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We consider quasi-two-dimensional gas of electrons in a typical Si-MOSFET,assuming repulsive contact interaction between electrons. Magnetisation andsusceptibility are evaluated within the mean-field approach. Finite thicknessof the inversion layer results in an interaction-induced electron wave functionchange, not found in both purely two-dimensional and three-dimensional (bulk)cases. Taking this self-consistent change into account leads to an increasedsusceptibility and ultimately to a ferromagnetic transition deep in thehigh-density metallic regime. We further find that in the paramagnetic state,magnetisation increases sublinearly with increasing in-plane magnetic field. Inthe opposite limit of low carrier densities, the effects of long-rangeinteraction become important and can be included phenomenologically viabandwidth renormalisation. Our treatment then suggests that with decreasingdensity, the metal-insulator transition is preceded by a ferromagneticinstability. Results are discussed in the context of the available experimentaldata, and arguments for the validity of our mean-field scheme are presented.

Stoner-type theory of Magnetism in Silicon MOSFETs