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The electronic structure and magnetic stability of substitutional rare-earth (Er) impurities in InGaN are calculated using the full potential linearized augmented plane wave (FP-LAPW) method with local density approximation functional (LSDA[Formula: see text]U). The calculation of formation energy shows that it is more energetically favorable for a substitutional rare earth (Er) atom to replace the In atom than the Ga atom. A semiconductor behavior with a direct band gap is predicted for the concentration InGaN:Er, which is the favored semiconductor when fabricating light emitting devices, with magnetic moment of 3.02 [Formula: see text]. The top of the valence band is formed predominantly with hybridized [Formula: see text]-states of Er and [Formula: see text]-states of N, while the bottom of the conduction band is formed by the hybrid Ga-s/Ga-p states with a small contribution of N-s states. Our calculations reveal that the coupling between rare earth-impurity atoms is ferromagnetic. We discuss the bands, total and partial densities of states.

We present first-principles calculations of the structural, electronic and magnetic properties of Gd-doped [Formula: see text] based on the density functional theory within [Formula: see text] schemes. It is found that Gd atom favors substituting for Al site. Compared with undoped [Formula: see text], the Gd-doped [Formula: see text] has become an indirect band gap semiconductor of reduced band gap. The magnetic moment [Formula: see text] per molecule mainly comes from Gd ion with little contribution from the Ga, Al and N atoms. It is confirmed that the ferromagnetic configuration is stable for [Formula: see text]. It is found also that there is hybridization between the forbital of the Gd atom and the [Formula: see text] orbital of the N atom.

The full potential linearized-augmented-plane-wave (FP-LAPW) method is generalized to a case of an all-electron fully-relativistic spin-polarized self-consistent band calculation based on the relativistic spin-density functional theory and the modified Becke–Johnson potential (TB-mBJ) plus an on-site coulomb U employed for greater generation of the band gap. The results show that these materials are semiconducting materials. The indirect energy gap obtained in this calculation is 1.63[Formula: see text]eV, 1.79[Formula: see text]eV and 1.96[Formula: see text]eV for EuS, EuSe and EuTe, respectively. It is clear from the plots that LSDA[Formula: see text][Formula: see text][Formula: see text]U is a poor technique for the calculation of the band gaps of chalcogenides (EuX). The calculated results for EuX (S, Se and Te) by mBJ[Formula: see text][Formula: see text][Formula: see text]U are in good agreement with the experimental values as compared to the other calculated results.

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