content_image/374377.jpg content_image/374376.jpg content_image/374378.jpg content_image/374380.jpg content_image/374381.jpg
Substituting this expression to (3) we have the equation for magnetization in the usual form: 

with 

and 

<img src='content_image/374377.jpg'>

<img src='content_image/374376.jpg'>

<img src='content_image/374378.jpg'>

One sees that the effective magnetic transition temperature T$_{RM}$ is renormalized by the magnetoelectrical coupling. Explicitly, since the renormalized transition temperature is determined from the condition A ( T$_{RM}$ ) = 0, this yields: 

<img src='content_image/374380.jpg'>

This is one of the interesting results. Namely, the renormalization is strong because of negative value of coupling constant γ$_{m}$ . Furthermore, the renormalization of T$_{f}$ does not appear if T$_{f}$ > T$_{M}$ . In the case of T$_{f}$ = T$_{M}$ the coupling would not change the critical temperatures and no renormalization would occur. 

The explicit stable solutions of equation (6) for ˜ M in the case e = 0 are: 

<img src='content_image/374381.jpg'>

We apply the solution obtained above to the discussion of selected magnetic and dielectric properties of BiMnO$_{3}$. 

## III. APPLICATION TO BiMnO$_{3}$ 

## A. Magnetic properties 

To visualize the influence of the magnetoelectric coupling on the magnetic properties of BiMnO$_{3}$, we fitted the temperature and applied magnetic field dependences of the magne- tization, based on the data of Kimura [16] and Chiba [19]. In Fig. 1 we display the fitted 

