In a stoichiometric oxide the energy for the magnetic ordering is due to superexchange. 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 valent. The oxide may then conduct. The same transfer integral enters both the 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 doped state and hence to have a high conductivity. In this paper the difference is explored between the materials in which there is true antiferromagnetism and those which are ferrimagnetic. In the antiferromagnets the carriers must destroy the magnetic order as they move. This behaviour is well known from the cuprates. In ferrimagnets the carriers may be able to move entirely on one sublattice. This occurs in Fe_{3}O_{4} and probably in the doped garnets. In the case where motion is on one sublattice then doping does not destroy the magnetism and there is a relatively small magnetoresistance. An interesting 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 materials where the conduction is only allowed when the antiferromagnetism has been quenched and that the conductivity in ferrimagnets is low.
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The p-d hybridised single-hole states of the transition-metal-oxygen tetrahedron (TMO_{4}) are collectivised due to the direct p-p hopping between oxygens of different clusters. The lowest-lying energy band is always narrow and fully occupied. The first excited band gets occupied as an effect of valence-uncompensated doping, so it can be almost localised. The possible hole excitations to the two higher energy bands, which are wider, may imply the Mott-like hopping form of charge transport in these systems.
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