Zener, Mean-Field, and Ab Initio Treatments

Another simple model [77] has been put forth to explain the possible mechanism with specific attention to (Ga,Mn)As. In this model, holes are assumed to hop only between Mn acceptor sites, where they interact with the Mn moments via phenomenological exchange interactions. In some other models [27], the ferromagnetic correlation mediated by holes originating from shallow acceptors in the ensemble of localized spins and a concentration of free holes (w3.5 x 10 /cm ) have been assumed for (Ga,Mn)As. 

With due reverence and deference to the models mentioned above, it is increasingly becoming clear that a true picture can only be obtained by performing first principles calculations. For example, it is stated that the mean-field theory overestimates the critical temperature substantially when the magnetic ion density is small. It has also become dear that in Mn-doped GaN magnetic ion concentration has a profound effect on the way the levels spUt and whether the ferromagnetic or antiferromagnetic state is stable. 

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