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Experimentaly, the susceptibility is a linear function of the squared magnetization for BiMnO$_{3}$ [16]. In some papers [16, 20] this is rationalized on the basis of Landau-theory yet this it is not the case. In fact, in this phenomenological approach the inverse susceptibility is a linear function of the squared magnetization and it comes about from the renormalization of dielectric constant by the coupling. Explicitly this may be written [21] Δ F ≈ ( α$_{0}$ ( T − T$_{f}$ ) / 2 + γ/ 2 M $^{2}$) P $^{2}$+ ... = χ − 1 e P $^{2}$+ ... . In Fig. 5 we plot the predicted Landau theory value of Δ ϵ/ϵ (0) as a function of the squared magnetization. The dependence is none linear. In the inset of Fig. 5 we show the inverse dielectric susceptibility as a function of the squared magnetization to be linear within the framework of Landau theory. 

<img src='content_image/335714.jpg'>

In case of χ$_{me}$ = 0 we calculate the inverse susceptibilities from the Landau functional as second derivative with respect to the order parameters, i.e. χ − 1 ϵ = ∂F 2 ∂P $_{2}$, χ − 1 m = ∂F 2 ∂M $_{2}$. Hence we obtain respectively: 

<img src='content_image/335712.jpg'>

<img src='content_image/335711.jpg'>

