Multipole Susceptibility of Multiorbital Anderson Model Coupled with Jahn-Teller Phonons

In order to clarify possible multipole states of Sm-based filled skutterudite compounds, we investigate multipole susceptibility of a multiorbital Anderson model dynamically coupled with Jahn-Teller phonons by using a numerical renormalization group method. Here we take a procedure to maximize the multipole susceptibility matrix to determine the multipole state. When the electron-phonon coupling term is simply ignored, it is found that the dominant multipole state is characterized by 2u octupole for the ${\mathrm{\Gamma }}_{67}^{-}$ quartet ground state, while the low-temperature phase is governed by magnetic fluctuations for the ${\mathrm{\Gamma }}_5^{-}$ doublet ground state. When we include the coupling between $f$ electrons in degenerate ${\mathrm{\Gamma }}_{67}^{-}$ ($e_{\mathrm{u}}$) orbitals and Jahn-Teller phonons with $E_{\mathrm{g}}$ symmetry, the mixed multipole state with 4u magnetic and 5u octupole moments is found to be dominant with significant 3g quadrupole fluctuations at low temperatures.