Doping dependence of spin excitations in the stripe phase of high-T-c superconductors

Based on the time-dependent Gutzwiller approximation for the extended Hubbard model, we calculate the energy and momentum dependence of spin excitations for striped ground states. Our starting point correctly reproduces the observed doping dependence of the incommensurability in La-based cuprates and the dispersion of magnetic modes in the insulating parent compound. This allows us to make quantitative predictions for the doping evolution of the dispersion of magnetic modes in the stripe phase including the energy omega(0) and intensity of the resonance peak as well as the velocity c of the spin-wave-like Goldstone mode. In the underdoped regime n(h)< 1/8, we find a weak linear dependence of omega(0) on doping, whereas the resonance energy significantly shifts to higher values when the charge concentration in the stripes starts to deviate from half-filling for n(h)> 1/8. The velocity c is nonmonotonous with a minimum at 1/8 in coincidence with a well known anomaly in T-c. Our calculations are in good agreement with available experimental data. We also compare our results with analogous computations based on linear spin-wave theory.