Thermodynamical properties of ${\mathrm{K}}_2$Os${\mathrm{Cl}}_6$ and ${\mathrm{K}}_2$Re${\mathrm{Cl}}_6$ at low temperatures and near their structural phase transitions

Specific-heat measurements on ${\mathrm{K}}_2$Os${\mathrm{Cl}}_6$ single crystals revealed anomalous behavior at low temperatures. The specific heat of the acoustic modes corresponds to a Debye temperature ${\Theta }_D$ of 63.6 ± 0.2 K. The contribution of low-lying optical modes including a rotary mode extend the description of the specific heat by the cubic law up to $\frac{T}{{\Theta }_D}\simeq \frac{1}{6}$. A small anomaly of unknown origin occurs, however, at $T=6.67\mathrm{}\pm 0.05$ K. The specific heat and entropy of ${\mathrm{K}}_2$Re${\mathrm{Cl}}_6$ and ${\mathrm{K}}_2$Os${\mathrm{Cl}}_6$ evaluated using the technique of the special points in the Brillouin zone agree well with experimental values outside of the regions of structural phase transitions at 103.4 and 110.9 K in ${\mathrm{K}}_2$Re${\mathrm{Cl}}_6$ and 46.1 K in ${\mathrm{K}}_2$Os${\mathrm{Cl}}_6$. These calculations permit the evaluation of excess entropies and specific-heat discontinuities associated with the transitions. The critical behavior around the structural phase transition at 46.1 ± 0.5 K in ${\mathrm{K}}_2$Os${\mathrm{Cl}}_6$ is also discussed. It is concluded that the range of the interaction associated with the transition is approximately the interoctahedral separation.