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

TL;DR

This paper investigates the antiferro-quadrupolar ordering in CeB$_6$, revealing its origin from crystal-field effects and spin-orbit interactions, and demonstrating how pressure stabilizes different magnetic states.

Contribution

The study provides a first-principles electronic-structure explanation for AFQ order in CeB$_6$, linking it to crystal-field splitting and spin-orbit interactions, and clarifies the role of pressure in stabilizing magnetic phases.

Findings

AFQ order arises from crystal-field splitting and spin-orbit interactions.

Electronic structure of CeB$_6$ matches experimental observations.

Hydrostatic pressure stabilizes AFQ and AFM states over ferromagnetic states.

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.