Interaction between band electrons and transition-metal ions in diluted magnetic semiconductors

We present a theoretical study of the effective exchange interaction arising from the hybridization between the valence-band states and the localized d orbitals of a transition-metal impurity in a II-VI semiconductor. The irreducible tensor method is used to deduce the effective Hamiltonian in the manifold of the ground multiplet of a 3dⁿ ion in a tetrahedral crystal field. There is no coupling in the cases of Sc²⁺ and Ti²⁺ ions. For Mn²⁺, Fe²⁺, and Co²⁺ the coupling reduces to the usual spin-exchange Kondo Hamiltonian, in agreement with experiments; the observed increase of the exchange parameter ‖N₀β‖ from Mn to Fe to Co in a given host is also explained. In the cases of V²⁺, Cr²⁺, Ni²⁺, and Cu²⁺ additional coupling terms involving the orbital degrees of freedom are obtained; these predict drastic modifications of the valence-band splitting in a magnetic field.