response in the ferromagnetoelectric state ( T < T$_{RM}$ ) is described by the tensor: By assuming e = 0, we obtain the following equations for ˜ M and ˜ P : After differentiating (13) and (14) with respect to both e and h , we obtain a system of linear equations for the susceptibility components in the form: with: Therefore the solution of (15) takes the form: with: ˜ A ≡ ( T$_{f}$ T$_{M}$ ) 2 ( T T$_{f}$ − 1 ) + 3 l ( T$_{f}$ T$_{M}$ ) 2 ˜ P 2 + γ$_{m}$ T$_{f}$ T$_{M}$ ˜ M $^{2}$, ˜ B ≡ T T$_{M}$ − 1 + 3 ˜ M 2 + γ$_{m}$ T$_{f}$ T$_{M}$ ˜ P $^{2}$, ˜ C ≡ 2 γ$_{m}$ T$_{f}$ T$_{M}$ ˜ P ˜ M . and In the zero field case and for temperature T < T$_{RM}$ , the corresponding expressions for magnetization and polarization are: 8 ˜ χ$_{me}$ = ˜ χ$_{em}$ = ˜ C ˜ C 2 − ˜ A ˜ B . (18) ˜ χ$_{e}$ = ˜ B ˜ A ˜ B − ˜ C $_{2}$, (17) ˜ χ$_{m}$ = ˜ A ˜ A ˜ B − ˜ C $_{2}$, (16) ˆ χ =   ˜ χ$_{e}$ ˜ χ$_{em}$ ˜ χ$_{me}$ ˜ χ$_{m}$  $_{}$, (11) ∂ ˜ M ∂h = ˜ χ$_{m}$, ∂ ˜ P ∂e = ˜ χ$_{e}$, ∂ ˜ M ∂e = ˜ χ$_{me}$, ∂ ˜ P ∂h = ˜ χ$_{em}$. (12) ∂ (Δ F ) ∂ ˜ M = ( T/T$_{M}$ − 1) ˜ M + ˜ M 3 + γ$_{m}$ T$_{f}$ T$_{M}$ ˜ M ˜ P 2 − h = 0 , (13) ∂ (Δ F ) ∂ ˜ P = l$^{(}$ T$_{f}$ T$_{M}$$^{)}$$^{2}$$^{(}$ T T$_{f}$ − 1$^{)}$ ˜ P + l$^{(}$ T$_{f}$ T$_{M}$$^{)}$$^{2}$ ˜ P 3 + γ$_{m}$ T$_{f}$ T$_{M}$ ˜ M 2 ˜ P − e = 0 . (14) ˜ B ˜ χ$_{m}$ + ˜ C ˜ χ$_{em}$ 1 , ˜ A ˜ χ$_{em}$ + ˜ C ˜ χ$_{m}$ = 0 , ˜ B ˜ χ$_{me}$ + ˜ C ˜ χ$_{e}$ = 0 , (15) ˜ A ˜ χ$_{e}$ + ˜ C ˜ χ$_{me}$ = 1 ,