  Two-dimensional (2D) electrons in an in-plane magnetic field become fully
spin polarized above a field B_P, which we can determine from the in-plane
magnetoresistance. We perform such measurements in modulation-doped AlAs
electron systems, and find that the field B_P increases approximately linearly
with 2D electron density. These results imply that the product |g*|m*, where g*
is the effective g-factor and m* the effective mass, is a constant essentially
independent of density. While the deduced |g*|m* is enhanced relative to its
band value by a factor of ~ 4, we see no indication of its divergence as 2D
density approaches zero. These observations are at odds with results obtained
in Si-MOSFETs, but qualitatively confirm spin polarization studies of 2D GaAs
carriers.
