Superexchange in A$\text{}^{II}$B$\text{}^{VI}$ Diluted Magnetic Semiconductors with Mn, Fe and Co Ions

A theory of superexchange, the dominant ion-ion spin interaction, for Mn-, Fe- and Co-based DMS is presented. The theory takes into account the band structure of A$\text{}^{II}$B$\text{}^{VI}$ compounds, the orbital dependence of the hybridization and the intra shell correlations of the d-electrons, which are essential in the case of the non-S-state ions. The general formulae relating the superexchange to the band structure and the ionic energy spectrum were obtained - the dominant part of the superexchange turns out to be inversely proportional to the square of the ionic spin. This explains the observed increase in the average values of d-d exchange constants, when passing from Mn via Fe to Co ions in DMS.