Fundamental switching field distribution of a single domain particle derived from the N\'eel-Brown model

Abstract

We present an analytical derivation of the switching field distribution for a single domain particle from the N\'eel-Brown model in the presence of a linearly swept magnetic field and influenced by thermal fluctuations. We show that the switching field distribution corresponds to a probability density function and can be obtained by solving a master equation for the not-switching probability together with the transition rate for the magnetization according to the Arrhenius-N\'eel Law. By calculating the first and second moments of the probability density function we succeed in modeling rate-dependent coercivity and the standard deviation of the coercive field. Complementary to the analytical approach, we also present a Monte Carlo simulation for the switching of a macrospin, which allows us to account for the field dependence of the attempt frequency. The results show excellent agreement with results from a Langevin dynamics simulation and therefore point out the importance to include the relevant dependencies in the attempt frequency. However, we conclude that the N\'eel-Brown model fails to predict switching fields correctly for common field rates and material parameters used in magnetic recording from the loss of normalization of the probability density function. Investigating the transition regime between thermally assisted and dynamic switching will be of future interest regarding the development of new magnetic recording technologies.