Phase transitions ofPbHPO4- andPbDPO4-type ferroelectrics investigated with a Green’s-function technique

A Green’s-function technique is used to study the effects of spin-phonon interactions in ${\mathrm{PbHPO}}_4$- and ${\mathrm{PbDPO}}_4$-type ferroelectrics including higher-order anharmonic terms. The renormalized energy and the damping of the spin-waves and the phonons have been evaluated. The anharmonicity effects play an important role in the vicinity of ${\mathit{T}}_{\mathit{c}}$ and above ${\mathit{T}}_{\mathit{c}}$. The transverse dynamic structure factor exhibits three peaks due to the coupling of the transverse soft mode and the acoustic-phonon mode. The width of the central peak is proportional to the phonon damping.