Light scattering in ferroelectric crystals

The ferroelectric phase transitions in the hydrogenbonded phosphates and arsenates isomorphous to KH PO have been studied using inelastic light scattering. Earlier measurements on KH0PO. (KDP) and KD POA (KD*P) have been £* 4r ft • TC extended to include KH2AsO4 (KDA), CsH2AsO4 (CsDA) and CsDQAsO. (CsD*A). The spectrum from O 3OOO cm" has <& TT been recorded and is compared with the results of a group theoretical analysis. In each case the low frequency Raman spectrum is characterised by a broad wing on the Rayleigh line which narrows and increases in intensity as the transition is approached. A strong anharmonic interaction between this ferroelectric mode and an optical mode of B2 symmetry is observed; the spectra fit well to a spectral distribution function obtained from a Green's function calculation, yielding the temperature dependence of the characteristic frequency and damping constant of the modes. There is no unique solution for the coupling due to the arbitrary phase of the modes, and so three models are considered:(i) The mode coupling here does not correspond closely to the Kobayashi scheme in which the overdamped ferroelectric mode is regarded as collective protontunneling with zero dipole moment. The overdamped mode must possess a large non-zero polarisability and further, the far infra-red reflectivity spectrum of CsDA indicates that the mode must be assigned a large dipole moment. The second collective proton mode predicted to appear in the Hainan spectrum is not observed. (ii) In considering real coupling it is found that the Debye relaxation time of the ferroelectric mode diverges at a temperature T which is lower than the actual transition temperature T . This effect may arise simply from \M» the mode coupling. (iii) With imaginary coupling it is found that T< T This result is interpreted in terms of a theory due v.* to Cowley and Coombs in which dielectric fluctucxtions couple to changes in local thermodynamic equilibrium so that there may be an additional response at low frequency. The ammonium salts (NH4 )H2PO4 (ADP) and (ND4 ) ^>2PO4 (AD*P) undergo transitions to an antiferroelectric phase at low temperature. Whereas the transition is due to a zone boundary instability at TA , zone centre soft modes f\ are observed which would become unstable at some lower temperature. A soft mode has also been observed in the Raman spectrum of the recently discovered ferroelectric 5PbO.3GeOQ . Near *£ 27OK there is a coupling with another lattice mode which results in a characteristic level repulsion and intensity transfer. The damping constant of the ferroelectric mode is found to diverge at T = 451K and a high resolution \*r study of the low frequency spectrum has revealed the presence of quasi-elastic scattering. The temperature dependence of this additional response is well described by the theory of Cowley and Coombs.