Spin Polarization and $\mathit{g}$ Factor of a Dilute GaAs Two-Dimensional Electron System

The effective $g$ factor $\left(g^{*}\right)$ of a dilute interacting two-dimensional electron system is expected to increase with respect to its bare value as the density is lowered, and to eventually diverge as the system makes a transition to a ferromagnetic state. We report here measurements of $g^{*}$ in dilute (density 0.8 to $6.5\times {10}^{10}{\mathrm{cm}}^{-2\mathrm{}}$), high-mobility GaAs two-dimensional electrons from their spin polarization in a parallel magnetic field. The data reveal a surprising trend. While $g^{*}$ is indeed significantly enhanced with respect to the band $g$ factor of GaAs, the enhancement factor decreases from about 6 to 3 as the density is reduced.