Magnetic fluctuations and resonant peak in cuprates: a microscopic theory

The theory for the dynamical spin susceptibility within the t-J model is developed, as relevant for the resonant magnetic peak and normal-state magnetic response in superconducting (SC) cuprates. The analysis is based on the equations of motion for spins and the memory-function presentation of magnetic response where the main damping of the low-energy spin collective mode comes from the decay into fermionic degrees of freedom. It is shown that the damping function at low doping is closely related to the c-axis optical conductivity. The analysis reproduces doping-dependent features of the resonant magnetic scattering.