Electrically induced shifts of the GaAs nuclear spin levels

The application of a dc homogeneous electric field in a GaAs crystal will induce a quadrupolar splitting of the nuclear-spin levels. This splitting has been observed for ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$, ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$, and ${}_{}{}^{75}{}_{}{}^{}\mathrm{As}$ using a pulsed NMR spectrometer. A constant ($R_{14}$) that relates the coupling between the induced field gradient and the applied electric field has been measured. The values found were $R_{14}\left(\mathrm{Ga}\right)=2.85\mathrm{}\times {10}^{10}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $R_{14}\left(\mathrm{As}\right)=3.16\mathrm{}\times {10}^{10}$ ${\mathrm{cm}}^{-1\mathrm{}}$. These results are in disagreement with those from a similar experiment reported by Gill and Bloembergen. The measured values of $R_{14}$ were found to be independent of the applied electric field strength. The two-electron bond-orbital model developed by Huang, Moriarty, Sher, and Breckenridge has been used to interpret the experimental measurements. In evaluating the theory, a Hartree-Fock atomic $s{p}^3$ hybrid wave-function basis set is used to find the induced field gradient caused by the electrostatic distortion of the bond. With no adjustable parameters, the value of $R_{14}\left(\mathrm{As}\right)$ calculated from the theory is smaller than the experimental number by a factor of 1.4, while the calculated $R_{14}\left(\mathrm{Ga}\right)$ is a factor of 4 too small.