RANGE OF VALIDITY OF KRAMERS ESCAPE RATES FOR NON-AXIALLY SYMMETRICALPROBLEMS IN SUPERPARAMAGNETIC RELAXATION

The range of validity of the Kramers escape rate for non-axially symme tric problems of superparamagnetic relaxation as a function of frictio n is investigated. A comparison of the exact smallest non-vanishing ei genvalue 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 s mallest non-vanishing eigenvalue for the particular non-axially symmet ric problem of a uniform magnetic held applied at an oblique angle to the easy axis of a particle having simple uniaxial anisotropy, that th e asymptotic formulae provide an acceptable approximation in the range s of damping for which they are expected to be valid. The range of val idity of the non-axially symmetric intermediate- to high-damping formu la as a function of the field angle (which is effectively a measure of the departure from axial symmetry) is also investigated.