Analytic expression for magnetic activation energy

We theoretically investigate the magnetic activation energy of permanent magnets. Practically, it is widely used in a phenomenological form as where is the activation energy in the absence of an external magnetic field is a real parameter, and is defined by the equation . 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 . Further, we apply our results to Nd₂Fe₁₄B magnets and confirm the validity of the proposed method by comparing with the Monte Carlo calculations.