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Using the full potential linearized augmented plane wave method based on the spin density functional theory, we investigate the ferromagnetic properties, the electronic structure, and the formation energy of Ga(0.9375)M(0.0625)N (M=vacancy, Ca). The calculations indicate that both cases prefer ferromagnetic ground state. The magnetic moments mainly come from the N atoms surrounding the defect centers, which are different from the conventional diluted magnetic semiconductor. High formation energy for the Ga vacancy Suggests that the defect concentration is too low to result in the ferromagnetic GaN. The formation energy for the two substitutional (Ca(Ga),Ca(N)) and two interstitial sites (tetrahedral T, Ca(i-T) and octahedral O, Ca(i-O)) doped configurations indicates that Ca prefers the substitutional Ga in GaN. The defect concentrations for the Ga(0.9375)Ca(0.0625)N under thermal equilibrium N-rich and N-realistic growth conditions are also discussed, respectively. The calculations show that defect concentration under N-rich condition can readily reach 7%, while under N-realistic growth condition, the maximum defect concentration is as low as 1.71% when the growth temperature increases to 1100 K (melting point of GaN). These results suggest that it would be a little difficult to achieve ferromagnetic state for Ga(0.9375)Ca(0.0625)N using the chemical-equilibrium fabrication method, such as chemical precipitation. Using the same method as that for Cu-doped ZnO [L. H. Ye et al., Phys. Rev. B 73, 033203 (2006)], the transition temperature of Ga(0.9375)Ca(0.0625)N may be close to room temperature. (C) 2008 American Institute of Physics.