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M ( H$_{a}$ ; T ) curves near the critical temperature ( T$_{RM}$ ≈ 100 K ). In the inset we plot the values of A ( T ) obtained from the fitting: it is indeed a linear function of T , as obtained in (7). By taking the value T$_{f}$ = 760 K [16, 19] we have obtained the renormalized value of T$_{RM}$ ≈ 100 . 5 K , the bare Curie temperature T$_{M}$ = 2 . 28 K , the magnetoelectric coupling constant γ$_{m}$ ≈ − 0 . 15, and l ≈ 0 . 024. One sees that the renormalization T$_{RM}$/T$_{M}$ is very large with the increase caused by the negative sign of the coupling constant γ . We consider the coupling in case of BiMnO$_{3}$ to be large because | γ$_{m}$ | ≈ √ l and as it can be seen from Eqs. (19-20) it directly effects the rapid increase of electric polarization and magnetization in ordered state and is the greatest possible value for the coupling. 

In Fig. 2 we fitted the temperature dependence of magnetization [19] in two ways: first (dotted line), by taking the averaged values from Table.I and second, by a direct fitting i.e. changing slightly the averaged values (dashed line). Those slight changes are justified, as they are within statistical error. One should mention that data used in Fig. 1 was taken for a different sample to that of Fig. 2. 

From these two figures one sees, that the overall behavior of the magnetization near T$_{RM}$ is well reproduced by the mean field approach, particularly for T → T$_{RM}$ and above. Hence, we parametrize the dielectric and magnetoelectric susceptibility components in the same manner next. 

<img src='content_image/364873.jpg'>

