Wavenumber dependence of multipolar interactions in the Anderson lattice

Multipolar interactions are derived in the orbitally degenerate Anderson lattice with a spherical Fermi surface and one conduction electron per unit cell of the simple cubic lattice. As the crystalline-electric-field (CEF) ground state of f¹ configuration, the four-fold degenerate Γ₈ is mainly studied. Intersite interactions up to a sufficiently distant pair are Fourier transformed to the wavenumber space. For the Γ₈ case, quadrupolar and octupolar interactions favor the staggered order with q = (1/2, 1/2, 1/2), while the dipolar interaction favors an incommensurate magnetic structure with a long modulation period.The latter is due to a Kohn anomaly which is found to be sharply peaked for interaction channels with large angular momenta. Implications of results are discussed for multipole orders in CeB₆, and the incommensurate magnetic structure in a quasi-cubic system CeB₂C₂.