Invariant Form of Hyperfine Interaction with Multipolar Moments - Observation of Octupolar Moments in NpO$_{2}$ and CeB$_{6}$ by NMR -

TL;DR

This paper derives an invariant hyperfine interaction form for multipolar moments, applying it to identify octupolar order in NpO₂ and CeB₆ via NMR, providing theoretical explanations for experimental spectral features and phase nature.

Contribution

It introduces a new theoretical framework for hyperfine interactions with multipolar moments, aiding the identification of octupolar order through NMR spectra analysis.

Findings

NMR spectral features support triple q AFO ordering in NpO₂.

Hyperfine fields explain observed NMR spectrum splitting.

Unique NMR signature indicates specific AFO order in CeB₆.

Abstract

The invariant form of the hyperfine interaction between multipolar moments and the nuclear spin is derived, and applied to discuss possibilities to identify the antiferro-octupolar (AFO) moments by NMR experiments. The ordered phase of NpO$_{2}$ and the phase IV of Ce$_{1-x}$La$_{x}$B$_{6}$ are studied in detail. Recent $^{17}$O NMR for polycrystalline samples of NpO$_{2}$ are discussed theoretically from our formulation. The observed feature of the splitting of $^{17}$O NMR spectrum into a sharp line and a broad line, their intensity ratio, and the magnetic field dependence of the shift and of the width can be consistently explained on the basis of the triple $\bq$ AFO ordering model proposed by Paix\~{a}o {\it et. al.} Thus, the present theory shows that the $^{17}$O NMR spectrum gives a strong support to the model. The 4 O sites in the fcc NpO$_2$ become inequivalent due to the secondary triple $\bq$ ordering of AF-quadrupoles: one cubic and three non-cubic sites. It turns out that the hyperfine field due to the antiferro-dipole and AFO moments induced by the magnetic field, and the quadrupolar field at non-cubic sites are key ingredients to understand the observed spectrum. The controversial problem of the nature of phase IV in Ce$_{1-x}$La$_{x}$B$_{6}$ is also studied. It is pointed out that there is a unique feature in the NMR spectra, if the $\Gamma_{5}$($T^{\beta}_{x}=T^{\beta}_{y}=T^{\beta}_{z}$) AFO ordering is realized in Ce$_{1-x}$La$_{x}$B$_{6}$. Namely, the hyperfine splitting of a B atom pair on the $({1/2},{1/2},\pm u)$ sites crosses zero on the $(1\bar{1}0)$ plane when the magnetic field is rotated around the $[001]$ axis.