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

TL;DR

This paper explains how incommensurate antiferromagnetic peaks in underdoped bilayer cuprates evolve with energy and doping, converging to a commensurate resonance, using the t-J model and fermion-spin theory.

Contribution

It provides a theoretical explanation for the coexistence and convergence of incommensurate peaks and resonance in underdoped bilayer cuprates based on bilayer interactions.

Findings

Incommensurate peaks appear at low energies and shift with doping.

The incommensurability parameter $oldsymbol{ extdelta}$ saturates at higher doping.

Peaks converge to the commensurate resonance at higher energies.

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\pm\delta)\pi,\pi] $ and $[\pi,(1\pm\delta)\pi]$ 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.