Kramers low-damping escape rate for fine ferromagnetic particles by the uniform asymptotic expansion of the first-passage-time method

The calculation of the low-damping Kramers escape rate (in the context of m agnetic relaxation of single-domain ferromagnetic particles i.e. superparam agnetism) for non-axially-symmetric potentials of the magneto-crystalline a nisotropy (which is of importance in view of recent experiments on the supe rparamagnetic relaxation time of individual small ferromagnetic particles) is considered in detail (in view of the intricate mathematical manipulation s which are required) using the uniform expansion of the transition rate me thod proposed by Matkowsky et al (1984 J. Star. Phys. 35 443) which has bee n adapted to spins by Klik and Gunther (1990 J. Stat. Phys. 60 473). The re sults agree with those of Klik and Gunther (up to a factor of 2) and with l ater calculations of the escape rate using the original Kramers energy diff usion method.