  The magnetoresistance of a low carrier density, disordered GaAs based
two-dimensional (2D) electron gas has been measured in parallel magnetic fields
up to 32 T. The feature in the resistance associated with the complete spin
polarization of the carriers shifts down by more than 20 T as the electron
density is reduced, consistent with recent theories taking into account the
enhancement of the electron-electron interactions at low densities.
Nevertheless, the magnetic field for complete polarization, Bp, remains 2-3
times smaller than predicted for a disorder free system. We show, in particular
by studying the temperature dependance of Bp to probe the effective size of the
Fermi sea, that localization plays an important role in determining the spin
polarization of a 2D electron gas.
