Lattice and central modes in the hyper-Raman spectra of the hydrogen-bonded ferroelectricsPbHPO4andPbDPO4

The hyper-Raman spectra of the hydrogen-bonded ferroelectrics ${\mathrm{PbHPO}}_4$ (LHP) and ${\mathrm{PbDPO}}_4$ are measured. The very weak intensity of the second-harmonic generation indicates that the space group of LHP in the paraelectric phase is centrosymmetric P2/c. The expected four ${\mathit{B}}_{\mathit{u}}$(X,Y) lattice modes in the paraelectric phase are all observed by hyper-Raman scattering for both compounds, but they do not show the softening. Therefore, the softening mode that was observed in the ferroelectric phase is assigned to the ${\mathit{A}}_{\mathit{g}}$ mode. On the other hand, the very strong relaxational central modes with ${\mathit{B}}_{\mathit{u}}$ symmetry are found by hyper-Raman scattering for both compounds in the paraelectric phase. It is concluded that the phase transition in ${\mathrm{PbHPO}}_4$ and ${\mathrm{PbDPO}}_4$ is of the order-disorder type. The softening of the ${\mathit{A}}_{\mathit{g}}$ lattice mode in the ferroelectric phase can be well elucidated by the coupling with the central mode for both compounds. The wave-vector dependence of the central mode shows that one-dimensional properties of ${\mathrm{PbHPO}}_4$ are very weak.