Interpolation formulae between axially symmetric and non-axially symmetric Kramers’ escape rates for single-domain ferromagnetic particles in the intermediate to high-damping limit

Abstract It is shown how the Kramers’ escape rate for single-domain ferromagnetic particles (Brown Jr., Phys. Rev. 130 (1963) 1677) with axially symmetric potentials of the magneto-crystalline anisotropy may be smoothly joined to Kramers’ escape rates for non-axially symmetric potentials by considering the problem of relaxation in a simple uniaxial potential of the magneto-crystalline anisotropy in a uniform field at an arbitrary angle to the anisotropy axis. There (unlike the axially symmetric potential result, which is valid for all values of the damping parameter, because it is described by a Fokker–Planck equation (FPE) in the latitude only), the three cases of the Kramers’ problem namely intermediate-to-high damping (IHD); very low damping (VLD) and the transition regime between the above regions naturally appear. The calculation is illustrated by considering for the most part the simplest problem, i.e. the IHD case for an arbitrary field angle. The problem of joining the two solutions for low damping is briefly outlined.