Multipolar Interaction Derived from d--f Hybridization in Pr-Based Filled Skutterudite Compounds

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The conduction bands of the skutterudite compounds are composed of p orbitals of the pnictogen cages and d orbitals of the transition metal ions. In this paper, we address the effect of hybridization between the d bands and localized 4f states in relation with ordering and fluctuation of multipole moments in Pr-based filled skutterudites. First, we study the properties of a non-degenerate d band around the zone center in the framework of a tight-binding band model. Introducing a realistic form of the d--f hybridization, we show that the a_{g} band can be hybridized only with the \Gamma_{8} orbitals of f electrons. Then, we derive d--f multipolar interactions from the hybridization in the localized limit of f electrons in which the basis states are restricted to the singlet--triplet crystal field states. It is found that the quadrupolar interaction of the O_{xy}-type becomes predominant in the case of the singlet ground state, whereas the triplet ground state apparently favors the magnetic interaction. The relationship with experimental results in the Pr skutterudites, especially in PrOs4Sb12 and PrFe4As12, is discussed in view of the nature of quadrupolar and magnetic interactions. It is shown that the complex non-collinear magnetic structure of Fe ions observed in the latter material is reproduced well by the effective d--f interaction.
2012-02-15