Theory of Coupled Multipole Moments Probed by X-ray Scattering in CeB$_6$

TL;DR

This paper presents a theoretical model explaining X-ray scattering observations in CeB$_6$, highlighting the effects of multipole order degeneracy, spin-orbit coupling, and surface orientation on reflection intensities.

Contribution

It introduces a minimal model for multipole orders in CeB$_6$ that accounts for temperature, magnetic field dependence, and surface effects observed in experiments.

Findings

X-ray reflection intensity depends on temperature, magnetic field, and surface orientation.

Degeneracy and spin-orbit coupling cause peculiar temperature and field dependences.

Prediction of non-monotonic intensity change under weak magnetic fields perpendicular to (111) surface.

Abstract

A minimal model for multipole orders in CeB$_6$ shows that degeneracy of the quadrupole order parameters and strong spin-orbit coupling lead to peculiar temperature and magnetic-field dependences of the X-ray reflection intensity at superlattice Bragg points. Furthermore, the intensity depends sensitively on the surface direction. These theoretical results explain naturally recent X-ray experiments in phases II and III of CeB$_6$. It is predicted that under weak magnetic field perpendicular to the (111) surface, the reflection intensity should change non-monotonically as a function of temperature.