Multipolar interactions in the Anderson lattice with orbital degeneracy

Microscopic investigation is performed for intersite multipolar interactions in the orbitally degenerate Anderson lattice, with CeB₆ taken as an exemplary target. In addition to the f⁰ intermediate state, f² Hund's-rule ground states are included as intermediate states for the interactions. The conduction-band states are taken as plane waves and the hybridization as spherically symmetric. The spatial dependences of multipolar interactions are given by the relative weight of partial wave components along the pair of sites. It is clarified how the the anisotropy arises in the interactions depending on the orbital degeneracy and the spatial configuration. The stability of the Γ₅ antiferro-quadrupole order in the phase II of CeB₆ is consistent with our model. Moreover, the pseudo-dipole interactions follow a tendency required by the phenomenological model for the phase III.