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The discovery of superconductivity in a $d^{9-{\delta}}$ nickelate has inspired disparate theoretical perspectives regarding the essential physics of this class of materials. A key issue is the magnitude of the magnetic superexchange, which relates to whether cuprate-like high-temperature nickelate superconductivity could be realized. We address this question using Ni L-edge and O K-edge spectroscopy of the reduced trilayer nickelate $d^{9-1/3}$ La4Ni3O8 and associated theoretical modeling. A magnon energy scale of ~80 meV resulting from a nearest-neighbor magnetic exchange of $J = 69(4)4$ meV is observed, proving that $d^{9-{\delta}}$ nickelates can host a large superexchange. This value, along with that of the Ni-O hybridization estimated from our O K-edge data, implies that trilayer nickelates represent an intermediate case between the infinite-layer nickelates and the cuprates, and suggests that they represent a promising route towards higher-temperature nickelate superconductivity., Comment: 7 pages not including supplmentary material; To appear in Physical Review Letters

The discovery of charge-density wave (CDW)-related effects in the resonant inelastic x-ray scattering (RIXS) spectra of cuprates holds the tantalizing promise of clarifying the interactions that stabilize the electronic order. Here, we report a comprehensive RIXS study of La2-xSrxCuO4 (LSCO) finding that CDW effects persist up to a remarkably high doping level of x = 0.21 before disappearing at x = 0.25. The inelastic excitation spectra remain essentially unchanged with doping despite crossing a topological transition in the Fermi surface. This indicates that the spectra contain little or no direct coupling to electronic excitations near the Fermi surface, rather they are dominated by the resonant cross-section for phonons and CDW-induced phonon-softening. We interpret our results in terms of a CDW that is generated by strong correlations and a phonon response that is driven by the CDW-induced modification of the lattice., 7 pages including references in long format

The discovery of superconductivity in a $d^{9-��}$ nickelate has inspired disparate theoretical perspectives regarding the essential physics of this class of materials. A key issue is the magnitude of the magnetic superexchange, which relates to whether cuprate-like high-temperature nickelate superconductivity could be realized. We address this question using Ni L-edge and O K-edge spectroscopy of the reduced trilayer nickelate $d^{9-1/3}$ La4Ni3O8 and associated theoretical modeling. A magnon energy scale of ~80 meV resulting from a nearest-neighbor magnetic exchange of $J = 69(4)4$ meV is observed, proving that $d^{9-��}$ nickelates can host a large superexchange. This value, along with that of the Ni-O hybridization estimated from our O K-edge data, implies that trilayer nickelates represent an intermediate case between the infinite-layer nickelates and the cuprates, and suggests that they represent a promising route towards higher-temperature nickelate superconductivity., 7 pages not including supplmentary material; To appear in Physical Review Letters

Charge density wave (CDW) correlations are prevalent in all copper-oxide superconductors. While CDWs in conventional metals are driven by coupling between lattice vibrations and electrons, the role of the electron-phonon coupling (EPC) in cuprate CDWs is strongly debated. Using Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS), we study the CDW and Cu-O bond-stretching phonons in the stripe-ordered cuprate La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4+\delta}$. We investigate the interplay between charge order and EPC as a function of doping and temperature, and find that the EPC is enhanced in a narrow momentum region around the CDW wave vector. By detuning the incident photon energy from the absorption resonance, we extract an EPC matrix element at the CDW wave vector of $M\simeq$ 0.36 eV, which decreases to $M\simeq$ 0.30 eV at high temperature in the absence of the CDW. Our results suggest a feedback mechanism in which the CDW enhances the EPC which, in turn, further stabilizes the CDW., Comment: 5 pages, 4 figures

Charge density wave (CDW) correlations are prevalent in all copper-oxide superconductors. While CDWs in conventional metals are driven by coupling between lattice vibrations and electrons, the role of the electron-phonon coupling (EPC) in cuprate CDWs is strongly debated. Using Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS), we study the CDW and Cu-O bond-stretching phonons in the stripe-ordered cuprate La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4+��}$. We investigate the interplay between charge order and EPC as a function of doping and temperature, and find that the EPC is enhanced in a narrow momentum region around the CDW wave vector. By detuning the incident photon energy from the absorption resonance, we extract an EPC matrix element at the CDW wave vector of $M\simeq$ 0.36 eV, which decreases to $M\simeq$ 0.30 eV at high temperature in the absence of the CDW. Our results suggest a feedback mechanism in which the CDW enhances the EPC which, in turn, further stabilizes the CDW., 5 pages, 4 figures

The magnetic correlations within the cuprates have undergone intense scrutiny as part of efforts to understand high-temperature superconductivity. We explore the evolution of the magnetic correlations along the nodal direction of the Brillouin zone in La2−xSrxCuO4, spanning the doping phase diagram from the antiferromagnetic Mott insulator at x=0 to the metallic phase at x=0.26. Magnetic excitations along this direction are found to be systematically softened and broadened with doping, at a higher rate than the excitations along the antinodal direction. This phenomenology is discussed in terms of the nature of the magnetism in the doped cuprates. Survival of the high-energy magnetic excitations, even in the overdoped regime, indicates that these excitations are marginal to pairing, while the influence of the low-energy excitations remains ambiguous.

The magnetic correlations within the cuprates have undergone intense scrutiny as part of efforts to understand high temperature superconductivity. We explore the evolution of the magnetic correlations along the nodal direction of the Brillouin zone in La2-xSrxCuO4, spanning the doping phase diagram from the anti-ferromagnetic Mott insulator at x = 0 to the metallic phase at x = 0.26. Magnetic excitations along this direction are found to be systematically softened and broadened with doping, at a higher rate than the excitations along the anti-nodal direction. This phenomenology is discussed in terms of the nature of the magnetism in the doped cuprates. Survival of the high energy magnetic excitations, even in the overdoped regime, indicates that these excitations are marginal to pairing, while the influence of the low energy excitations remains ambiguous., 8 pages, 6 figures

The recently discovered structural reconstruction in the cuprate superlattice (SrCuO 2) n /(SrTiO 3) 2 has been investigated across the critical value of n = 5 using resonant inelastic x-ray scattering (RIXS). We find that at the critical value of n, the cuprate layer remains largely in the bulk-like two-dimensional structure with a minority of Cu plaquettes being reconstructed. The partial reconstruction leads to quenching of the magnons starting at the Î "-point due to the minority plaquettes acting as scattering points. Although comparable in relative abundance, the doped charge impurities in electron-doped cuprate superconductors do not show this quenching of magnetic excitations.

The recently discovered structural reconstruction in the cuprate superlattice (SrCuO$_2$)$_n$/(SrTiO$_3$)$_2$ has been investigated across the critical value of $n=5$ using resonant inelastic x-ray scattering (RIXS). We find that at the critical value of $n$, the cuprate layer remains largely in the bulk-like two-dimensional structure with a minority of Cu plaquettes being reconstructed. The partial reconstruction leads to quenching of the magnons starting at the $\Gamma$-point due to the minority plaquettes acting as scattering points. Although comparable in relative abundance, the doped charge impurities in electron-doped cuprate superconductors do not show this quenching of magnetic excitations., Comment: Accepted for publication in Scientific Reports

We probe the collective magnetic modes of La$_2$CuO$_4$ (LCO) and underdoped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) by momentum resolved Resonant Inelastic X-ray Scattering (RIXS) at the Cu $L_3$ edge. In LCO the single magnon dispersion measured by RIXS coincides with the one determined by inelastic neutron scattering. For LSCO the spin dynamics shows a branch dispersing up to $\sim$400 meV coexisting with a branch at lower energy. Only the latter has been observed with neutrons so far and is considered a key signature of doped cuprates. The presence of the high-energy branch indicates that LSCO is in a dynamic inhomogeneous spin state., Comment: 5 pages, 4 figures

In the early days of high temperature superconductivity it was already recognized that magnetic properties of these materials are intimately related to the superconducting ones . When doped, the long-range ordered antiferromagnetic background of pristine copper-oxide insulators melts away and makes room for a spin liquid and superconductivity. By resonant inelastic x-ray scattering (RIXS) in the soft regime we probe the hitherto inaccessible dynamical multiple-spin correlations of the magnetic background in a series of parent compounds and in high Tc materials [NCCO (Nd2-xCexCuO4) and LSCO (La2-xSrxCuO4)]. High resolution measurements allows the clear observation of dispersing bimagnon excitations. In the undoped compounds the theory, fits the data on these coherent spin excitations without free parameters. In nearly optimally doped LSCO we observe the appearance of a new collective excitation at an energy of 250 +/- 60 meV having the signature of a coupled bimagnon-charge mode. It has a strongly reduced dispersion and lies in a so far unexplored region of momentum and energy space in the mid-infrared., Comment: 16 pages, 3 figures embedded

While electron-phonon coupling (EPC) is crucial for Cooper pairing in conventional superconductors, its role in high-$T_c$ superconducting cuprates is debated. Using resonant inelastic x-ray scattering at the oxygen $K$-edge, we studied the EPC in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) and Nd$_{1+x}$Ba$_{2-x}$Cu$_3$O$_{7-\delta}$ (NBCO) at different doping levels ranging from heavily underdoped ($p =0.07$) to overdoped ($p=0.21$). We analyze the data with a localized Lang-Firsov model that allows for the coherent excitations of two phonon modes. While electronic band dispersion effects are non-negligible, we are able to perform a study of the relative values of EPC matrix elements in these cuprate families. In the case of NBCO, the choice of the excitation energy allows us to disentangle modes related to the CuO$_3$ chains and the CuO$_2$ planes. Combining the results from the two families, we find the EPC strength decreases with doping at $\mathbf{q_\parallel}=(-0.25, 0)$ r.l.u., but has a non-monotonic trend as a function of doping at smaller momenta. This behavior is attributed to the screening effect of charge carriers. We also find that the phonon intensity is enhanced in the vicinity of the charge-density-wave (CDW) excitations while the extracted EPC strength appears to be less sensitive to their proximity. By performing a comparative study of two cuprate families, we are able to identify general trends in the EPC for the cuprates and provide experimental input to theories invoking a synergistic role for this interaction in $d$-wave pairing., Comment: 10 pages, 5 figures

We measured high resolution Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS) of the undoped cuprates La$_2$CuO$_4$, Sr$_2$CuO$_2$Cl$_2$, CaCuO$_2$ and NdBa$_2$Cu$_3$O$_6$. The dominant spectral features were assigned to $dd$ excitations and we extensively studied their polarization and scattering geometry dependence. In a pure ionic picture, we calculated the theoretical cross sections for those excitations and used them to fit the experimental data with excellent agreement. By doing so, we were able to determine the energy and symmetry of Cu-3$d$ states for the four systems with unprecedented accuracy and confidence. The values of the effective parameters could be obtained for the single ion crystal field model but not for a simple two-dimensional cluster model. The firm experimental assessment of $dd$ excitation energies carries important consequences for the physics of high $T_c$ superconductors. On one hand, having found that the minimum energy of orbital excitation is always $\geq 1.4$ eV, i.e., well above the mid-infrared spectral range, leaves to magnetic excitations (up to 300 meV) a major role in Cooper pairing in cuprates. On the other hand, it has become possible to study quantitatively the effective influence of $dd$ excitations on the superconducting gap in cuprates., 22 pages, 11 figures, 1 table

International audience; X-ray magnetic circular dichroism provides evidence of an out-of-plane spin moment in undoped and doped cuprates. In La2CuO4 this moment is related to the canting of the antiferromagnetically ordered Cu2+ spins caused by the Dzyaloshinskii-Moriya interaction within the CuO2 planes. This canting gives rise to the well-known weak ferromagnetism in high magnetic fields. We find a similar behavior in doped compounds, both in the normal and in the superconducting state, but with a different temperature dependence typical of paramagnetic systems. This result suggests that, together with short-range in-plane antiferromagnetic correlations, the Dzyaloshinskii-Moriya interaction survives up to optimal doping and in the superconducting state.