  We theoretically investigate the magnetic activation energy of permanent
magnets. Practically, it is widely used in a phenomenological form as
$\mathcal{F}_\mathrm{B}(H_\mathrm{ext})=\mathcal{F}_\mathrm{B}^0\left(1-H_\mathrm{ext}/H_0\right)^n,$
where $\mathcal{F}_\mathrm{B}^0$ is the activation energy in the absence of an
external magnetic field $H_\mathrm{ext}$, $n$ is a real parameter, and $H_0$ is
defined by the equation $\mathcal{F}_\mathrm{B}(H_0)=0$. We derive the general
and direct expressions for these phenomenological parameters under the
restriction of uniform rotation of magnetization and on the basis of the
perturbative theory with respect to $H_\mathrm{ext}$. Further,we apply our
results to Nd$_2$Fe$_{14}$B magnets and confirm the validity of the proposed
method by comparing with the Monte Carlo calculations.
