Soft-x-ray emission spectroscopy study of ${\mathrm{La}}_2$${\mathrm{CuO}}_4$ and three high-${\mathit{T}}_{\mathit{c}}$ superconductors

High-resolution x-ray emission spectroscopy measurements have been performed on sintered samples of ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$, ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathrm{\delta }}$, ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (δ<0.1), and compressed polycrystalline ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathrm{\delta }}$. The Cu Lα and O Kα emission bands, which reflect the local partial Cu 3d and O 2p states, respectively, are compared to photoelectron spectra and ground-state local-density-approximation (LDA) densities-of-states (DOS) calculations. Our results show that solid-state effects are dominant. In particular, the differences in shape of the O Kα emission bands follow the trends predicted by LDA, although it must be stressed that they mainly arise from O 2p states at oxygen sites not directly involved in the Cu-O planes. The Cu-side 3d states, on the other hand, vary little from one cuprate to the next and are more strongly localized than expected from LDA predictions. The Anderson-impurity model calculations of Kotani and co-workers are discussed, and it is concluded that they provide a satisfactory explanation of the Cu Lα emission data, which reflect strong on-site Coulomb interaction. We conclude that the apparently good agreement between LDA-calculated DOS and low-energy photoemission experiments recently reported results from the high sensitivity of the latter to O 2p states. Discrepancies are to be expected in excitation spectra that involve mainly 3d electrons.