Theoretical study of two biquadratically coupled order parameters: Application to two-dimensional multiferroics

Abstract A phenomenological model with a biquadratic coupling between two order parameters is studied in materials that exhibit both a stable magnetization and a stable electrical polarization. The model makes it possible to transfer the coupling of the order parameters from the displacement modes towards the fluctuation modes and to reconsider the problem in terms of two independent order parameters each characterizing a given sub-system. In this new configuration, both phase transitions are second order phase transitions and the results show clearly the possibility of mixed phases. Since the calculations appear to be general to any two order parameters coupled biquadratically, two-dimensional multiferroics are provided as analysis support in order to demonstrate the usefulness of the approach. We clearly show that, the magnetoelectric coupling is conditioned by a dependence between the magnetic and ferroelectric transitions through the order parameters fluctuations.