Hybridization Effects and Multipole Orders in Pr Skutterudites

Theoretical account is given of 4f-electron dynamics and multipole orders inPr skutterudites with particular attention to (i) mechanism of the crystallineelectric field (CEF) splitting leading to a pseudo-quartet ground state;(ii)Kondo effect due to exchange interactions involving the pseudo-quartet;(iii)multipole orders in the lattice of the pseudo-quartet in magneticfield.Competition between the point-charge interaction andhybridization between4f and conduction electrons is identified as the key for controlling the CEFsplitting. It is found that one of two pseudo-spins forming the pseudo-quartethas a ferromagnetic exchange, while the other has an antiferromagnetic exchangewith conduction electrons. The Kondo effect is clearly seen in the resistivitycalculated by the NCA, provided the low-lying triplet above the singlet ismainly composed of the $\Gamma_4$-type wave functions.If the weight of the$\Gamma_5$-type is large in the triplet, the Kondo effect does not appear.Thisdifference caused by the nature of the triplet explains the presence of theKondo effect inPrFe$_4$P$_{12}$, and its absence in PrOs$_4$Sb$_{12}$.By takingthe minimal model with antiferro-quadrupole (AFQ) and ferro-type intersiteinteractions for dipoles and octupoles between nearest-neighbors,the mean-fieldtheory reproduces the overall feature of the multiple ordered phases inPrFe$_4$P$_{12}$. The AFQ order with the $\Gamma_3$-type symmetry is found tobe stable only as a mixture of $O_2^0$ and $O_2^2$ components.Comment: 21 pages, to be published in proc. YKIS200