Influence of the gyromagnetic term in the effect of an oblique magnetic field on the superparamagnetic relaxation time

The effect of a uniform magnetic field applied at an oblique angle psi to the easy axis of magnetization on the superparamagnetic (longitudinal or Neel) relaxation time is illustrated by considering the simplest possible case where the field is applied normal to the easy axis. This is accomplished by numerically solving the Fokker-Planck equation for the smallest non-vanishing eigenvalue lambda(1). It is demonstrated that the asymptotic formula for the Kramers escape rate for general non-axially symmetric potentials evaluated for the particular case psi = pi/2 yields an acceptable asymptotic approximation to the behaviour of lambda(1) for sufficiently high-potential barrier heights and a wide range of values of the dimensionless damping factor. The effect of the gyromagnetic term which gives rise to coupling between the longitudinal and transverse modes of motion corresponds to an increase (higher when the dimensionless damping factor a is smaller) of the smallest non-vanishing eigenvalue lambda(1) and so to a decrease of the Neel relaxation time tau.