Nuclear Magnetic Resonance ofB11at the Three Boron Sites in Rare-Earth Tetraborides

An experimental study has been made of the ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ Knight shift at the three different crystallographic boron sites in polycrystalline Nd${\mathrm{B}}_4$. The three central transitions strongly overlap and cannot be analyzed, but it was possible to derive three different Knight shifts [+0.33(3), +0.26(4), and +0.23(3)% at 77 K for the sites $4e$, $8j$, and $4h$, respectively, uncorrected for pseudocontact and demagnetization fields] from the satellites, which are separated from each other by their different quadrupole interactions [${\nu }_Q=420\mathrm{}\left(6\right)\mathrm{}$ kHz and $\eta =0\mathrm{}$ for site $4e$, ${\nu }_Q=443\mathrm{}\left(10\right)\mathrm{}$ kHz and $\eta =0.51\mathrm{}\left(2\right)\mathrm{}$ for site $8j$, and ${\nu }_Q=622\mathrm{}\left(6\right)\mathrm{}$ kHz and $\eta <0.05\mathrm{}$ for site $4h$, at both 296 and 77 K]. A detailed account is given of the method of extracting the various shift and quadrupole parameters from the powder satellite spectra. We first analyzed La${\mathrm{B}}_4$, in which the shifts are zero (±0.02%) with respect to ${\mathrm{Na}}_2$ ${\mathrm{B}}_2$ ${\mathrm{O}}_4$ and in which the quadrupole interactions are ${\nu }_Q=343\mathrm{}\left(4\right)\mathrm{}$ kHz and $\eta =0\mathrm{}$ for $4e$, ${\nu }_Q=412\mathrm{}\left(4\right)\mathrm{}$ kHz and $\eta =0.53\mathrm{}\left(1\right)\mathrm{}$ for $8j$, and ${\nu }_Q=544\mathrm{}\left(4\right)\mathrm{}$ kHz and $\eta =0.045\mathrm{}\left(20\right)\mathrm{}$ for $4h$ (4-300 K). In Nd${\mathrm{B}}_4$, relatively large anisotropic contributions to the shifts are found to originate mainly from dipolar fields due to the rare-earth magnetic moments. After correction for pseudocontact shifts, the isotropic hyperfine fields at boron per unit spin $S$ are about -2 kG. Preliminary measurements on Gd${\mathrm{B}}_4$ and Ho${\mathrm{B}}_4$ give the same sign for this field. An attempt is made to fit the observed isotropic shifts in Nd