Wavenumber Dependence of Multipolar Interactions in the Anderson Lattice

TL;DR

This paper investigates how multipolar interactions in the Anderson lattice depend on wavenumber, revealing favored ordering patterns and anomalies that influence magnetic and multipole structures in specific materials.

Contribution

It provides a detailed analysis of the wavenumber dependence of multipolar interactions in the Anderson lattice, especially for the $ ext{CeB}_6$ and related compounds, highlighting the role of Kohn anomalies.

Findings

Quadrupolar and octupolar interactions favor staggered order at q=(1/2,1/2,1/2)

Dipolar interactions favor incommensurate magnetic structures due to Kohn anomalies

Implications for multipole orders in CeB$_6$ and magnetic structures in CeB$_2$C$_2$

Abstract

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 $f^1$ configuration, the four-fold degenerate $\Gamma_8$ is mainly studied. Intersite interactions up to a sufficiently distant pair are Fourier transformed to the wavenumber space. For the $\Gamma_8$ case, quadrupolar and octupolar interactions favor the staggered order with $\mib{q} = (1/2,1/2,1/2)$, 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 CeB$_6$, and the incommensurate magnetic structure in a quasi-cubic system CeB$_2$C$_2$.