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$_6$.

Highlights

  • We examine the RKKY interactions of CeB6 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

  • The RKKY couplings K OΓ (q) for several multipole moments as a function of the wavevector q along the high symmetry line in the Brillouin zone (BZ) are plotted as shown in Fig. 2, where the positive coupling for a certain multipole with (OΓ, q) enhances the corresponding multipole fluctuation and its positive maximum value gives a leading multipole ordering mode

  • The couplings of the Γ5g quadrupole O xy and Γ2u ocutupole T xyz for q = (π, π, π) become largest among all moments and q, which corresponds to the AFQ ordering of CeB6 as phase II

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Summary

Takemi Yamada and Katsurou Hanzawa

We examine the RKKY interactions of CeB6 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 Γ8 subspace Both of the Γ5g quadrupole O xy and the Γ2u octupole T xyz couplings are largely enhanced with q = (π, π, π) which naturally explains the antiferro-quadrupolar phase of the phase II, and are enhanced with q = (0, 0, 0) corresponding to the elastic softening of C44.

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