The future trend in the microelectronic technologies is to exploit the fundamental degrees of freedom, spin and charge of electron for enhancing the operational speed, transfer efficiency, and storage capacity of the electronic devices in the digital society 5.0 era. Herein, within the density functional theory, we have studied the electronic- and magnetic-characteristics of bulk diluted magnetic semiconductor materials based on the III-V compound GaN, using the ab-initio full potential method and the generalized gradient approximation. We have shown that \(\left( {{\text{Ga}},{\text{Cr}}} \right){\text{N}}\) and \(\left( {{\text{Ga}},{\text{Cr}},{\text{V}}} \right){\text{N}}\) compounds have half-metallic nature with a total spin-polarization at the Fermi level \(E_{F}^{ }\) . Furthermore, we have found that these systems exhibit a ferromagnetic behavior, whose stability is ensured by the double-exchange and ferromagnetic super-exchange mechanisms. In addition, we have used Monte Carlo simulation to extend the study of the ground state to finite temperatures. We have found that the studied diluted magnetic semiconductors show second-order phase transition with high Curie temperatures, well above room temperature. These results indicate that the three-dimensional diluted magnetic semiconductors of III-V type, namely \({\text{GaN}}\) doped and co-doped with transition metals, are desirable for spintronic applications.