Analysis of the temperature-dependent specific heat of Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$

The compounds PrOs$_4$Sb$_{12}$ and NdOs$_4$Sb$_{12}$ have attracted interest due to their properties at low temperatures, where they exhibit unconventional heavy-fermion superconductivity and ferromagnetism respectively. The series of compounds Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$ is being studied in order to understand the interaction between these effects. Previous studies have shown that there is competition between the superconducting and ferromagnetic effects and that for particular concentrations of Nd and Pr, the two phenomena coexist within the sample. In order to understand this system, the specific heat was measured in the normal state from 10 – 300 K. Thermodynamic parameters were extracted from the specific heat data for each sample, including the Debye Temperature, Einstein Temperature, and electronic specific heat coefficient. These provide information about the properties of the lattice and conduction electrons. The Einstein and Debye temperatures were both found to have a minimum around $x = 0.55$, which suggests a form of lattice-softening taking place at the Nd concentration where the superconductivity disappears and a possible quantum critical point may occur.