Simultaneous Superconducting and Antiferroquadrupolar Transitions in   PrRh$_{2}$Zn$_{20}$
  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. 
T. Onimaru, N. Nagasawa, K. T. Matsumoto, K. Wakiya, K. Umeo, S.   Kittaka, T. Sakakibara, Y. Matsushita, T. Takabatake
cond-mat.str-el cond-mat.mtrl-sci cond-mat.supr-con