Lattice dynamics in the paraelectric phase of PbHfO₃ studied by inelastic x-ray scattering

We report the results of an inelastic x-ray scattering study of the lattice dynamics in the paraelectric phase of the antiferroelectric lead hafnate PbHfO₃. The study reveals an avoided crossing between the transverse acoustic and transverse optic phonon modes propagating along the [1 1 0] direction with [1  −1 0] polarization. The static susceptibility with respect to the generally incommensurate modulations is shown to increase on cooling for the entire Γ-M direction. We consider different approaches to the data analysis that correspond to different models for the temperature evolution of the dynamic susceptibility function. A number of similarities and differences between the lattice dynamics of PbHfO₃ and PbZrO₃ are described. (paper)