Generalized Neel-Brown theory for a temperature-dependent magnetic anisotropy

In order to switch its direction, a macroscopic magnetic moment of a superparamagnetic system has to overcome an energy barrier which is due to magnetic anisotropies in the material. The switching rate is usually described by a Neel-Brown-Arrhenius law, in which the energy barrier is a constant for a given temperature. However, magnetic anisotropies are in general depending on temperature. We take this temperature dependence into account and derive a generalized Neel-Brown theory for the switching rate. Importantly enough, this generalization has a tremendous effect on the physical interpretation of switching processes obtained in experiments on the basis of the conventional Arrhenius law. In particular, the assumption of a temperature-independent anisotropy may result in an overestimation of the attempt frequency by several orders of magnitude.