Dependence of the relaxation time of the magnetization of a ferromagnetic particle on the anisotropy of the particle

Abstract

The Pokker-Planck-Smoluchowski equation for the density of orientations of an assembly of single domain ferromagnetic particles (Brown's equation) is used to calculate the dependence of the relaxation time of the magnetization of a uniaxially anisotropic ferromagnetic particle on its internal anisotropy. This is accomplished by separating the variables in Brown's equation using an expansion in spherical harmonics which allows that equation to be represented as an infinite set of differential-difference equations in the time domain. This set may be solved by successively limiting the size of the system matrix with the set of differential-difference equations viewed as an infinite set of ordinary differential equations or by regarding them as a three-term recurrence relation which may be solved in the frequency domain by continued fraction methods. The 3×3 truncation of the system matrix yields acceptable solutions for small anisotropy values while 20 convergents of the continued fraction yield well behaved solutions for large anisotropy. The results for large anisotropy are also obtained using a semiclassical method due to Crothers which may be extended to include the effect of a uniform external magnetic field.