Abstract
In this work, we study the magnetization of magnetite (Fe3O4) with different exchange interactions and crystal fields using variational method based on the Bogoliubov inequality for the Gibbs free energy within the mean field theory. The magnetic behavior was investigated in the absence and presence of crystal fields. The investigations also revealed that the transition temperature depends on the crystal fields of the octahedral and tetrahedral sites. Magnetite exhibits ferrimagnetic phase with second order transition to paramagnetic phase at 850K. This result is confirmed using the mean field theory within the Heisenberg model. Important factors that can affect the magnetic behavior of the system are exchange interactions and crystal field. Indeed, a new magnetic behavior was observed depending on these parameters. A first order phase transition from ferrimagnetic to ferromagnetic was found at low temperature, and a second order transition from ferromagnetic to paramagnetic was observed at high temperature.
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