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$_6$.
تحميل البحث