Isotopic investigation of the lattice dynamics in CuBr

Abstract

We present a detailed investigation of the Raman spectra of isotopically tailored CuBr at low temperature. The transverse optic (TO) phonon of CuBr exhibits an almost perfect Lorentzian line shape, whereas the longitudinal optic (LO) phonon displays a complex broad structure. The change of the TO frequency with the variation of the isotope composition can be well described within the virtual crystal approximation (VCA), which corresponds to a $\ensuremath{\omega}\ensuremath{\propto}{\ensuremath{\mu}}^{\ensuremath{-}1/2}$ dependence on the reduced mass \ensuremath{\mu}. Slight deviations from this general trend are attributed to anharmonic renormalization and agree semiquantitatively with results extracted from previous measurements of the temperature dependence of the Raman spectra. In the LO case, the broad structure is resolved into three separate features, A, B, and C. While A and B are rather broad, C is a narrow peak located at the high-energy side of the LO structure. Two different trends are observed when analyzing the evolution of the LO structure with isotope substitution: peak B shows a $\ensuremath{\propto}{\ensuremath{\mu}}^{\ensuremath{-}1/2}$ behavior, analogous to that of the TO phonon, whereas peaks A and C shift almost only with the copper mass. The LO line shape is explained in terms of the Fermi resonance (FR) model, i.e., an interaction between the LO mode and a combination band of two acoustic phonons. We have performed a shell model calculation, with parameters taken from inelastic neutron scattering measurements, in order to obtain the one- and two-phonon densities of states (DOS). This calculation yields Raman line shapes in remarkable agreement with the experimental observations.