Temperature dependence of transverse- and longitudinal-optic modes in TiO2(rutile)

Abstract

The temperature dependence of the infrared reflectivity of rutile, Ti${\mathrm{O}}_2$, is reported in the range 275-900 ${\mathrm{cm}}_{-1\mathrm{}}$ and from room temperature up to 1500 K, for both the $A_{2u}$- and $E_u$-type mode spectra. Reflectivity spectra are fitted with the aid of a four-parameter dispersion model based on the factorized form of the dielectric function. The equivalence between the classical dielectric response function and the phonon propagator provides a correlation between adjusted frequencies and damping and their quantum counterparts in terms of the phonon self-energy. The temperature dependence of the anharmonic frequency shift for the ferroelectric (FE) $A_{2u}\left(\mathrm{TO}\right)$ mode which has been shown to be linear in the vicinity of room temperature looks more rapid at high temperature. This may indicate the occurrence of an anharmonic coupling that involves the sixth-order Hamiltonian, which acts as a quadratic function of temperature to stabilize the FE mode together with quartic anharmonicity. The behavior of TO and LO phonon damping with increasing temperature shows that the phonon lifetimes in rutile are limited by anharmonic three-phonon coupling. Phonon lifetimes are found shorter than in other oxide crystals. Moreover, the ratio of the damping function evaluated at the harmonic frequency on the frequency of the $A_{2u}\left(\mathrm{TO}\right)$ mode is six times higher than the same ratio averaged on all other modes. Thus rather large anharmonicities are revealed in rutile that are correctly described by lowest-order terms in the phonon self-energy.