Specific heat of ${\mathrm{Pr}}_{0.6}\left({\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x{)}_{0.4}{\mathrm{MnO}}_3\right(0\mathrm{}<~x<~1)$

We present the results of a specific heat study of the ${\mathrm{Pr}}_{0.6}\left({\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x{)}_{0.4}{\mathrm{MnO}}_3\right(0\mathrm{}<~x<~1)$ manganite system as a function of doping concentration x and temperature. The low-temperature specific heat data indicate that these materials have Debye temperatures of 333–344 K and reveal the presence of a ${1/T}^2$ hyperfine term. For $x>~0.25$ the samples are metallic ferromagnets at low temperature with $\gamma$ values of 4.5–5.7 mJ/mol ${\mathrm{K}}^2.$ However, no $T^{3/2}$ term associated with the presence of ferromagnetic spin waves can be resolved in the data. As x decreases below $x=0.25,$ the materials become increasingly insulating in character and antiferromagnetic order is preferred. The $x=0.0\mathrm{}$ sample is an antiferromagnetic charge ordered insulator. In this doping regime, the low-temperature specific heat contains an additional contribution which is attributed to the presence of antiferromagnetic spin waves. The high-temperature specific heat data clearly show the onset of the charge and magnetic ordering. The entropy loss accompanying the magnetic transition in each of these materials is much smaller than expected. This discrepancy is attributed to a combination of factors, including the localization of charge carriers around the metal-insulator transition which occurs at the Curie temperature $T_C$ in the $x>~0.25$ ferromagnetic materials and the presence of short range magnetic correlations, well above the magnetic ordering temperature.