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For T$_{RM}$ < T < T$_{f}$ , i.e. in the ferroelectric state, we obviously have: 

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In Fig. 3 we plot the temperature dependence of the polarization in the vicinity of T$_{RM}$ , i.e. at temperatures T < T$_{f}$ . One sees that even though the ferroelectric ordering temperature is well above T$_{RM}$ , the weaker-scale magnetic interaction significantly enhances the polarization. This enhancement is also present on application of a magnetic field. This is a second (in addition to the renormalization of T$_{M}$ ) important cross-effect correlating magnetic and electric properties in these systems. One should also note that the electric polarization increases with increasing magnetic field, as one may expect from the negative sign of the magnetoelectric coupling. Unfortunately, no experimental results are available to us to confront our findings with those for BiMnO$_{3}$. 

