  Superconducting and antiferroquadrupolar (AFQ) transitions in a Pr-based
compound PrRh2Zn20 have been found to occur simultaneously at Tc=TQ=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 (CEF) ground state of the trivalent Pr ion is the non-Kramers Gamma3
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 TQ decreases in B || [100]
but increases in B || [110] and B || [111] with increasing B up to 6 T. This
anisotropic behavior of TQ(B) can be well explained by a two-sublattice
mean-field calculation, which corroborates the AFQ ordered state below TQ. The
entropy release at TQ is only 10% of Rln2 expected for the Gamma3 doublet,
suggesting possible interplay between the quadrupolar degrees of freedom and
the superconductivity.
