Localization of electrons in Mott insulators, makes an interesting challenge in DFT calculation on these crystals. Many calculations have been done to obtain Heisenberg exchange interaction coefficients in these crystals. In NiO crystal, Heisenberg exchange coefficient for second neighbors is significant, that reduces the influence of first neighbors Heisenberg energy in this crystal. Also, negativity of this value can indicate antiferromagnetic state by ferromagnetic plates of (111) as ground state of energy. The band gap of NiO has been obtained 3.8 to 4.3eV, as for this scale, this crystal is insulator, but ab. initio calculations of DFT predicts a very smaller gap. We need an appropriate correction to calculate this crystal’s properties. In this thesis we use Hubbard correction for calculate localized electrons. Also, we use full potential LAPW method to simulate the crystal appropriate. Using LAPW method and Hubbard correction, we calculate Heisenberg exchange interaction coefficients for first to fourth nearest neighbors, afterwards, we calculate Neel’s temperature for NiO bulk crystal using the mean-field approximation. We also calculate biquadratic exchange coefficient for this crystal. For this, we need non-collinear calculations. For non-collinear and LAPW calculations, we use Fleur code.
