Invariant Form of Hyperfine Interaction with Multipolar Moments - Observation of Octupolar Moments in NpO${}_2$ and CeB${}_6$ by NMR -

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 Paixão {\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 ${\Gamma }_5$($T_x^{\beta }=T_y^{\beta }=T_z^{\beta }$) 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.

22 pages, 2 figures