Abstract
The nonlinear response of an assembly of superparamagnetic particles due to a sudden change both in the magnitude and in the direction of a strong external uniform DC magnetic field is evaluated. The desired system of moments (the expectation values of the spherical harmonics 〈 Y l, m 〉( t)), which governs the kinetics of the magnetization M of an individual particle, is derived by averaging the stochastic Gilbert equation augmented by a random field over its realizations. As an example, the nonlinear transient response of particles possessing cubic anisotropy is considered. Here, the solution of the moment system is obtained using the matrix continued fraction method. The spectrum of the appropriate relaxation function and the relaxation time of the magnetization are calculated for typical values of the anisotropy, dissipation, and nonlinearity parameters. In general, the relaxation time and spectrum depend strongly on the dissipation parameter due to the coupling between the transverse and longitudinal modes. This behavior is particularly pronounced in the nonlinear regime.
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