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

Abstract

The recently discovered coexistence of incommensurate antiferromagnetic neutron scattering peaks and commensurate resonance in underdoped YBa$_2$Cu$_3$O$_{6+x}$ 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\pmδ)π,π] $ and $[π,(1\pmδ)π]$ at low energies with $δ$ initially increasing with doping at low dopings and then saturating at higher dopings. These incommensurate peaks are suppressed, and the parameter $δ$ is reduced with increasing energy. Eventually it converges to the $[π,π]$ resonance peak. Thus the recently observed coexistence is interpreted in terms of bilayer interactions.