Spin Susceptibility of an Ultra-Low Density Two Dimensional Electron System

We determine the spin susceptibility in a two dimensional electron system in GaAs/AlGaAs over a wide range of low densities from 2$\times10^{9}$cm$^{-2}$ to 4$\times10^{10}$cm$^{-2}$. Our data can be fitted to an equation that describes the density dependence as well as the polarization dependence of the spin susceptibility. It can account for the anomalous g-factors reported recently in GaAs electron and hole systems. The paramagnetic spin susceptibility increases with decreasing density as expected from theoretical calculations.