In this work, using the ab-initio calculations, we have investigated the phantom magnetism when the diamagnetic solids, carbon and nitrogen with $$d^{0}$$ doped CdTe. We have applied in these calculations the combination between the Korringa–Kohn–Rostoker and coherent potential approximation method within the local density approximation and generalized gradient approximation (GGA). In this study, the doped compound presents a metallic behavior for both the approximations characterized by a small moment of about 0.299/0.326 and 0.249/0.266 $$\mu _{{\mathrm{B}}}$$ for 24% of C and N, respectively. The polarization has shown a low and decreasing value from 43.73/59.56 to 0.29/2.26% for 9% and 24% of C impurity concentration, respectively. Unlike for the case of N, this parameter varies from 76.7/72.86 to 85.29/83.63% for 9% and 24% concentration, respectively. In addition, we have determined the mechanism of ferromagnetic coupling for the C- and N-doped CdTe. Furthermore, the stability of the compound is investigated by comparing the energy difference between the spin glass and ferromagnetic states. It is found that below the percolation threshold, contrary to the case of doping by N except for 20% using GGA, the C impurities lead to the most ferromagnetic stable phase. While the system changes its stability above this threshold when doped by the C impurities. Finally, we have estimated and discussed the Curie temperature using the mean field approximation.
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