Phase transition studies of BiMnO₃: Mean field theory approximations

We studied the phase transition and magneto-electric coupling effect of BiMnO₃ by employing mean field theory approximations. To capture the ferromagnetic and ferroelectric transitions of BiMnO₃, we construct an extended Ising model in a 2D square lattice, wherein, the magnetic (electric) interactions are described in terms of the direct interactions between the localized magnetic (electric dipole) moments of Mn ions with their nearest neighbors. To evaluate our model, we obtain magnetization, magnetic susceptibility and electric polarization using mean field approximation calculations. Our results reproduce both the ferromagnetic and the ferroelectric transitions, matching very well with the experimental reports. Furthermore, consistent with experimental observations, our mean field results suggest that there is indeed a coupling between the magnetic and electric ordering in BiMnO₃