The Ferromagnetic p-d Exchange in Diluted Magnetic Semiconductors

The antiferromagnetic type of the interaction between the Γ$\text{}_{8}$-band electrons and the Mn$\text{}^{2+}$ ions in A$\text{}^{II}$B$\text{}^{IV}$ diluted magnetic semiconductors has been explained by invoking the p-d hybridization mechanism. In this paper it is shown that for particular electronic configurations of the magnetic ions in diluted magnetic semiconductors the p-d hybridization can lead to a ferromagnetic interaction between the valence-band electrons and the localized spins. This happens when all the one-electron d-orbitals which hybridize with p-band states are empty (e.g., as in Sc$\text{}^{2+}$ and Ti$\text{}^{2+}$ ions). The appropriate p-d Hamiltonian is derived and the ferromagnetic exchange constants are evaluated.