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It is shown that $f$-electron multipole is naturally defined as spin-chargeone-electron density operator in the second-quantized form with the use oftensor operator on the analogy of multipole expansion of electromagneticpotential from charge distribution in electromagnetism. Due to this definitionof multipole, it is possible to determine multipole state from a microscopicviewpoint on the basis of the standard linear response theory for multipolesusceptibility. In order to discuss multipole properties of filledskutterudites, we analyze a seven-orbital impurity Anderson model by employinga numerical renormalization group method. We show our results on possiblemultipole states of filled skutterudite compounds.

Multipole as $f$-Electron Spin-Charge Density in Filled Skutterudites