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We provide a prescription to construct a microscopic model for heavylanthanide systems such as Yb and Tm compounds by exploiting a $j$-$j$ couplingscheme. Here we consider a situation with a large spin-orbit coupling, in which$j$=5/2 sextet is fully occupied, while $j$=7/2 octet is partially occupied,where $j$ denotes total angular momentum. We evaluate crystalline electricfield potentials and Coulomb interactions among the states of the $j$=7/2 octetto construct a local Hamiltonian in the $j$-$j$ coupling scheme. Then, it isfound that the local $f$-electron states composed of the $j$=7/2 octet agreequite well with those of seven $f$ orbitals even for a realistic value of thespin-orbit coupling. As an example of the application of the present model, wediscuss low-temperature multipole states of Yb- and Tm-based filledskutterudites by analyzing multipole susceptibility of the Anderson model inthe $j$-$j$ coupling scheme with the use of a numerical renormalization grouptechnique. From the comparison with the numerical results of the seven-orbitalAnderson model, it is concluded that the multipole state is also wellreproduced by the $j$-$j$ coupling model, even when we include thehybridization between conduction and $f$ electrons for the realistic value ofthe spin-orbit coupling. Finally, we briefly discuss future applications of thepresent prescription for theoretical research on heavy lanthanide compounds.

Construction of a Microscopic Model for Yb and Tm Compounds on the Basis of a $\mib{j}$-$\mib{j}$ Coupling Scheme