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,Y-m> (t)] which govern the kinetics of the magnetization 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 M in terms of the angular momentum operators and on the subsequent evaluation of the matrix elements in terms of the Clebsch-Gordan coefficients. [S0031-9007(99)08847-X].