Conductivity and magnetism of magnetic oxides

In a stoichiometric oxide the energy for the magnetic ordering is due to su perexchange. This depends on the virtual transfer of a d electron from the transition ion to the neighbouring oxygen. When the oxide is p-doped there are compensating holes on the oxygen or the transition ion becomes mixed va lent. The oxide may then conduct. The same transfer integral enters both th e expression for the antiferromagnetic superexchange and the band width of the mobile carriers. Thus materials with a large antiferromagnetic exchange energy will be expected to have a relatively wide conduction band in the d oped state and hence to have a high conductivity. In this paper the differe nce is explored between the materials in which there is true antiferromagne tism and those which are ferrimagnetic. In the antiferromagnets the carrier s must destroy the magnetic order as they move. This behaviour is well know n from the cuprates. In ferrimagnets the carriers may be able to move entir ely on one sublattice. This occurs in Fe3O4 and probably in the doped garne ts. In the case where motion is on one sublattice then doping does not dest roy the magnetism and there is a relatively small magnetoresistance. An int eresting feature is that unlike the cuprates the ferrimagnets do not become good metals at any doping but exhibit hopping conductivity. We explain the apparent paradox that the best conductivity is actually observed in materi als where the conduction is only allowed when the antiferromagnetism has be en quenched and that the conductivity in ferrimagnets is low.