content_image/353741.jpg content_image/353740.jpg content_image/353742.jpg content_image/353743.jpg content_image/353744.jpg content_image/353746.jpg content_image/353747.jpg content_image/353745.jpg content_image/353739.jpg content_image/353738.jpg content_image/353737.jpg
response in the ferromagnetoelectric state ( T < T$_{RM}$ ) is described by the tensor: 

with: 

By assuming e ̸ = 0, we obtain the following equations for ˜ M and ˜ P : 

<img src='content_image/353741.jpg'>

<img src='content_image/353740.jpg'>

<img src='content_image/353742.jpg'>

<img src='content_image/353743.jpg'>

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: 

<img src='content_image/353744.jpg'>

<img src='content_image/353746.jpg'>

<img src='content_image/353747.jpg'>

<img src='content_image/353745.jpg'>

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 . 

Therefore the solution of (15) takes the form: 

and 

<img src='content_image/353739.jpg'>

<img src='content_image/353738.jpg'>

<img src='content_image/353737.jpg'>

In the zero field case and for temperature T < T$_{RM}$ , the corresponding expressions for magnetization and polarization are: 

