Octupole Ordering Model for the Phase IV of CexLa1-xB6

TL;DR

This paper proposes an octupole ordering model for phase IV of CexLa1-xB6, explaining lattice distortion, elastic constant softening, and magnetic properties using mean field theory, with some discrepancies in internal magnetic field magnitude.

Contribution

It introduces a novel octupole ordering model for CexLa1-xB6's phase IV, linking lattice distortion and magnetic phenomena to octupole moments with b3_{5u} symmetry.

Findings

The model explains lattice distortion along [111] direction.

It accounts for the cusp in magnetization and elastic constant softening.

The internal magnetic field from octupoles is smaller than observed.

Abstract

An octupole ordering model is studied by the mean field theory, and its relevance to the phase IV of CexLa1-xB6 is discussed. The observed lattice distortion along the [111] direction is interpreted in terms of the \Gamma_{5g}-type ferro-quadrupole moment induced by an antiferro-octupole ordered state with \Gamma_{5u} symmetry. The octupole model also accounts for the cusp in the magnetization as in the N\'{e}el transition, and the softening of the elastic constant C_{44} below the ordering temperature. However, the internal magnetic field due to the octupole moment is smaller than the observed one by an order of magnitude. Also discussed is the possibility of a pressure induced antiferromagnetic moment in the octupole-ordered state.