Isotope effects on the optical phonons of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$: Eigenvector and infrared charge determination

Using Raman spectroscopy and far-infrared ellipsometry we have investigated several ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ ceramics which were made from different isotopically pure Cu or Ba precursors. The observed shifts of Raman- and infrared-active phonons reveal insight into their relative Ba and Cu normal mode content. This allows us to examine mode eigenvectors obtained from lattice dynamical calculations. Our Raman results demonstrate that the 121 ${\mathrm{cm}}^{\mathrm{-}1}$ and 153 ${\mathrm{cm}}^{\mathrm{-}1}$ ${\mathrm{A}}_{\mathrm{g}}$ phonons are only very weakly mixed and represent almost pure Ba and Cu vibrations, respectively, whereas they suggest considerable Ba-Cu-O mixing in the case of the ${\mathrm{B}}_{2\mathrm{g}}$ and ${\mathrm{B}}_{3\mathrm{g}}$ phonons at 140 ${\mathrm{cm}}^{\mathrm{-}1}$ and 142 ${\mathrm{cm}}^{\mathrm{-}1}$. The analysis of the infrared-active ${\mathrm{B}}_{1\mathrm{u}}$ modes yields a substantial contribution of Cu to the 150 ${\mathrm{cm}}^{\mathrm{-}1}$ and the 280 ${\mathrm{cm}}^{\mathrm{-}1}$ phonons and of Ba to the 150 ${\mathrm{cm}}^{\mathrm{-}1}$ mode. Making use of proposed eigenvectors, which are shown to be compatible with the observed isotope shifts, we determine effective charges for all ions from measured infrared oscillator strengths on a ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ crystal. We find that the proposed eigenvectors are compatible with earlier experiments of the oxygen isotope effect as well as the replacement of Y by rare earth elements.