The resonance peak in the high-Tc cuprates

I present a theory in which the resonance peak observed in inelastic neutron scattering experiments on YBa₂Cu₃O_6+x and Bi₂Sr₂CaCu₂O_8+x arises from a dispersing spin mode. I argue that it is heavily damped in the normal state and becomes visible in the superconducting state due to a drastic decrease in the spin damping. I show that a spin-fermion model correctly describes the doping dependence of the peak position and of its integrated intensity. Finally, I derive a criterion for the existence of the resonance peak in other cuprate superconductors.