The relaxation behavior of an assembly of noninteracting single-domain ferromagnetic particles in the presence of a constant magnetic field is studied by solving the corresponding Fokker-Planck equation. The analysis is performed by first converting that equation into a hierarchy of differential-recurrence relations by expanding the solution in Legendre polynomials. The spectrum of eigenvalues and their associated amplitudes is then determined by matrix methods where all the desired physical quantities such as the magnetization correlation time and complex magnetic susceptibility may be computed numerically. In order to ensure the accuracy of the results obtained this solution is compared with an exact solution derived in terms of matrix continued fractions. It is shown that the conventional assumption in the theory of superparamagnetism, that except in the very early stages of relaxation to equilibrium the only appreciable time constant is the one associated with the smallest nonvanishing eigenvalue, is no longer true when an applied constant magnetic field exceeds a certain critical value. The breakdown of this assumption manifests itself in (a) a dramatically large deviation of the magnetization correlation time (area under the curve of the decay of the magnetization) from the inverse of the lowest eigenvalue, and (b) in the presence of relatively strong high-frequency modes superimposed on the Néel one usually assigned to the lowest eigenvalue. The results are compared with available experimental data.

• Received 2 February 1995

DOI:https://doi.org/10.1103/PhysRevB.51.15947