Theory of spin dynamics in high-Tc copper oxide superconductors. Application to neutron scattering.

Abstract

A theory of spin dynamics in copper oxide superconductors is developed. The theory is based on the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}J$ model and the diagrammatic technique for Hubbard operators. The dynamic spin susceptibility calculated for metallic hole concentrations includes two different contributions. The contribution arises from the subsystem of localized Cu spins with quantum short-range correlations. The itinerant contribution arises from the subsystem of propagating carrier quasiparticles. As a result of their competition, the spin dynamics evolves continuously within the metallic state from normal-metal behavior at high doping (overdoped regime) to quantum spin-liquid-type dynamics with magnonlike excitations at low doping through non-Fermi-liquid behavior in all intermediate regimes. Based on the theory, a detailed analysis of momentum and energy dependences of the dynamic spin susceptibility for different doping regimes is performed in order to compare the theoretical predictions with the experimental results discovered by inelastic neutron scattering. We are able to understand the strange shape of $\mathrm{Im}\ensuremath{\chi}$ versus $\ensuremath{\omega}$ and its exotic evolution with doping, the existence of the resonance peak, the gap and pseudogap effects, and many other unusual features observed for $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ as well as the incommensurate and gapless behavior for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$.