Excess Low Temperature Specific Heat and Related Phonon Density of States in a Modulated Incommensurate Dielectric

We report the first very low temperature (from 93 mK to 7.3 K) specific heat data of a modulated incommensurate dielectric (Cl${\mathrm{C}}_{6}$${\mathrm{H}}_{4}$${)}_{2}$S${\mathrm{O}}_{2}$. They reveal three different contributions in excess of that of normal acoustic phonons: low frequency excitations predominant below 0.2 K, a phason branch above 0.7 K, and optical phonon and amplitudon branches around 4.5 K. This analysis is done considering neutron scattering results also.