Effect of an oblique magnetic field on the superparamagnetic relaxation time. II. Influence of the gyromagnetic term

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Abstract
The effect of a uniform magnetic field applied at an oblique angle to the easy axis of magnetization on the superparamagnetic (longitudinal or Néel) relaxation time is investigated by numerically solving the Fokker-Planck equation for the smallest nonvanishing eigenvalue. It is demonstrated that the reciprocal of the asymptotic formula for the Kramers escape rate in the intermediate to high damping limit for general nonaxially symmetric potentials when applied to the present problem, yields an acceptable asymptotic approximation to the Néel time for moderate to high values of the damping. Alternatively the corresponding Kramers low dissipation formula (energy controlled diffusion) provides an acceptable approximation for very small values of the damping. The effect of the gyromagnetic term which gives rise to coupling between the longitudinal and transverse modes of motion generally corresponds to an increase of the smallest nonvanishing eigenvalue and so to a decrease of the Néel relaxation time. The integral relaxation time or area under the slope of the curve of the decay of the magnetization is also evaluated. It is demonstrated that for sufficiently high values of the uniform field (much less, however, than that required to destroy the bistable nature of the potential) the reciprocal of the lowest nonvanishing eigenvalue (proportional to the Néel time, or the time of reversal of the magnetization) and the integral relaxation time may differ exponentially from one another signifying the contributions of modes other than that associated with the overbarrier (Néel) relaxation process to the overall relaxation process. The overall behavior is qualitatively similar (apart from the azimuthal dependence) to that of the axially symmetric case which arises due to the depletion of the shallower of the two potential wells by the uniform field, so that the fast processes in the deeper of the two wells may come to dominate the relaxation process at sufficiently high values of the uniform field.