On the calculation of the Neel relaxation time in uniaxial single-domain ferromagnetic particles

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Abstract
Nanometre-sized particles of ferrite, commonly used in magnetic fluids, are single-domain. The direction of magnetic moment of these small, uniaxial, ferromagnetic particles is known to fluctuate due to thermal agitation, and can relax through the Neel-type relaxation mechanism. The relaxation time of such fluctuations is usually determined by means of Brown's equations for high and low barrier heights. More recently, modified equations catering for a continuous range of barrier heights have been proposed. Comparison of these equations shows that, even in the most extreme case only a factor of approximately 1.7 distinguishes the corresponding eigenvalues (which represent the inverse of the relaxation time). It is concluded that the major source of error in predicting the relaxation time arises, not primarily due to the particular equations used, but because of the large uncertainty in obtaining precise experimental data needed to determine the components, f0 and sigma , of these equations. For example, for a small change in anisotropy constant K by a factor of 2.5 (typical values for the system considered here are (2-5)*104 J m-3), the calculated values of Neel relaxation times using Brown's equation differ by a factor of about 37, corresponding to times of 1.6*10-7 to 4.3*10-9. An experimental value of 5*10-9 s determined from the frequency of the maximum of the loss-peak of the imaginary part of the complex susceptibility is at the outer limit of these calculated values.

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