Systematics of the Hyperfine and Exchange Interactions in the Chromium Chalcogenide Spinels

The NMR of nuclei at each site in the cadmium and mercury chromium chalcogenide spinels has been studied at 1.4°K. Experimentally, we find an approximately linear relation between the isotropic hyperfine field of ${}_{}{}^{53}{}_{}{}^{}\mathrm{Cr}$ nuclei and the near-neighbor chromium-chromium exchange constants. This observation is interpreted in terms of a systematic variation in covalency and constant overalp for these compounds. The ${}_{}{}^{77}{}_{}{}^{}\mathrm{Se}$ isotropic hyperfine field is large and oppositely directed to the magnetization. This field can be understood in terms of a spin polarization of Se $s$ orbitals by the unpaired Cr spins. The Cr and Se results are consistent with a theoretical formulation due to Huang and Orbach. The ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$, ${}_{}{}^{201}{}_{}{}^{}\mathrm{Hg}$, ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$, and ${}_{}{}^{113}{}_{}{}^{}\mathrm{Cd}$ hyperfine fields are found to be isotropic, large, and positive with respect to the magnetization. These fields are shown to be mainly due to overlap of unfilled outer $s$ shells of these nonmagnetic ions with the Cr $3d$ orbits.