Trends of exchange interactions in dilute magnetic semiconductors

We discuss the importance of different exchange mechanisms like double exchange, p-d exchange and anti-ferromagnetic as well as ferromagnetic superexchange in dilute magnetic semiconductors (DMSs). Based on the coherent potential approximation for the electronic structure of the DMSs we show that the different mechanisms exhibit different dependences on the concentration of the magnetic impurities, on the hybridization with the wavefunctions of neighbouring impurities and on the position of the Fermi level in the band gap. However, common to all mechanisms is that, as long as half-metallicity is preserved, they are determined by the hybridization with the orbitals of neighbouring impurities and of the resulting energy gain due to the formation of bonding and anti-bonding hybrids. By calculating the exchange coupling constants J(ij) (E-F) as a function of the position of the Fermi level we obtain a universal trend for the exchange interactions with band filling.