Electronic and magnetic structures of Fe3O4 ferrimagnetic investigated by first principle, mean field and series expansions calculations

• Ab initio calculations, based on DFT approach and FLAPW are used to study the electronic properties of Fe3O4.
• Magnetic moments of Fe1 and Fe2 are estimated to −/+3.44 µB.
• HTSE method is used to calculate the Néel temperature of Fe3O4.

Self-consistent ab initio calculations, based on density functional theory (DFT) approach and using a full potential linear augmented plane wave (FLAPW) method, are performed to investigate both electronic and magnetic properties of the Fe3O4. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Fe plans. Magnetic moment considered to lie along (010) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The exchange interactions between the magnetic atoms Fe–Fe in Fe3O4 are given using the mean field theory. The high temperature series expansions (HTSEs) of the magnetic susceptibility of with the magnetic moments, mFe in Fe3O4 is given up to seventh order series in (1/kBT). The Néel temperature TN is obtained by HTSEs of the magnetic susceptibility series combined with the Padé   approximant method. The critical exponent γγ associated with the magnetic susceptibility is deduced as well.