Raman-active phonons in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Y}}_{\mathit{x}}$${\mathrm{Cu}}_2$${\mathrm{O}}_{8+\mathit{d}}$ (x=0–1): Effects of hole filling and internal pressure induced by Y doping for Ca, and implications for phonon assignments

The phonon Raman spectra of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{Ca}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Y}}_{\mathit{x}}$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_{8+\mathit{d}}$ (x=0-1) have been investigated in a number of well-defined single-crystal and polycrystalline samples. From the polarization and Y-doping dependence, and from a comparison with previous reports on Bi-based cuprates, we identify the (6${\mathit{A}}_{1\mathit{g}}$+1${\mathit{B}}_{1\mathit{g}}$) symmetry modes that are Raman allowed within the ideal body-centered-tetragonal unit cell. A large number of extra ‘‘disorder-induced’’ phonon bands are observed in the ab-plane polarized spectra. In contrast to most previous reports, we argue that the c-axis polarized phonon band around 629 ${\mathrm{cm}}^{\mathrm{-}1}$ is due to the O(2${)}_{\mathrm{Sr}}$ ${\mathit{A}}_{1\mathit{g}}$ vibration, while the exclusively ab-plane polarized band around 463 ${\mathrm{cm}}^{\mathrm{-}1}$ is induced by the O(3${)}_{\mathrm{Bi}}$ ${\mathit{A}}_{1\mathit{g}}$ vibration. With increasing Y doping we find that the vibrational modes involving atoms in the ${\mathrm{CuO}}_2$ planes rapidly increase in intensity as a result of the reduced metallic screening in the hole-depleted Y-doped samples. We also find that Y substitution gives rise to a substantial hardening of the O(1${)}_{\mathrm{Cu}}$ ${\mathit{A}}_{1\mathit{g}}$ and ${\mathit{B}}_{1\mathit{g}}$ phonons by ∼40 ${\mathrm{cm}}^{\mathrm{-}1}$, whereas the O(2${)}_{\mathrm{Sr}}$ ${\mathit{A}}_{1\mathit{g}}$ phonon is found to soften by ∼20 ${\mathrm{cm}}^{\mathrm{-}1}$, when x increases from 0 to 1. The phonon frequency changes can be explained by the ‘‘internal pressure’’ induced by the decrease in the average Ca/Y ion size and an additional ‘‘charge-transfer’’ induced by the change in the Cu and Bi valences with Y doping. © 1996 The American Physical Society.