Cumulative effects of fluctuations and magnetoelectric coupling in two-dimensional RMnO3 (R = Tb, Lu and Y) multiferroics

Highlights: • Fluctuations of order parameters. • Magnetoelectric coupling. • Modified Landau theory. • Renormalized quadratic coefficient. This work investigates the cumulative effects of fluctuations of order parameters and magnetoelectric coupling on the two-dimensional ${\mathrm{RMnO}}_3$ (R = Tb, Lu and Y). The study is carried out through a modified Landau model resulting from microscopic considerations. It is shown that during the transition from the paramagnetic (paraelectric) to ferromagnetic (ferroelectric) phases, the appearance of the spontaneous magnetization and polarization strongly depends on the fluctuations of order parameters and the magnetoelectric coupling. The prevalence of the fluctuation effects on the magnetoelectric constraints is also exhibited. This study can be used to understand the mechanism of magnetization induced by a ferroelectric phase transition and vice versa observed in multiferroic compounds.