Isotope effect on the optical phonons of ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ studied by far-infrared ellipsometry and Raman scattering

The phonon spectra of ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ polycrystalline samples with different isotope substitution for Ba, Cu, and O have been studied using far-infrared ellipsometry and Raman scattering. The observed isotope shifts of Raman- and infrared-active phonons provide insight into their relative Ba, Cu, and O normal mode content. This allows us to examine mode eigenvectors obtained from lattice dynamical calculations using ab initio electronic structures based on the full potential linear muffin-tin-orbital within the local density approximation. Our Raman results demonstrate that the $104{\mathrm{cm}}^{-1}$ $A_g$ phonon is only very weakly mixed, representing almost pure Ba vibrations. Correspondingly the $151{\mathrm{cm}}^{-1}$ phonon represents pure Cu vibrations. The 339, 436, and $498{\mathrm{cm}}^{-1}$ phonon modes involve mainly O vibrations. Considerable $\mathrm{Cu}\text{−}\mathrm{O}$ mixing takes place in the case of the $A_g$ phonons at 257 and $605{\mathrm{cm}}^{-1}$ and for the $B_{3g}$ phonon at $314{\mathrm{cm}}^{-1}$. These results are in good agreement with the ab initio calculations. The far-infrared experiments reveal that the modes with energies of 115, 297, 502, and $592{\mathrm{cm}}^{-1}$ are mixed vibrations of O and Cu atoms. The phonon mode at $130{\mathrm{cm}}^{-1}$ corresponds to a $\mathrm{Ba}\text{−}\mathrm{Cu}\text{−}\mathrm{O}$ complex whereas the modes at 191 and $357{\mathrm{cm}}^{-1}$ reflect almost pure Cu and O vibrations, respectively.

Figure 1

(Color online) Crystallographic unit cell of ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$.

Figure 2

(Color online) Displacement pattern of the calculated $A_g$ Raman eigenmodes of ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$. The calculated eigenfrequencies are given in parentheses for $Y124$ and the corresponding modes in $Y123$.

Figure 3

(Color online) Raman scattering (a) and far-infrared ellipsometry (b) spectra for oxygen substituted ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ measured at $10\mathrm{K}$. The arrows indicate the isotope shifts of the corresponding phonon modes. (Please note the axis break and change of the scale.)

Figure 4

(Color online) Raman scattering (a) and far-infrared ellipsometry (b) spectra for copper substituted ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ measured at $10\mathrm{K}$. The arrows indicate the isotope shifts of the corresponding phonon modes. (Please note the axis break.)

Figure 5

(Color online) Raman scattering (a) and far-infrared ellipsometry (b) spectra for barium substituted ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ measured at $10\mathrm{K}$. The arrows indicate the isotope shifts of the corresponding phonon modes.