Temperature dependence of Raman scattering and soft modes in TlTiOPO4

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Abstract
The Raman scattering of TlTiOPO4 has been studied from 110 K up to above the ferroelectric-to-centrosymmetric phase transition at Tc approximately=850 K. At low temperatures the analysis of the spectra includes the electrostatic interactions involved in the polar modes which are responsible for the variations in the frequencies and in the intensities as a function of the wavevector direction. Most of the non-polar (A2) and polar (B1, B2 and A1) modes among the 189 expected ones have been tabulated. The frequencies of the lines related to internal vibrations of the tetrahedral PO4 groups do not significantly depend upon the temperature. On the contrary, a soft transverse mode belonging to the A1 irreducible representation has been observed in the ferroelectric phase. The square of its frequency decreases linearly with the temperature and vanishes at Tc. This mode is connected with the Tl+ motion but its coupling with internal TiO6 modes is evidenced through the temperature variation of Raman lines at higher frequencies.