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 magnetic relaxation of single-domain ferromagnetic particles i.e. superparamagnetism) for non-axially-symmetric potentials of the magneto-crystalline anisotropy (which is of importance in view of recent experiments on the superparamagnetic relaxation time of individual small ferromagnetic particles) is considered in detail (in view of the intricate mathematical manipulations which are required) using the uniform expansion of the transition rate method proposed by Matkowsky et al (1984 J. Stat. Phys. 35 443) which has been adapted to spins by Klik and Gunther (1990 J. Stat. Phys. 60 473). The results agree with those of Klik and Gunther (up to a factor of 2) and with later calculations of the escape rate using the original Kramers energy diffusion method.