Magnetic interactions in the metallic phase of the copper oxides: A Fermi-liquid description

One of the central issues in the field of high-temperature superconductivity is whether the normal state can be described by Fermi-liquid theory. Recent photoemission experiments along with a growing body of Fermi-liquid-based theoretical work have provided some support for this viewpoint. However, one major concern in ascertaining the validity of a Fermi-liquid approach is whether the magnetic interactions in the metallic cuprates are sufficiently strong so as to undermine the usual Fermi-liquid description. In this paper we address this question by examining the nature of the magnetic interactions in the metallic state. These interactions, which are dominantly between the Cu spins, arise via the intermediating oxygenlike states. Since the oxygen character changes as the hole doping is increased, it is expected that the Cu-Cu interactions are doping sensitive and evolve away from their value in the insulating limit. We deduce these interactions within a physical picture in which the Cu d electrons are nearly localized and the oxygen bandwidth assumes a finite value. While our qualitative results are general, we use a 1/N expansion as a convenient theoretical tool. In the extended Hubbard Hamiltonian the exchange terms are evaluated at order (1/${\mathit{N}}^2$). Both superexchange (${\mathit{J}}_{\mathit{S}}$) and Ruderman-Kittel-Kasuya-Yosida interactions (${\mathit{J}}_{\mathit{R}}$) emerge on a similar footing. With increasing carrier concentration, ${\mathit{J}}_{\mathit{S}}$ decreases rapidly, while ${\mathit{J}}_{\mathit{R}}$ abruptly increases from zero. We find that, because of the reduction in the strength of the superexchange, there is an enhanced stability of the Fermi-liquid phase. The dynamical susceptibility is also calculated within this scheme and the consequences for NMR and neutron experiments are discussed elsewhere.