Magnetic polaron percolation on a rutile lattice: A geometrical exploration in the limit of low density of magnetic impurities

The evolution of magnetic polaron clusters on a rutile lattice has been explored, and the results are used to discuss the origin of ferromagnetism in transition-metal (TM)-doped rutile TiO2 oxides. It is shown that percolation on a rutile lattice is characterized by a threshold different from that found for the percolation of randomly distributed spheres, which has been so far assumed as a model to treat the percolation of magnetic polarons in diluted magnetic semiconductors. Furthermore, unlike previous investigations, we explicitly considered the condition of small density n(i) of TM impurities, i.e., a regime that is quite far from that usually regarded for polaron formation, dominated by a high density n(i) of TM ions. Assuming that ferromagnetic coupling arises between polarons that share common TM impurities, we show the effect of this constraint on the magnetic properties of the sample compared to those reported for the ni n(i)>> n(h) regime.