New Approach to the Theory of Superexchange Interactions

The theory of indirect exchange in poor conductors is examined from a new viewpoint in which the $d$ (or $f$) shell electrons are placed in wave functions assumed to be exact solutions of the problem of a single $d$-electron in the presence of the full diamagnetic lattice. Inclusion of $d$-electron interactions leads to three spin-dependent effects which, in the usual order of their sizes, we call: superexchange per se, which is always antiferromagnetic; direct exchange, always ferromagnetic; and an indirect polarization effect analogous to nuclear indirect exchange. Superexchange itself is shown to be closely related to the poor conductivity, in agreement with experiment. By means of crystal field theory the parameters determining superexchange can be estimated, and in favorable cases (NiO, LaFe${\mathrm{O}}_3$) the exchange integrals can be evaluated with accuracy of several tens of percent. Qualitative understanding of the whole picture of exchange in iron group oxides and fluorides follows from these ideas.