Spin susceptibility and the pi-excitation in underdoped cuprates

The dynamical spin susceptibility chi'' at wave vector (pi, pi) and the spectrum pi'' of the spin-triplet particle--particle excitation with center of mass momentum (pi, pi) (pi-excitation) are considered in the slave-boson formulation of the t--J-model. Propagators are calculated in a diagrammatic t-matrix approximation in the d-wave superconducting state for a wide doping range. The resulting spectra chi'' and pi'' both show a resonance at a doping dependent energy, in qualitative agreement with recent numerical cluster calculations. In underdoped systems, the peak position is comparable to that found in neutron scattering experiments. The peak in chi'' as well as pi'' is at low doping entirely caused by spin fluctuations, whereas the triplet particle--particle channel does not contribute as a collective mode.