The influence of electrostatic potentials on the apparent s-d exchange energy in III-V diluted magnetic semiconductors

The muffin-tin model of an effective-mass electron interacting with magnetic ions in semiconductors is extended to incorporate electrostatic potentials that are present in the case of Mn-based III-V compounds (${Ga}_{1-x} {Mn}_x {N}$, ${Ga}_{1-x} {Mn}_x {As}$). Since the conduction band electron is repelled from negatively charged magnetic ions and attracted by compensating donors, the \emph{apparent} value of the s-d exchange coupling $N_0 \alpha$ is reduced. It is shown that the magnitude of this effect increases when x diminishes. Our model may explain an unusual behavior of electron spin splitting observed recently in those two materials in the Mn concentration range x <= 0.2%.