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.