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Electronic structure of Mn ions and the magnetic $\mathrm{Mn}\text{\penalty1000-\hskip0pt}\mathrm{Mn}$ coupling in (Ga,Mn)N are investigated within density functional theory. The properties of (Ga,Mn)N are found to critically depend on the position of the Fermi level, which alters the charge state of Mn ions and induces substantial lattice relaxation. The exchange splittings of Mn $d$ levels decrease threefold with the decreasing Fermi level, with the magnetic couplings being similarly affected. The results are in excellent agreement with experiment for low Mn concentration and highlight the role of inhomogeneities at the high concentration limit.

Fermi-level effects on the electronic structure and magnetic couplings in (Ga,Mn)N