Doping Dependence of Bilayer Resonant Spin Excitations in $\bf (Y,Ca)Ba_2Cu_3O_{6+x}$

TL;DR

This study investigates how resonant spin excitations in a bilayer high-$T_c$ superconductor vary with doping, revealing a scaling relationship consistent with the spin-exciton model and identifying a critical doping level where modes align with the superconducting gap.

Contribution

It provides the first comprehensive doping-dependent analysis of odd and even resonant spin modes in a bilayer cuprate superconductor, confirming the spin-exciton model predictions.

Findings

Resonant modes and continuum threshold coincide above doping $ ho \,\simeq \,0.19$

A scaling relationship links mode energies and spectral weights

Resonant modes are identified as bound states in the superconducting gap

Abstract

Resonant magnetic modes with odd and even symmetries were studied by inelastic neutron scattering experiments in the bilayer high-$T_c$ superconductor $\rm Y_{1-x}Ca_{x}Ba_2Cu_3O_{6+y}$ over a wide doping range. The threshold of the spin excitation continuum in the superconducting state, deduced from the energies and spectral weights of both modes, is compared with the superconducting d-wave gap, measured on the same samples by electronic Raman scattering in the $B_{1g}$ symmetry. Above a critical doping level of $\delta \simeq 0.19$, both mode energies and the continuum threshold coincide. We find a simple scaling relationship between the characteristic energies and spectral weights of both modes, which indicates that the resonant modes are bound states in the superconducting energy gap, as predicted by the spin-exciton model of the resonant mode.