An antiferroquadrupolar ordering at T(Q)=0.11  K has been found in a Pr-based superconductor PrIr(2)Zn(20). The measurements of specific heat and magnetization revealed the non-Kramers Γ(3) doublet ground state with the quadrupolar degrees of freedom. The specific heat exhibits a sharp peak at T(Q)=0.11  K. The increment of T(Q) in magnetic fields and the anisotropic B-T phase diagram are consistent with the antiferroquadrupolar ordered state below T(Q). The entropy release at T(Q) is only 20% of Rln2, suggesting that the quadrupolar fluctuations play a role in the formation of the superconducting pairs below T(c)=0.05  K.

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Superconducting and antiferroquadrupolar (AFQ) transitions in a Pr-based compoundPrRh 2 Zn 20 have been found to occur simultaneously at T c =T 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 (CEF) ground state of the trivalent Pr ion is the non-Kramers Γ 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 Q decreases in B || [100] but increases in B|| [110] and B || [111] with increasing B up to 6 T. This anisotropic behavior of T Q (B) can be well explained by a two-sublattice mean-field calculation, which corroborates the AFQ ordered state below T Q . The entropy release at T Q is only 10% of Rln2 expected for the Γ 3 doublet, suggesting possible interplay between the quadrupolar degrees of freedom and the superconductivity.

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Orbital degrees of freedom in condensed matters could play important roles in forming a variety of exotic electronic states by interacting with conduction electrons. In 4f -electron systems, because of strong intra-atomic spin-orbit coupling, an orbitally degenerate state inherently carries quadrupolar degrees of freedom. The present work has focussed on a purely quadrupole-active system PrIr2Zn20 showing superconductivity in the presence of an antiferroquadrupole order at TQ = 0.11 K. We observed non-Fermi liquid (NFL) behaviors emerging in the electrical resistivity ρ and the 4f contribution to the specific heat, C 4f , in the paramagnetic state at T > TQ. Moreover, in magnetic fields B ≤ 6 T, all data set of ρ(T ) and C 4f (T ) are well scaled with characteristic temperatures T0's. This is the first observation of the NFL state in the nonmagnetic quadrupole-active system, whose origin is intrinsically different from that observed in the vicinity of the conventional quantum critical point. It implies possible formation of a quadrupole Kondo lattice resulting from hybridization between the quadrupoles and the conduction electrons with an energy scale of kBT0. At T ≤0.13 K, ρ(T ) and C 4f (T ) exhibit anomalies as B approaches 5 T. This is the manifestation of a field-induced crossover toward a Fermi-liquid ground state in the quadrupole Kondo lattice.PACS numbers: