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Some of the highest transition temperatures achieved for Mn-doped GaAs havebeen in delta-doped heterostructures with well-separated planes of Mn. But inthe absence of magnetic anisotropy, the Mermin-Wagner theorem implies that asingle plane of magnetic ions cannot be ferromagnetic. Using a Heisenbergmodel, we show that the same mechanism that produces magnetic frustration andsuppresses the transition temperature in bulk Mn-doped GaAs, due to thedifference between the light and heavy band masses, can stabilize ferromagneticorder for a single layer of Mn in a GaAs quantum well. This comes at the priceof quantum fluctuations that suppress the ordered moment from that of a fullysaturated ferromagnet. By comparing the predictions of Heisenberg andKohn-Luttinger models, we conclude that the Heisenberg description of aMn-doped GaAs quantum well breaks down when the Mn concentration becomes large,but works quite well in the weak-coupling limit of small Mn concentrations.This comparison allows us to estimate the size of the quantum fluctuations inthe quantum well.Comment: 7 pages, 3 figures: to appear in PR

Single layer of Mn in a GaAs quantum well: A ferromagnet with quantum fluctuations