Raman-active phonons of a twin-free ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ crystal: A complete polarization analysis

A complete Raman analysis has been performed on a high-quality ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ crystal made free of twins by a mechanical detwinning process. Marked a-b anisotropy is observed in the intensity of the ${\mathit{A}}_{\mathit{g}}$ phonons at 116, 335, and 495 ${\mathrm{cm}}^{\mathrm{-}1}$. At room temperature, the ${\mathrm{\alpha }}_{\mathit{y}\mathit{y}}$ component of the polarizability tensor of the 116-${\mathrm{cm}}^{\mathrm{-}1}$ phonon is strongly coupled to an electronic continuum, the ${\mathrm{\alpha }}_{\mathit{x}\mathit{x}}$ component is less strongly coupled, and the coupling of the ${\mathrm{\alpha }}_{\mathit{z}\mathit{z}}$ component is not apparent in the Raman line shape. ${\mathit{B}}_{2\mathit{g}}$ and ${\mathit{B}}_{3\mathit{g}}$ phonon pairs are reproducibly found at 70 and 83 ${\mathrm{cm}}^{\mathrm{-}1}$, 142 and 140 ${\mathrm{cm}}^{\mathrm{-}1}$, 210 and 303 ${\mathrm{cm}}^{\mathrm{-}1}$, and 579 and 526 ${\mathrm{cm}}^{\mathrm{-}1}$. Comparison of the observed ${\mathit{B}}_{2\mathit{g}}$-${\mathit{B}}_{3\mathit{g}}$ pairs to literature calculations of frequencies is made.