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Range of validity of Kramers escape rates for non-axially symmetric problems in superparamagnetic relaxation

The range of validity of the Kramers escape rate for non-axially symmetric problems of superparamagnetic relaxation as a function of friction is investigated. A comparison of the exact smallest non-vanishing eigenvalue of the Fokker-Planck equation with the asymptotic expressions for the Kramers escape rate in very low-damping and intermediate- to high-damping regimes is made. It is demonstrated, by calculating the smallest non-vanishing eigenvalue for the particular non-axially symmetric problem of a uniform magnetic field applied at an oblique angle to the easy axis of a particle having simple uniaxial anisotropy, that the asymptotic formulae provide an acceptable approximation in the ranges of damping for which they are expected to be valid. The range of validity of the non-axially symmetric intermediate- to high-damping formula as a function of the field angle (which is effectively a measure of the departure from axial symmetry) is also investigated.