Acoustic anomalies inTb2(MoO4)3and the "missing"A1optic mode

Abstract

Anomalies in both the acoustic- and optic-phonon spectra associated with the ferroelectric and ferroelastic phase transition in terbium molybdate have been quantitatively measured by simultaneous Brillouin and Raman spectroscopy. The most striking singular behavior observed is the divergent damping of both the ${A}_{1}$ optic phonon and the ${C}_{11}$ acoustic phonon upon approach to ${T}_{0}$ from below. ${T}_{0}$ was determined to be 159\ifmmode^\circ\else\textdegree\fi{}C for our sample by measurement of the pyroelectric response. The ${A}_{1}$-mode frequency determined from the Raman spectrum shows little temperature dependence, while the ${C}_{11}$ elastic constant determined from the Brillouin spectra decreases by about 60% between room temperature and ${T}_{0}$. There is no evidence of a dynamic central peak. The observed anomalies in the acoustic velocity and damping are incompatible with a model based on bilinear coupling between the acoustic mode and the ${A}_{1}$ mode seen in the Raman spectrum. However, a satisfactory account of all the experimental observations (including the anomalies in ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{C}}_{11}$ and ${C}_{22}$) can be obtained by assuming the presence of a second ${A}_{1}$ optic phonon with a negligible Raman scattering cross section. We note that the dynamic variables below ${T}_{0}$ are not simply related to the distortion, as has often been assumed previously. On the basis of this model we use the acoustic velocities and damping to determine the frequency and damping parameters of this unseen mode. It is emphasized that the singular behavior of the damping of the observed ${A}_{1}$ mode has yet to receive adequate theoretical explanation.