Diffraction from Ordered States of Higher Multipoles

TL;DR

This paper discusses methods to identify higher multipole electronic orders, like octupoles and hexadecapoles, using resonant X-ray scattering and azimuthal angle dependence, with specific case studies and predictions.

Contribution

It introduces resonant X-ray scattering techniques for detecting higher multipole orders and interprets experimental data for specific compounds, proposing new identification methods.

Findings

Azimuthal angle dependence indicates antiferro-octupole order in Ce$_{0.7}$La$_{0.3}$B$_6$.

Predicted eightfold azimuthal pattern for hexadecapole order in PrRu$_4$P$_{12}$.

Hexadecapole contributions can be identified via non-resonant Bragg scattering due to absence of quadrupole components.

Abstract

Possible ways of identification are discussed of an electronic order of higher multipoles such as octupoles and hexadecapoles. A particularly powerful method is resonant X-ray scattering (RXS) using quadrupolar resonance processes called E2.The characteristic azimuthal angle dependence of Ce$_{0.7}$La$_{0.3}$B$_6$ is interpreted as evidence of antiferro-octupole order. For PrRu$_4$P$_{12}$, eightfold pattern against azimuthal angle is predicted if its metal-insulator transition is a consequence of a hexadecapole order. In non-resonant superlattice Bragg scattering, hexadecapole contribution may also be identified because of absence of quadrupole component.