The $a$-axis optical properties of a detwinned single crystal of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.50}$ in the ortho-II phase (Ortho-II Y123, $T_c=59\mathrm{K}$) were determined from reflectance data over a wide frequency range $(70–42000{\mathrm{cm}}^{-1})$ for nine temperature values between 28 and $295\mathrm{K}$. Above $200\mathrm{K}$ the spectra are dominated by a broad background of scattering that extends to $1\mathrm{eV}$. Below $200\mathrm{K}$ a shoulder in the reflectance appears and signals the onset of scattering at $400{\mathrm{cm}}^{-1}$. In this temperature range we also observe a peak in the optical conductivity at $177{\mathrm{cm}}^{-1}$. Below $59\mathrm{K}$, the superconducting transition temperature, the spectra change dramatically with the appearance of the superconducting condensate. Its spectral weight is consistent, to within experimental error, with the Ferrell-Glover-Tinkham (FGT) sum rule. We also compare our data with magnetic neutron scattering on samples from the same source that show a strong resonance at $31\mathrm{meV}$. We find that the scattering rates can be modeled as the combined effect of the neutron resonance and a bosonic background in the presence of a density of states with a pseudogap. The model shows that the decreasing amplitude of the neutron resonance with temperature is compensated for by an increasing of the bosonic background yielding a net temperature-independent scattering rate at high frequencies. This is in agreement with the experiments.

• Received 10 May 2005

DOI:https://doi.org/10.1103/PhysRevB.73.014508