Convergence of energy-dependent incommensurate antiferromagnetic neutron scattering peaks to commensurate resonance in underdoped bilayer cuprates

The recently discovered coexistence of incommensurate antiferromagnetic neutron scattering peaks and commensurate resonance in underdoped YBa2Cu3O6+x is calling for an explanation. Within the t-J model, the doping and energy dependence of the spin dynamics of the underdoped bilayer cuprates in the normal state is studied based on the fermion-spin theory by considering the bilayer interactions. Incommensurate peaks are found at [(1+/-delta)pi,pi] and [pi,(1+/-delta)pi] at low energies, with delta initially increasing with doping at low dopings and then saturating at higher dopings. These incommensurate peaks are suppressed, and the parameter delta is reduced with increasing energy. Eventually it converges to the [pi,pi] resonance peak. Thus the recently observed coexistence is interpreted in terms of bilayer interactions.