Neutron-scattering study of the incommensurate phase transition ofRb2ZnBr4

A neutron-scattering study is presented of the modulation phase transition, at $T_c=82\mathrm{}°$C, of ${\mathrm{Rb}}_2$Zn${\mathrm{Br}}_4$. A derivation is given of the structure factor for the diffuse scattering that appears near the transition which is described with a complex order parameter, i.e., amplitude as well as phase fluctuations of the order parameter are treated. The displacive character of the modulation is established and the spectra of the critical diffuse scattering in the high-temperature phase are interpreted with the help of a soft-phonon model. The soft excitations are overdamped near $T_c$ and become underdamped only far above the transition temperature. The frequency of these excitations remains very low, i.e., below 0.1 THz. The acoustical branches and one optical dispersion branch along crystal axes were measured, at room temperature, and found to be stable in the entire temperature region of interest. In the low-temperature phase a broad diffuse scattering distribution was found around the satellite reflections. The Spectra of this diffuse scattering are overdamped and no propagating excitations, corresponding to a soft mode, were observed in the low-temperature phase. Since phase or amplitude fluctuations of the order parameter will give rise to scattering close to the satellite positions our data provide evidence for an overdamped phase or amplitude excitation branch.