The large variations in $T_c$ across the cuprate families is one of the major unsolved puzzles in condensed matter physics and is poorly understood. Although there appears to be a great deal of universality in the cuprates, several orders of magnitude changes in $T_c$ can be achieved through changes in the chemical composition and structure of the unit cell. In this paper we formulate a systematic examination of the variations in electron-phonon coupling to oxygen phonons in the cuprates, incorporating a number of effects arising from several aspects of chemical composition and doping across cuprate families. It is argued that the electron-phonon coupling is a very sensitive probe of the material-dependent variations in chemical structure, affecting the orbital character of the band crossing the Fermi level, the strength of local electric fields arising from structural-induced symmetry breaking, doping-dependent changes in the underlying band structure, and ionicity of the crystal governing the ability of the material to screen $c$-axis perturbations. Using electrostatic Ewald calculations and known experimental structural data, we establish a connection between the material’s maximal $T_c$ at optimal doping and the strength of coupling to $c$-axis modes. We demonstrate that materials with the largest coupling to the out-of-phase bond-buckling $\left(B_{1g}\right)$ oxygen phonon branch also have the largest $T_c$’s. In light of this observation we present model $T_c$ calculations using a two-well model where phonons work in conjunction with a dominant pairing interaction, presumably due to spin fluctuations, indicating how phonons can generate sizeable enhancements to $T_c$ despite the relatively small coupling strengths. Combined, these results can provide a natural framework for understanding the doping and material dependence of $T_c$ across the cuprates.

Using x-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS), charge dynamics at and near the $\text{Fe}L$ edges is investigated in Fe-pnictide materials and contrasted to that measured in other Fe compounds. It is shown that the XAS and RIXS spectra for 122 and 1111 Fe pnictides are each qualitatively similar to Fe metal. Cluster diagonalization, multiplet, and density-functional calculations show that Coulomb correlations are much smaller than in the cuprates, highlighting the role of Fe metallicity and strong covalency in these materials. The best agreement with experiment is obtained using Hubbard parameters $U\lesssim 2\text{eV}$ and $J\approx 0.8\text{eV}$.

High-resolution x-ray absorption measurements reveal a rare-earth-dependent splitting of the $\text{Ni}K$ edge in the insulating, charge-disproportionated state of the whole $R{\text{NiO}}_3$ perovskite family. The splitting is five times larger for ${\text{LuNiO}}_3$ [2.5(1) eV] than for ${\text{PrNiO}}_3$ [0.5(3) eV], suggesting that the charge transfer between ${\text{Ni}}^{3+\delta }$ and ${\text{Ni}}^{3-\delta }$ decreases by approaching the itinerant limit and is larger for the heavier lanthanides than suggested in previous studies. The spectroscopic signature of the two Ni sites remains visible above the metal-insulator transition, in agreement with the persistence of dynamic ${\text{Ni}}^{3+\delta }/{\text{Ni}}^{3-\delta }$ charge fluctuations in the metallic phase. This last result generalizes the occurrence of charge disproportionation as alternative to Jahn-Teller distortions to the dynamic regime, giving further support to recent theoretical work [I. I. Mazin, D. I. Khomskii, R. Lengsdorf, J. A. Alonso, W. G. Marshall, R. M. Ibberson, A. Podlesnyak, M. J. Martínez-Lope, and M. M. Abd-Elmeguid, Phys. Rev. Lett. 98, 176406 (2007)].

We investigate magnetic excitations in the spin-ladder compound ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ using high-resolution Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS). Our findings demonstrate that RIXS couples to two-triplon collective excitations. In contrast to inelastic neutron scattering, the RIXS cross section changes only moderately over the entire Brillouin zone, revealing high sensitivity also at small momentum transfers, allowing determination of the two-triplon energy gap as $100\pm 30\mathrm{meV}$. Our results are backed by calculations within an effective Hubbard model for a finite-size cluster, and confirm that optical selection rules are obeyed for excitations from this spherically symmetric quantum spin-liquid ground state.

Motivated by the absence of cooperative Jahn-Teller effect and of magnetic ordering in ${\mathrm{LiNiO}}_2$, a layered oxide with triangular planes, we study a general spin-orbital model on the triangular lattice. A mean-field approach reveals the presence of several singlet phases between the $\mathrm{SU}\left(4\right)$ symmetric point and a ferromagnetic phase, a conclusion supported by exact diagonalizations of finite clusters. We argue that one of the phases, characterized by a large number of low-lying singlets associated to dimer coverings of the triangular lattice, could explain the properties of ${\mathrm{LiNiO}}_2$, while a ferro-orbital phase that lies nearby in parameter space leads to a new prediction for the magnetic properties of ${\mathrm{NaNiO}}_2$.

We present an approach to computing multiplets for core spectroscopies, whereby the crystal field is constructed explicitly from the positions and charges of surrounding atoms. The simplicity of the input allows the consideration of crystal fields of any symmetry and in particular facilitates the study of spectroscopic effects arising from low-symmetry environments. The interplay between polarization directions and the crystal field can also be conveniently investigated. The determination of the multiplets proceeds from a Dirac density functional atomic calculation, followed by the exact diagonalization of the Coulomb, spin-orbit, and crystal-field interactions for the electrons in the open shells. The eigenstates are then used to simulate x-ray absorption spectroscopy and resonant inelastic x-ray scattering spectra. In examples ranging from high-symmetry down to low-symmetry environment, comparisons with experiments are done with unadjusted model parameters as well as with semiempirically optimized ones. Furthermore, predictions for the RIXS of low-temperature MnO and for Dy in a molecular complex are proposed.