Lattice dynamics of ${\mathrm{K}}_2$Pt${\mathrm{}\left(\mathrm{CN}\right)\mathrm{}}_4$${\mathrm{Br}}_{0.3}$.3.2 ${\mathrm{D}}_2$O (KCP) studied by inelastic neutron scattering

The lattice-dynamical properties of the "quasi-one-dimensional conductor" ${\mathrm{K}}_2$Pt${\mathrm{}\left(\mathrm{CN}\right)\mathrm{}}_4$ ${\mathrm{Br}}_{0.3}$.3.2 ${\mathrm{D}}_2$O (KCP) has been studied by neutron inelastic scattering at temperatures between 20 and 240 K with special attention to the relation to the partial three-dimensional ordering at $T\approx 100$ K. We have investigated the general lattice dynamics by measuring the acoustic-phonon dispersion relations. Secondly, extensive measurements have been carried out to clarify the nature of the excitations in the vicinity of the $2k_F$ anomaly, which are restricted to extremely narrow wave-vector regions. In these regions we present normalized intensity contours, which may be directly compared with theoretical calculations. At all temperatures below 160 K we find a maximum in the scattering at the $2k_F$ anomaly with an energy of 2.5 meV, as has recently been found by Comès et al. At lower temperatures the inelastic scattering becomes well separated in energy from the elastic scattering, signifying a phonon gap. We find it plausible to ascribe the apparent disappearance of this gap at higher temperatures to phonon lifetime effects, leading to the conclusion that the phonon frequency does not, at any temperature, condense to $\omega =0\mathrm{}$. At all temperatures, we find the scattering in the $2k_F$ anomaly to be connected with the regular phonons. Furthermore, the inelastic scattering intensities at the $2k_F$ anomaly is found to vary slowly with the wave-vector component perpendicular to the Pt chains and does not seen to reflect the buildup of the transverse, static correlations at lower temperatures. Our results extend previous neutron inelastic studies in several ways, and are found to be in fair agreement with the recent infrared (ir) and Raman scattering data.