A method is proposed that allows for a more precise evaluation of the spin splitting of electronic levels induced by the exchange interaction between effective-mass electrons and localized magnetic moments in dilute magnetic semiconductors. The method is nonperturbative, surpasses the molecular-field approximation (MFA), and is developed in the spirit of the muffin-tin model. Surprisingly, the corrections to the MFA exhibit a strong variation with the concentration of magnetic ions, accounting for the hitherto unexplained dependence of the apparent p-d exchange integral on x in ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$S.

• Received 19 June 1992

DOI:https://doi.org/10.1103/PhysRevB.46.9853