In this paper, we investigated the properties of transition metal (TM)-doped - using first-principles calculations and Monte Carlo simulations. - is a wide-bandgap semiconductor material with enhanced performance and lower fabrication costs on sapphire substrates compared to - . Doping with TMs can modify electrical transport, optical absorption, and magnetic properties, yet theoretical studies on this are scarce. Our study focused on V, Cr, Mn, and Fe impurities. We introduced a newly proposed scheme for efficiently determining the ground-state defect configuration during structural relaxation. We adopt a recent, novel image charge correction method to accurately calculate formation enthalpy and thermodynamic transition levels for spin-polarized transition metal ion doping, without employing the empirical dielectric constant. Results showed Cr ions tend to neutral substitutional Ga, while V, Mn, and Fe impurity ions tend to carry a negative charge in common n-type - . Magnetic moments and spin-splitting impurity levels primarily arise from transition metal impurities and their d orbitals. We used the generalized four-state method to calculate exchange interaction constants between substitution lattice sites and identified (anti) ferromagnetic couplings at specific distances in a 120-atom supercell, which are negligible in total energy calculations. Monte Carlo simulations indicated a Curie temperature of 360 K in n-type - : Mn system with 12.5% doping, suggesting intrinsic ferromagnetic ordering based on the Heisenberg model. Our study contributes to understanding TM-doped - electronic structure and magnetic properties through improved methodologies. The approach can be applied in research involving other TM-doped oxides or wide-bandgap semiconductors.
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