Structural phase transitions in ${\mathrm{Sr}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ and ${\mathrm{Sr}}_3{\mathrm{Ir}}_4{\mathrm{Sn}}_{13}$ are currently of interest due to the evidence of strong correlation with their superconductivity. To further obtain additional insight into the thermodynamic properties of the phase transitions, we have performed a study of single-crystalline ${\mathrm{Sr}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ and ${\mathrm{Sr}}_3{\mathrm{Ir}}_4{\mathrm{Sn}}_{13}$ by means of the specific-heat and thermal-expansion measurements, mainly focusing on the features around the phase-transition temperature $T^{*}\simeq 138$ and 147 K, respectively. In particular, the specific-heat data have been analyzed in the framework of the critical fluctuation model in addition to a mean-field contribution. Relatively large critical exponents were obtained for ${\mathrm{Sr}}_3{\mathrm{Ir}}_4{\mathrm{Sn}}_{13}$, suggesting a shorter coherence length associated with the phase transition. For each compound, an enhancement in the mean-field jump compared to the BCS value has been quantitatively identified, revealing the strong-coupling characteristics for the observed phase transitions. Furthermore, prominent changes in the coefficient of linear thermal expansion and bulk modulus across $T^{*}$ have been identified, providing new information about the structural phase transitions in the title compounds.

• Received 8 March 2016
• Revised 3 May 2016

DOI:https://doi.org/10.1103/PhysRevB.93.245119