  We calculate the critical density of the zero-temperature, first-order
ferromagnetic phase transition in n-doped GaAs/AlGaAs quantum wells. We find
that the existence of the ferromagnetic transition is dependent upon the choice
of well width. We demonstrate rigorously that this dependence is governed by
the interplay between different components of the exchange interaction and that
there exists an upper limit for the well width beyond which there is no
transition. We predict that some narrow quantum wells could exhibit this
transition at electron densities lower than the ones that have been considered
experimentally thus far. We use a screened Hartree-Fock approximation with a
polarization-dependent effective mass, which is adjusted to match the critical
density predicted by Monte Carlo calculations for the two-dimensional electron
gas.
