Anderson Hamiltonian description of the experimental electronic structure and magnetic interactions of copper oxide superconductors

Abstract

We describe valence-band and core-level photoemission data for copper oxide superconductors using the Anderson Hamiltonian applied to an impurity-cluster configuration-interaction model. We obtain experimental values of the parameters of the model, the copper\ensuremath{\rightleftarrows}oxygen chargetransfer energy $\ensuremath{\Delta}\ensuremath{\sim}0.4$ eV, the $d\ensuremath{-}d$ Coulomb interaction $U\ensuremath{\sim}6$ eV, and the ligand-$d$ hybridization $T\ensuremath{\sim}2.4$ eV. Using these parameters, we evaluate the linear Cu-O-Cu superexchange interaction $J$ and find it is dominated by the charge-transfer fluctuations. The magnitude obtained for $J$ is much larger than typical N\'eel temperatures of these materials, and is somewhat larger than that estimated from applying the resonating-valence-bond picture to ${\mathrm{La}}_{2}$Cu${\mathrm{O}}_{4}$. We point out that for $\ensuremath{\Delta}\ensuremath{\ll}U$ and $T\ensuremath{\gg}\ensuremath{\Delta}$ the charge-transfer degrees of freedom, and the lattice aspects of the Anderson lattice Hamiltonian, should not be neglected in constructing models for the high-${T}_{c}$ superconductivity. We also emphasize our resonant-photoemission result that the very small density of states at or near the Fermi level in all these materials has a substantial contribution from Cu $3d$ states, suggesting their importance for the superconductivity. We report other details of the resonant-photoemission data involving La and Ba states in the materials containing these elements.