Spontaneous spin polarization in doped semiconductor quantum wells

We calculate the critical density of the zero-temperature, first-order ferromagnetic phase transition in n-doped GaAs/AlGaAs quantum wells. We predict that this transition could be observed in narrow quantum wells at electron densities somewhat lower than the ones that have been considered experimentally thus far, and that there exists an upper limit for the well width beyond which there would be no transition as long as only one subband is populated. Our calculations are done within 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 strictly two-dimensional electron gas.