Ferromagnetism in disordered, low carrier density systems without magnetic ions
Ravin N. Bhatt
Department of Electrical Engineering and Princeton Center for Theoretical Physics Princeton University, Princeton, NJ 08544, USA
Ferromagnetism is believed to occur in several “single-band” models of electronic systems with low density of mobile carriers – from the electron gas, to Hubbard models near half filling in the large U limit. In real electronic materials, effects of disorder often come into play at low carrier densities, limiting the applicability of such models. Thus, for example, ferromagnetism has not been seen in semiconductors with shallow, non-magnetic dopants at any density, despite the full freedom to tune the ratio of the electron kinetic energy and e-e interaction. This is in contrast with the situation in diluted magnetic semiconductors, where ferromagnetism is achieved with relatively high transition temperatures at these low carrier densities.

We explore, in the limit of low carrier densities, how the addition of a set of (locally magnetically degenerate) electronic states in diluted magnetic semiconductors, leads to ferromagnetism, and what are the important factors for this change in magnetic behavior.  These considerations suggest that the regime where ferromagnetism is most likely in semiconductors doped with non-magnetic impurities, is one that has not been previously explored. In particular, we show that high spin ground states are obtained in finite systems, implying local ferromagnetic tendencies, possibly leading to a percolative form of ferromagnetism in the thermodynamic limit. The occurrence of high spin ground states of doped semiconductor quantum dots will also be discussed.