Observation of the effects of phonon dispersion on the Fröhlich-interaction-induced second-order Raman scattering in Pb2Sr2PrCu3O8.

Abstract

The one- and two-phonon Raman-scattering spectrum of single-crystal ${\mathrm{Pb}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{PrCu}}_{3}$${\mathrm{O}}_{8}$ is examined under resonance conditions. Strong features appear in the one-phonon spectrum at the positions of longitudinal optical (LO) infrared modes as the laser energy approaches that of the charge transfer gap. These Fr\"ohlich-interaction-induced modes are accompanied by a second-order spectrum composed of overtones and combinations of the LO and ordinary Raman-allowed phonons. We examine the dependence on incident photon energy of both the line shape and center position of the highest-frequency two-phonon feature, which can be unambiguously attributed to a pure overtone of an infrared LO vibration. Due to the two-phonon nature of the scattering process the crystal momentum q is no longer restricted to small wave vectors and one can expect to observe effects of phonon dispersion. We find, indeed, changes in the line shape as the gap is approached, accompanied by a decrease in the center frequency to a value close to twice that of the q\ensuremath{\approxeq}0 one-LO-phonon (1-LO) mode. A detailed comparison to the free electron theory for two-LO-phonon (2-LO) scattering by Zeyher [Phys. Rev. B 9, 4439 (1974)] is carried out. Relationships between the effective lattice mass characterizing the dispersion of this LO branch and the electron and hole effective band masses are established, and an estimate of the effective electron and hole band masses is made based on the magnitude of the phonon dispersion in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6}$ as measured by neutron-scattering experiments.