Asymptotic superparamagnetic time constants for cubic anisotropy. I. Positive anisotropy

It is shown that the relaxation rate of superparamagnetic particles with a positive cubic anisotropy is determined by two (and only two) time constants, in the limit of a high energy-barrier. Their ratio in this limit tends towards 3/2. These findings are confirmed by numerical calculations that correct for an error in previous ones. In addition, theoretical expressions for the time constants are derived, which show an exp(EBkT) behavior when EBkT. Here EB is the barrier energy, T is the absolute temperature, and k is Boltzmann's constant. The numerical computations give reasonably close results to the theoretical expressions, but an asymptotic tendency towards them is not as yet identified with full confidence, in the limited region EB≤20kT, where these computations were carried out.