RKKY interactions of CeB6 based on effective Wannier model

TL;DR

This paper investigates the RKKY interactions in CeB$_6$ using an effective Wannier model, revealing enhanced multipole couplings that explain various antiferro-ordered phases.

Contribution

It introduces a detailed Wannier-based approach to calculate multipole RKKY interactions in CeB$_6$, linking microscopic electronic structure to complex magnetic and quadrupolar orderings.

Findings

Enhanced $m{q}=( ext{pi}, ext{pi}, ext{pi})$ couplings explain antiferro-quadrupolar phase II.

Couplings at $m{q}=(0,0,0)$ relate to elastic softening of $C_{44}$.

Large $m{q}=(0,0, ext{pi})$ couplings suggest possible antiferro-octupolar order in phase IV.

Abstract

We examine the RKKY interactions of CeB$_6$ between multipole moments based on the effective Wannier model obtained from the bandstructure calculation including 14 Ce-$f$ orbitals and 60 conduction orbitals of Ce-$d,s$ and B-$p,s$. By using the $f$-$c$ mixing matrix elements of the Wannier model together with the conduction band dispersion, the multipole couplings with the RKKY oscillation are obtained for the active moments in $\Gamma_{8}$ subspace. Both of the $\Gamma_{5g}$ quadrupole $O_{xy}$ and the $\Gamma_{2u}$ octupole $T_{xyz}$ couplings are largely enhanced with $\bm{q}=(\pi,\pi,\pi)$ which naturally explains the antiferro-quadrupolar phase of the phase II, and are also enhanced with $\bm{q}=(0,0,0)$ corresponding to the elastic softening of $C_{44}$. Also the couplings of the $\Gamma_{5u}$ octupole $T_{z}^{\beta}$ is quite large for $\bm{q}=(0,0,\pi)$ which is related to the antiferro-octupolar ordering of a possible candidate for the phase IV of Ce$_{x}$La$_{1-x}$B$_6$.