Measuring the magnetic-field-dependent chemical potential of a low-density three-dimensional electron gas inn-GaAs and extracting its magnetic susceptibility

We report the magnetic-field-dependent shift of the electron chemical potential in bulk, $n$-type GaAs at room temperature. A transient voltage of $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{V}$ was measured across a Au-${\mathrm{Al}}₂{\mathrm{O}}₃$-GaAs metal-oxide-semiconductor capacitor in a pulsed magnetic field of $\ensuremath{\sim}6\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. Several spurious voltages larger than the signal that had plagued earlier researchers performing similar experiments were carefully eliminated. The itinerant magnetic susceptibility of GaAs is extracted from the experimentally measured data for four different doping densities, including one as low as $5\ifmmode\times\else\texttimes\fi{}{10}¹⁵\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. Though the susceptibility in GaAs is dominated by Landau-Peierls diamagnetism, the experimental technique demonstrated can be a powerful tool for extracting the total free carrier magnetization of any electron system. The method is also virtually independent of the carrier concentration and is expected to work better in the nondegenerate limit. Such experiments had been successfully performed in two-dimensional electron gases at cryogenic temperatures. However, an unambiguous report on having observed this effect in any three-dimensional electron gas has been lacking. We highlight the 50 year old literature of various trials and discuss the key details of our experiment that were essential for its success. The technique can be used to unambiguously yield only the itinerant part of the magnetic susceptibility of complex materials such as magnetic semiconductors and hexaborides, and thus shed light on the origin of ferromagnetism in such systems.