Magnetic fluctuations and resonant peak in cuprates: Towards a microscopic theory

Abstract

Magnetic fluctuations and evolution of the resonant peak with doping in superconducting cuprates are studied within the planar $t\ensuremath{-}J$ model. The analysis is based on the equations of motion for spins and the memory-function approach to dynamics of magnetic response where the main damping of the low-energy spin collective mode comes from the decay into fermionic degrees of freedom. In general the normal-state damping is large, leading to a overdamped collective mode. At an intermediate doping in the superconducting phase, a d-wave gap leads to a sharp resonant peak with reduced intensity and downward dispersion. At low doping the damping function is closely related to the c-axis optical conductivity, and the resonant-peak behavior is determined by two energy scales: the pseudogap and the coherent superconducting gap.