Nuclear spin-lattice relaxation inn-type insulating and metallic GaAs single crystals

Abstract

The coupling of electron and nuclear spins in $n\text{\ensuremath{-}}\mathrm{Ga}\mathrm{As}$ changes significantly as the donor concentration $n$ increases through the insulator-metal critical concentration ${n}_{\mathrm{C}}\ensuremath{\sim}1.2\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The present measurements of the $^{71}\mathrm{Ga}$ relaxation rates $W$ made as a function of magnetic field $(1--13\phantom{\rule{0.3em}{0ex}}\mathrm{T})$ and temperature $(1.5--300\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ for semi-insulating GaAs and for three doped $n\text{\ensuremath{-}}\mathrm{Ga}\mathrm{As}$ samples with donor concentrations $n=5.9\ifmmode\times\else\texttimes\fi{}{10}^{15}$, $7\ifmmode\times\else\texttimes\fi{}{10}^{16}$, and $2\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, show marked changes in the relaxation behavior with $n$. Korringa-like relaxation is found in both metallic samples for $T<30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, while for $T>30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ phonon-induced nuclear quadrupolar relaxation is dominant. The relaxation rate measurements permit determination of the electron probability density at $^{71}\mathrm{Ga}$ sites. A small Knight shift of $\ensuremath{-}3.3\phantom{\rule{0.3em}{0ex}}\mathrm{ppm}$ was measured on the most metallic $(2\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$ sample using magic-angle spinning at room temperature. For the $n=5.9\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ sample, a nuclear relaxation model involving the Fermi contact hyperfine interaction, rapid spin diffusion, and exchange coupled local moments is proposed. While the relaxation rate behavior with temperature for the weakly metallic sample, $n=7\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, is similar to that found for the just-insulating sample, the magnetic field dependence is quite different. For the $5.9\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ sample, increasing the magnetic field leads to a decrease in the relaxation rate, while for the $7\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ sample this results in an increase in the relaxation rate ascribed to an increase in the density of states at the Fermi level as the Landau level degeneracy is increased.