The magnetic excitation spectrum of the t-t'-J-model is studied in mean-field
theory and compared to inelastic neutron-scattering (INS) experiments on YBCO
and BSCCO superconductors. Within the slave-particle formulation the dynamical
spin response is calculated from a renormalized Fermi liquid with an effective
interaction ~J in the magnetic particle--hole channel. We obtain the so-called
41meV resonance at wave vector (pi,pi) as a collective spin-1 excitation in the
d-wave superconducting state. It appears sharp (undamped), if the underlying
Fermi surface is hole-like with a sufficient next-nearest-neighbor hopping
t'<0. The double-layer structure of YBCO or BSCCO is not important for the
resonance to form. The resonance energy \omega_{res} and spectral weight at
optimal doping come out comparable to experiment. The observed qualitative
behavior of \omega_{res} with hole filling is reproduced in the underdoped as
well as overdoped regime. A second, much broader peak becomes visible in the
magnetic excitation spectrum if the 2D wave-vector is integrated over. It is
caused by excitations across the maximum gap, and in contrast to the resonance
its energy is almost independent of doping. At energies above or below
\omega_{res} the commensurate resonance splits into incommensurate peaks,
located off (pi,pi). Below \omega_{res} the intensity pattern is of `parallel'
type and the dispersion relation of incommensurate peaks has a negative
curvature. This is in accordance with recent INS experiments on YBCO.Comment: 17pp including 14 figure
