Magnetic relaxation of a system of superparamagnetic particles weakly coupled by dipole-dipole interactions

Long range dipole-dipole interactions in the thermal fluctuations of the magnetization of an assembly of single-domain ferromagnetic particles are considered, ignoring orientational correlations between the particles, so that the evolution of the magnetization orientations may be described by a nonlinear Fokker-Planck equation (FPE) reducing to the usual linear one in the limit of infinite dilution [W. F. Brown Jr., Phys. Rev. 130, 1677 (1963)]. The thermally activated relaxation time scale of the assembly is estimated, leading to a simple and transparent modification of the axially symmetric asymptotes for the superparamagnetic relaxation time.