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 Gamma(-)(67) quartet ground state, while the low-temperature phase is governed by magnetic fluctuations for Gamma(-)(5) doublet ground state. When we include the coupling between f electrons in degenerate Gamma(-)(67) (e(u)) orbitals and Jahn-Teller phonons with E-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.