Resonance peak in underdoped cuprates

The magnetic susceptibility measured in neutron scattering experiments in underdoped YBa$_2$Cu$_3$O$_{7-y}$ is interpreted based on the self-consistent solution of the t-J model of a Cu-O plane. The calculations reproduce correctly the frequency and momentum dependencies of the susceptibility and its variation with doping and temperature in the normal and superconducting states. This allows us to interpret the maximum in the frequency dependence -- the resonance peak -- as a manifestation of the excitation branch of localized Cu spins and to relate the frequency of the maximum to the size of the spin gap. The low-frequency shoulder well resolved in the susceptibility of superconducting crystals is connected with a pronounced maximum in the damping of the spin excitations. This maximum is caused by intense quasiparticle peaks in the hole spectral function for momenta near the Fermi surface and by the nesting.