Dispersive spin excitations in highly overdoped cuprates revealed by resonant inelastic x-ray scattering

Using resonant inelastic x-ray scattering (RIXS) at the Cu $L$-absorption edge, we have observed intense, dispersive spin excitations in highly overdoped Tl${}_2$Ba${}_2$CuO${}_{6+\delta }$ (superconducting $T_c=6$ K), a model compound whose normal-state charge transport and thermodynamic properties have been shown to exhibit canonical Fermi-liquid behavior. Complementary RIXS experiments on slightly overdoped Tl${}_2$Ba${}_2$CuO${}_{6+\delta }$ ($T_c=89$ K) and on Y${}_{1-x}$Ca${}_x$Ba${}_2$Cu${}_3$O${}_{6+\delta }$ compounds spanning a wide range of doping levels indicate that these excitations exhibit energies and energy-integrated spectral weights closely similar to those of antiferromagnetic magnons in undoped cuprates, indicating the persistence of substantial antiferromagnetic spin correlations over a wide doping range. The surprising coexistence of such correlations with Fermi-liquid-like charge excitations in highly overdoped cuprates poses a challenge to current theoretical models of correlated-electron metals.

Figure 1

Left column: Doping dependence of the RIXS response measured in the $\sigma$ (red) and $\pi$ (black) scattering geometries for ${\mathbf{Q}}_{\parallel }=0.8\Gamma X=(0.4,0)$ r.l.u. Right column: Detailed view of the low-energy part of the data. In each panel, the intensity scale has been normalized to the area of the $dd$ excitation in the $\pi$ channel. Inset: Intensities for spin-flip (SF) and non-spin-flip (NSF) scattering from in-plane Cu sites with $3d_{x^2-y^2}^9$ ground-state symmetry in the $\pi$ channel relative to $\sigma$ (Refs. 13, 29, 32, and 33).

Figure 2

Low-energy part of the RIXS spectra of overdoped Y${}_{0.85}$Ca${}_{0.15}$Ba${}_2$Cu${}_3$O${}_{6+x}$ (left panel), moderately overdoped Tl${}_2$Ba${}_2$CuO${}_{6+\delta }$ ($T_c=89$ K, middle panel), and strongly overdoped Tl${}_2$Ba${}_2$CuO${}_{6+\delta }$ ($T_c=6$ K) in the $\pi$ scattering geometry for various in-plane momentum transfers $Q_{\parallel }$. The fitting procedure is detailed in Ref. 13. The slightly more intense elastic line in the $T_c=89$ K sample, compared to the other two samples, originates from the lower quality of its surface. The data were normalized to the energy-integrated spectral weight of the $dd$ excitations, which is proportional to the density of CuO${}_2$ layers.

Figure 3

Energy and full width at half maximum (FWHM) of the magnetic excitations in the three overdoped compounds, as well as in antiferromagnetic YBa${}_2$Cu${}_3$O${}_{6.1}$ and underdoped YBa${}_2$Cu${}_3$O${}_{6.6}$ (Ref. 13) as a function of the in-plane momentum transfer $Q_{\parallel }$. The solid line for YBa${}_2$Cu${}_3$O${}_{6.1}$ is the result of a fit to the 2D bilayer Heisenberg model. The scattering geometry implies that only the optical magnon branch contributes to the RIXS intensity (Ref. 13). The solid line for the underdoped compound is a guide to the eyes. In both panels, the dashed area corresponds to the experimental energy resolution (130 meV FWHM).

Figure 4

Energy-integrated intensity of the magnetic excitations, normalized to the $dd$ excitation intensity, as a function of doping.