The effect of an oblique magnetic field on the superparamagnetic relaxation time

Abstract

The effect of a constant magnetic field, applied at an angle ψ to the easy axis of magnetization, on the Néel relaxation time τ of a single domain ferromagnetic particle with uniaxial anisotropy is investigated by calculating the smallest non-vanishing eigenvalue of the appropriate Fokker-Planck equation as a function of ψ. The curve of λ 1 versus ψ is symmetric about ψ = 90°. Thus the maximum decrease in τ occurs at ψ = 45° with maximum increase to a value exceeding that at ψ = 0, at ψ = 90°, the ψ = 0 value being again attained at ψ = 180°. The results are shown to be consistent with the behaviour predicted by the Kramers theory of the rate of escape of particles over potential barriers. This theory when applied to the potential barriers for the ψ = 90° orientation for rotation in space yields a simple approximate formula for the escape rate which is in reasonable agreement with the exact λ 1 calculated from the Fokker-Planck equation.