Revealing the nature of antiferro-quadrupolar ordering in Cerium Hexaboride: CeB${}_6$

Abstract

Cerium-hexaboride (CeB${}_6$) f-electron compound displays a rich array of low-temperature magnetic phenomena, including `magnetically hidden' order, identified as multipolar in origin via advanced x-ray scattering. From first-principles electronic-structure results, we find that the \emph{antiferro-quadrupolar} (AFQ) ordering in CeB${}_6$ arises from crystal-field splitting and yields band structure in agreement with experiments. With interactions of $p$-electrons between Ce and B${}_6$ being small, the electronic state of CeB${}_6$ is suitably described as Ce(4$f^1$)${}^{3+}$(e${}^{-}$)(B${}_6$)${}^{2-}$. The AFQ state of orbital spins is caused by an exchange interaction induced through spin-orbit interaction, which also splits J=5/2 state into ${\Gamma }_8$ ground state and ${\Gamma }_7$ excited state. Within the smallest antiferromagnetic (111) configuration, an orbital-ordered AFQ state appears during charge self-consistency, and supports the appearance of `hidden' order. Hydrostatic pressure (either applied or chemically induced) stabilizes the AFM (AFQ) states over a ferromagnetic one, as observed at low temperatures.

arXiv comment6 pages, 4 figures

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