Matrix Elements of the System of Moment Equations Governing the Kinetics of Superparamagnetic Particles

An exact equation for the matrix elements of the system of moments [the expectation values of the spherical harmonics $〈Y_{n,m}〉\left(t\right)$], which govern the kinetics of the magnetization $\mathbf{M}$ of a single domain particle, is derived. This derivation is based on the representation of the stochastic Gilbert equation augmented by a random field and the corresponding Fokker-Planck equation for the distribution function of the orientations of $\mathbf{M}$ in terms of the angular momentum operators and on the subsequent evaluation of the matrix elements in terms of the Clebsch-Gordan coefficients.