Raman study of the coupling of crystal-field excitations to phonons in ${\mathrm{NdBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

A double peak observed near 300 ${\mathrm{cm}}^{\mathrm{-}1}$ in the Raman and inelastic-neutron-scattering spectra of the high-${\mathit{T}}_{\mathit{c}}$ superconductor ${\mathrm{NdBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ is due to a strong coupling and mixing of the ${\mathit{B}}_{1\mathit{g}}$-symmetry Raman phonon and crystal-field (CF) excitations of the ${\mathrm{Nd}}^{3+}$ 4f electrons of the same symmetry. In this paper, we describe in detail a model based on the coupling of extended phonons and localized CF excitations. Higher phonon quantum numbers have to be taken into account at room temperature. We show that this interpretation is compatible with measurements of the dependence on temperature, oxygen isotopic substitution, laser wavelength, and oxygen content. We obtain from our model the CF-phonon coupling constant as well as the frequencies of the unperturbed phonon and CF excitation. We also discuss the breaking of the polarization selection rules for the highest phonon based on the substitution of Ba by Nd ions.