An approximate formula for the relaxation time of a single domain ferromagnetic particle with uniaxial anisotropy and collinear field

Abstract

Recently there have been renewed efforts to solve the Fokker–Planck equation resulting from Brown’s model [Phys. Rev. 130, 1677 (1963)] of single domain ferromagnetic particle relaxation for the case of uniaxial anisotropy and zero external field. In particular, the usefulness of a simple analytic formula for the relaxation time based on the reciprocal of the lowest non-zero eigenvalue resulting from this model has been stressed. Here we suggest an improved analytic formula which we extend to the case of applied collinear field and compare it with the exact numerical solution and previous analytic expressions. The results are presented in terms of the pre-factor dependence which is commonly taken as constant. The formula exhibits good agreement with the exact results throughout the full range of anisotropy and reduced external field values.