Hybridization effects and multipole orders in Pr skutterudites

TL;DR

This paper provides a theoretical analysis of 4f-electron behavior, multipole orders, and Kondo effects in Pr skutterudites, explaining experimental differences through detailed electronic interactions and minimal models.

Contribution

It introduces a comprehensive theoretical framework for understanding CEF splitting, Kondo effects, and multipole orders in Pr skutterudites, highlighting the role of hybridization and triplet wave function composition.

Findings

Kondo effect depends on triplet wave function composition.

Antiferro-quadrupole order is stable as a mixture of specific components.

Differences in Kondo effect presence explained by triplet wave function nature.

Abstract

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 andhybridization 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 $\Gamma_4$-type wave functions.If the weight of the $\Gamma_5$-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 inPrFe$_4$P$_{12}$, and its absence in PrOs$_4$Sb$_{12}$.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 PrFe$_4$P$_{12}$. The AFQ order with the $\Gamma_3$-type symmetry is found to be stable only as a mixture of $O_2^0$ and $O_2^2$ components.