A multi-bands Hubbard model of intrinsic long range magnetic order in diluted magnetic semiconductors

Recently, new long range ferromagnetic order has been discovered both experimentally and theoretically in carrier free semiconductor. However, there lacks quantitative model to explain the coupling mechanism that may extend to 7th nearest neighbors. In this work, we derived a multi-bands Hubbard model to explain the long range mechanism mediated by localized d states. Based on this model and combining with DFT calculations, we discovered a long range AFM order in DMS systems. Our model provides fundamental understandings of the new type of magnetic order in DMS.