Construction of a Microscopic Model for Yb and Tm Compounds on the Basis of a $\mib{j}$-$\mib{j}$ Coupling Scheme
arXiv:1004.4707 · doi:10.1143/JPSJ.79.094705
Abstract
We provide a prescription to construct a microscopic model for heavy lanthanide systems such as Yb and Tm compounds by exploiting a - coupling scheme. Here we consider a situation with a large spin-orbit coupling, in which =5/2 sextet is fully occupied, while =7/2 octet is partially occupied, where denotes total angular momentum. We evaluate crystalline electric field potentials and Coulomb interactions among the states of the =7/2 octet to construct a local Hamiltonian in the - coupling scheme. Then, it is found that the local -electron states composed of the =7/2 octet agree quite well with those of seven orbitals even for a realistic value of the spin-orbit coupling. As an example of the application of the present model, we discuss low-temperature multipole states of Yb- and Tm-based filled skutterudites by analyzing multipole susceptibility of the Anderson model in the - coupling scheme with the use of a numerical renormalization group technique. From the comparison with the numerical results of the seven-orbital Anderson model, it is concluded that the multipole state is also well reproduced by the - coupling model, even when we include the hybridization between conduction and electrons for the realistic value of the spin-orbit coupling. Finally, we briefly discuss future applications of the present prescription for theoretical research on heavy lanthanide compounds.
12 pages, 8 figures.
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