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The invariant form of the hyperfine interaction between multipolar momentsand the nuclear spin is derived, and applied to discuss possibilities toidentify the antiferro-octupolar (AFO) moments by NMR experiments. The orderedphase of NpO$_{2}$ and the phase IV of Ce$_{1-x}$La$_{x}$B$_{6}$ are studied indetail. Recent $^{17}$O NMR for polycrystalline samples of NpO$_{2}$ arediscussed theoretically from our formulation. The observed feature of thesplitting of $^{17}$O NMR spectrum into a sharp line and a broad line, theirintensity ratio, and the magnetic field dependence of the shift and of thewidth can be consistently explained on the basis of the triple $\bq$ AFOordering model proposed by Paix\~{a}o {\it et. al.} Thus, the present theoryshows that the $^{17}$O NMR spectrum gives a strong support to the model. The 4O 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 turnsout that the hyperfine field due to the antiferro-dipole and AFO momentsinduced by the magnetic field, and the quadrupolar field at non-cubic sites arekey ingredients to understand the observed spectrum. The controversial problemof the nature of phase IV in Ce$_{1-x}$La$_{x}$B$_{6}$ is also studied. It ispointed 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 isrealized in Ce$_{1-x}$La$_{x}$B$_{6}$. Namely, the hyperfine splitting of a Batom 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.Comment: 22 pages, 2 figure

journal of the physical society of japan

Invariant Form of Hyperfine Interaction with Multipolar Moments – Observation of Octupolar Moments in NpO2 and Ce1-xLaxB6 by NMR –