The magnetic properties of the iron selenite compound \(Bi_{25}FeO_{40}\) were studied using the mean field approximation based on the Gibbs-Bogoliubov inequality. To do this, we presented the phase diagram in the ground state of the system, revealing the existence of several stable ferromagnetic ordered phases depending on the values of anisotropy and external magnetic field. We also studied the effect of different physical parameters on the thermal variation of magnetisation, magnetic susceptibility and the hysteresis behaviour of the system. Phase diagrams at finite temperature were also presented. The results show that the saturation value in the ground state, the critical temperature and the blocking temperature (in the presence of an external magnetic field) are sensitive to variations in physical parameters. We also revealed the existence of first-order phase transitions between ordered phases, as well as second-order transitions between ordered and disordered phases. Finally, we showed that, for certain values of the physical parameters, the system exhibits multiple-loop hysteresis behaviour, and that the area of the central loop varies as a function of these parameters. Finally, our study fills a gap in the literature: to our knowledge, no previous work, such as by Monte Carlo simulations, had systematically mapped the phase diagrams (ground state and finite temperature) or studied the effects of physical parameters on the magnetic properties and hysteresis behaviour of \(Bi_{25}FeO_{40}\) . This will be useful as a reference for future numerical and experimental studies.
