Hybridization and multipole orders of 4f electrons in Pr skutterudites

TL;DR

This paper investigates the hybridization and multipole ordering of 4f electrons in Pr skutterudites, explaining contrasting behaviors through crystal field effects and proposing models for multipole fluctuations and orders.

Contribution

It introduces a model based on a pseudo-quartet for 4f electrons, explaining differences in Pr skutterudites and predicting experimental signatures of multipole orders.

Findings

Contrasting behaviors in PrFe4P12 and PrOs4Sb12 explained by triplet wave functions and CEF splittings.

Proposed a model with strong AFQ fluctuations and static monopole/hexadecapole order for PrFe4P12.

Predicted an eightfold intensity pattern in resonant X-ray scattering for identifying hexadecapole orders.

Abstract

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 $\Gamma_3$-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.