Double dispersion of the magnetic resonant mode in cuprates

The magnetic excitation spectra in the vicinity of the resonant peak, as observed by inelastic neutron scattering in cuprates, are studied within the memory-function approach. It is shown that at intermediate doping the superconducting gap induces a double dispersion of the peak, with an anisotropy rotated between the downward and upward branch. Similar behavior, but with a spin-wave dispersion at higher energies, is obtained for the low-doping case assuming a large pairing pseudogap.