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($\frac{E_B}{\mathrm{kT}}$) behavior when $E_B\gg \mathrm{kT}$. Here $E_B$ 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 $E_B\le 20kT$, where these computations were carried out.