In-plane copper-oxygen bond-stretching mode anomaly in underdoped La 2 − x Sr x Cu O 4 + δ measured with high-resolution inelastic x-ray scattering

We have measured the lattice dynamics of underdoped ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4+\ensuremath{\delta}}$ $(x=0.08)$ using high resolution inelastic x-ray scattering spectroscopy. The very good intrinsic $\mathbf{Q}$ resolution of this experiment allows us to differentiate between the two proposed scenarios for the Cu-O bond stretching phonon broadening reported at $\mathbf{q}=(0.25,0,0)$. The results suggest that this phonon broadening is due to intrinsic damping rather than to a steep dispersion, having important implications on the interpretation of phonon anomalies in cuprates.