Superconducting and antiferroquadrupolar (AFQ) transitions in a Pr-based compound PrRh${}_2$Zn${}_{20}$ have been found to occur simultaneously at $T_{\mathrm{c}}$ $=$ $T_{\mathrm{Q}}$ $=$ 0.06 K. The superconducting transition manifests itself by zero resistance and large diamagnetic susceptibility. The specific heat exhibits a Schottky anomaly peaking at 14 K, and magnetization curves measured at 2 K show anisotropic behaviors. The analysis of these data indicates that the crystalline electric field ground state of the trivalent Pr ion is the non-Kramers ${\Gamma }_3$ doublet with the quadrupolar degrees of freedom. A sharp peak in the specific heat at 0.06 K has been attributed not to the superconducting transition but to the AFQ transition because the ordering temperature $T_{\mathrm{Q}}$ decreases in $\mathit{B}$ $\left|\right|$ [100] but increases in $\mathit{B}$ $\left|\right|$ [110] and $\mathit{B}$ $\left|\right|$ [111] with increasing $B$ up to 6 T. This anisotropic behavior of $T_{\mathrm{Q}}$($B$) can be well explained by a two-sublattice mean-field calculation, which corroborates the AFQ ordered state below $T_{\mathrm{Q}}$. The entropy release at $T_{\mathrm{Q}}$ is only 10$\%$ of $R$ ln 2 expected for the ${\Gamma }_3$ doublet, suggesting possible interplay between the quadrupolar degrees of freedom and the superconductivity.

• Received 20 August 2012

DOI:https://doi.org/10.1103/PhysRevB.86.184426