Hybridization and multipole orders of 4f electrons in Pr skutterudites

Characteristics of hybridization and multipole orders of $4f$-electrons in Pr skutterudites are explained in terms of a pseudo-quartet composed of crystalline electric field (CEF) singlet and the triplet. It is shown that the contrasting behaviors observed in PrFe${}_4$P${}_{12}$ and PrOs${}_4$Sb${}_{12}$ are ascribed to the difference in triplet wave functions and the CEF splittings.Since a macroscopic degeneracy remains even in the ordered phase with the ${\mathrm{\Gamma }}_3$-type antiferro-quadrupole (AFQ) order,a model with strong AFQ fluctuation and static monopole/hexadecapole order is proposed for PrFe${}_4$P${}_{12}$.The remaining cubic symmetry explains qualitatively the behavior of staggered magnetization observed by NMR and neutron scattering. For identification of possible hexadecapole orders in PrFe${}_4$P${}_{12}$ andPrRu${}_4$P${}_{12}$, eightfold intensity pattern is predicted in the azimuthal angle scan of resonant X-ray scattering. In PrOs${}_4$Sb${}_{12}$, the ferromagnetic exchange coupling with the conduction band does not lead to magnetic Kondo effect, but a momentum-dependent quadrupole coupling can give rise to enhanced effective mass, which should be sensitive to disorder.