Multipolar Interactions in the Anderson Lattice with Orbital Degeneracy

TL;DR

This paper investigates the microscopic origins of multipolar interactions in the orbitally degenerate Anderson lattice, specifically in CeB$_6$, revealing how orbital degeneracy and spatial configuration influence anisotropic interactions and phase stability.

Contribution

It introduces a detailed model including $f^0$ and $f^2$ intermediate states, elucidating the anisotropy and stability of multipolar orders in CeB$_6$.

Findings

Consistent explanation of the $ ext{Gamma}_5$ antiferro-quadrupole order in CeB$_6$

Reproduction of pseudo-dipole interactions aligning with phenomenological models

Clarification of how orbital degeneracy affects interaction anisotropy

Abstract

Microscopic investigation is performed for intersite multipolar interactions in the orbitally degenerate Anderson lattice, with CeB$_6$ taken as an exemplary target. In addition to the $f^0$ intermediate state, $f^2$ 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 $\Gamma_5$ antiferro-quadrupole order in the phase II of CeB$_6$ is consistent with our model. Moreover, the pseudo-dipole interactions follow a tendency required by the phenomenological model for the phase III.