Magnetic fluctuations of filled skutterudites emerging in the transition region between singlet and triplet states

In order to clarify magnetic properties of filled skutterudites, we investigate the Anderson model including seven $f$ orbitals hybridized with $a_{\rm u}$ conduction band. By using the numerical renormalization group method, we evaluate magnetic susceptibility and entropy of $f$ electron for $n$=1$\sim$13, where $n$ is local $f$-electron number. Then, we find that $f$-electron states are clearly distinguished as itinerant $\Gamma_7$ and localized $\Gamma_8$ in the filled skutterudite structure. For $n$=2 corresponding to Pr-based filled skutterudites, even if the ground state is $\Gamma_1$ singlet, there remain significant magnetic fluctuations from $\Gamma_4^{(2)}$ triplet state with small excitation energy. We envision a scenario that unconventional superconductivity is induced by such magnetic fluctuations in a limited region in which singlet and triplet states are interchanged.