC and NSC processes at Cu $L_3$-edge. We show that these new excitations only appear in the second-order terms of the ultra-fast core-hole lifetime expansion and arise from long-range spin fluctuations. These results thus open a new window to the spin dynamics of quantum magnets., Comment: 10 pages, 4+3 figures

We utilized high-energy-resolution resonant inelastic X-ray scattering (RIXS) at both the Ta and Ni $L_3$-edges to map out element-specific particle-hole excitations in Ta$_2$NiSe$_5$ across the phase transition. Our results reveal a momentum dependent gap-like feature in the low energy spectrum, which agrees well with the band gap in element-specific joint density of states calculations based on ab initio estimates of the electronic structure in both the low temperature monoclinic and the high temperature orthorhombic structure. Below $T_c$, the RIXS energy-momentum map shows a minimal gap at the Brillouin zone center ($\sim$ 0.16 eV), confirming that Ta$_2$NiSe$_5$ possesses a direct band gap in its low temperature ground state. However, inside the gap, no signature of anticipated collective modes with an energy scale comparable to the gap size can be identified. Upon increasing the temperature to above $T_c$, whereas the gap at the zone center closes, the RIXS map at finite momenta still possesses the gross features of the low temperature map, suggesting a substantial mixing between the Ta and Ni orbits in the conduction and valence bands, which does not change substantially across the phase transition. Our experimental observations and comparison to the theoretical calculations lend further support that the phase transition and the corresponding gap opening in Ta$_2$NiSe$_5$ is largely structural by nature with possible minor contribution from the putative exciton condensate., Comment: The manuscript has been accepted by Physical Review B

We present a comparative study of magnetic excitations in the first two Ruddlesden-Popper members of the Hg-family of high-temperature superconducting cuprates, which are chemically nearly identical and have the highest critical temperature ($T_\mathrm{c}$) among all cuprate families. Our inelastic photon scattering experiments reveal that the two compounds' paramagnon spectra are nearly identical apart from an energy scale factor of $\sim130\%$ that matches the ratio of $T_\mathrm{c}$'s, as expected in magnetic Cooper pairing theories. By relating our observations to other cuprates, we infer that the strength of magnetic interactions determines how high $T_\mathrm{c}$ can reach. Our finding can be viewed as a magnetic analogue of the isotope effect, thus firmly supporting models of magnetically mediated high-temperature superconductivity., Comment: 6 pages, 4 figures, SM available via link in pdf

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 non-dispersive high-energy peaks result from the Cu$^{2+}$ $dd$ orbital excitations. These high-energy modes show good agreement with the {\it ab-initio} quantum chemistry calculation based on a single cluster, 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 Mueller Ansatz calculations. The localized $dd$ excitations and the observation of the strongly dispersive magnetic excitations suggest that orbiton dispersion is below the resolution detection limit. Our results can reconcile with the strong {\it local} Jahn-Teller effect in KCuF$_3$, which predominantly drives orbital ordering., Comment: 6 pages, 4 figures

Charge density waves (CDWs) are ubiquitous in under-doped 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 under-doped Bi$_2$Sr$_{1.4}$La$_{0.6}$CuO$_{6+\delta}$ 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 over-doped Bi$_2$Sr$_{1.8}$La$_{0.2}$CuO$_{6+\delta}$, 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 quasi-static CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates., Comment: 25 pages + Supplementary Information. Proc. Natl Acad. Sci. USA, (2020)

Motivated by the recent synthesis of Ba$_2$CuO$_{3+\delta}$ (BCO), a high temperature superconducting cuprate with putative $d_{3z^2-r^2}$ ground state symmetry, we investigated its electronic structure by means of Cu $L_3$ x-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS) at the Cu $L_3$ edge on a polycrystalline sample. We show that the XAS profile of BCO is characterised by two peaks associated to inequivalent Cu sites, and that its RIXS response features a single, sharp peak associated to crystal-field excitations. We argue that these observations are only partially compatible with the previously proposed crystal structure of BCO. Based on our spectroscopic results and on previously published powder diffraction measurements, we propose a crystalline structure characterized by two inequivalent Cu sites located at alternated planes along the $c$ axis: nominally trivalent Cu(1) belonging to very short Cu-O chains, and divalent Cu(2) in the oxygen deficient CuO$_ {1.5}$ planes. We also analyze the low-energy region of the RIXS spectra to estimate the magnitude of the magnetic interactions in BCO and find that in-plane nearest neighbor superexchange exceeds 120~meV, similarly to that of other layered cuprates. Although these results do not support the pure $d_{3z^2-r^2}$ ground state scenario, they hint at a significant departure from the common quasi-2D electronic structure of superconducting cuprates of pure $d_{x^2-y^2}$ symmetry.