Doping and temperature dependence of c-axis optical phonons in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{y}}$ single crystals

Measuring the far-infrared reflectivity of ${\mathrm{YBa}}_2$ ${\mathrm{CuO}}_3$ ${\mathrm{O}}_{\mathit{y}}$ crystals with radiation polarized parallel to the c axis, we determined the doping and temperature dependence of c-axis infrared active phonons. Superconductivity related effects on the phonon self-energies are weak for the overdoped crystal, but pronounced for the optimally doped crystal. The differences are attributed to a lower symmetry of the optimally doped crystal due to disorder in the oxygen sublattice which manifests in a splitting of the apical oxygen vibration into well distinct modes above 600 ${\mathrm{cm}}^{\mathrm{-}1}$. For the underdoped crystals anomalies are observed well above ${\mathit{T}}_{\mathit{c}}$. The onset temperature of the anomalies increases with decreasing doping, suggesting a relationship with the spin-gap temperature. The dramatic decrease in oscillator strength of the in-plane oxygen bending mode is related to a growth of a new broad excitation centered between 450 and 400 ${\mathrm{cm}}^{\mathrm{-}1}$.