Hybridization effects and multipole orders in Pr skutterudites

Theoretical account is given of 4f-electron dynamics and multipole orders in Pr skutterudites with particular attention to (i) mechanism of the crystalline electric 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 magnetic field. Competition between the point-charge interaction and hybridization between 4f and conduction electrons is identified as the key for controlling the CEF splitting. It is found that one of two pseudo-spins forming the pseudo-quartet has a ferromagnetic exchange, while the other has an antiferromagnetic exchange with conduction electrons. The Kondo effect is clearly seen in the resistivity calculated by the NCA, provided the low-lying triplet above the singlet is mainly composed of the Γ₄-type wave functions. If the weight of the Γ₅-type is large in the triplet, the Kondo effect does not appear. This difference caused by the nature of the triplet explains the presence of the Kondo effect in PrFe₄P₁₂, and its absence in PrOs₄Sb₁₂. By taking the minimal model with antiferro-quadrupole (AFQ) and ferro-type intersite interactions for dipoles and octupoles between nearest-neighbors, the mean-field theory reproduces the overall feature of the multiple ordered phases in PrFe₄P₁₂. The AFQ order with the Γ₃-type symmetry is found to be stable only as a mixture of O₂⁰ and O₂² components.