Ab initio Derivation of Low-Energy Model for Alkali-Cluster-Loaded Sodalites

An effective low-energy model describing magnetic properties of alkali-cluster-loaded sodalites is derived by {\em ab initio} downfolding. We start with constructing an extended Hubbard model for maximally localized Wannier functions. {\em Ab initio} screened Coulomb and exchange interactions are calculated by constrained random phase approximation. We find that the system resides in the strong coupling regime and thus the Heisenberg model is derived as a low-energy model of the extended Hubbard model. We obtain antiferromagnetic couplings $\sim$ $O$(10 K), being consistent with the experimental temperature dependence of the spin susceptibility. Importance of considering the screening effect in the derivation of the extended Hubbard model is discussed.