Conductivity and Magnetism of Magnetic Oxides

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$\text{}_{3}$O$\text{}_{4}$ 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.