A systematic Raman study in the visible and the near IR has been carried out on $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_x$ samples, with isotopic substitution of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and for oxygen concentrations in the range $x=6.44-6.98\mathrm{}$. A small but clear deviation from harmonic behavior has been detected for the frequency shift of the in-phase mode and, to a less extent, of the apex mode, relative to the out-of-phase phonon. The deviation increases towards low concentrations of oxygen. A disagreement of the present work for the apical mode, with a previous investigation using IR excitation, is attributed to the contribution of several phases to the apex mode in the underdoped region and the possible IR resonance of the "ortho-II" phase.

• Received 29 February 1996

DOI:https://doi.org/10.1103/PhysRevB.54.6721