The diluted magnetic semiconductor, (Ga, Mn) N has recently attracted intense research interest for the purpose of spintronics application. The material is believed to circumvent the difficulty of combining data processing and mass storage facilities in a single crystal besides solving non-volatility problems. The concentration x, of Mn that substitutes for a fraction of Ga in the compound is thought to contribute a large concentration of magnetic moments and holes. The material studied is focused on dilute magnetic semiconductors (DMS) like <i>Ga<sub>1-X</sub>Mn<SUB>X</SUB>N</i> that play a key role in semiconductor spintronics. Due to their ferromagnetic properties they can be used in magnetic sensors and as spin injectors. The basic problems for applications are, however, the relatively low Curie temperatures of these systems. Therefore, we focus on the understanding of the magnetic properties and on a reliable calculation of Curie temperatures from first principles. We have developed a theoretical framework for calculating critical temperatures by combining first principles calculations and in terms of the Ruderman–Kittel–Kasuya–Yosida quantum spin model in Green’s function approach. Magnetic properties of the group-III nitride semiconductors are introduced here with basic material parameters (temperature, concentration, heat capacity, etc. Temperature dependencies of the spin wave specific heat, inverse magnetic susceptibility and reduced magnetization are determined. Therefore, the dependence of the Neel temperature on the manganese ion concentration is linear thus for our calculation the highest Neel temperature obtained T=146.3k within the concentration of 0.2.