1.2.1.2 Anisotropy

As far as anisotropy is concerned, taking the first-order variation of the energy $F_$an is equivalent to write the following equation:

$$\delta F_ =\int_\Omega \frac{\partial f_\text{an}}{\partial \textbf{{m}}}\cdot \delta \textbf{{m}} dV \quad.$$ (1.59)

For instance, referring to the case of uniaxial anisotropy and, therefore, to Eq. (1.43), the latter equation becomes

$$\delta F_ =\int_\Omega -2K_1 (\textbf{{m}}\cdot\mathbf{e}_ )\mathbf{e}_ \cdot \delta \textbf{{m}} dV \quad.$$ (1.60)