Fluctuation theory of magnetic relaxation for two-dimensional ensembles of dipolar interacting nanoparticles

The fluctuation theory of magnetic relaxation has been developed for the two-dimensional ensembles of ferromagnetic nanoparticles. The particles have random locations on a square lattice, interact via dipolar interaction, and their easy axes of magnetization are perpendicular to the lattice plane. The derivation of the equation that describes the time evolution of the magnetization has been based on the Fokker-Planck equation for the distribution function of a nanoparticle magnetic moment. The influence of the mean value and the fluctuations of the dipolar magnetic field on the process of magnetic relaxation is studied in detail. It has been shown that, in contrast to the case of noninteracting nanoparticles which is characterized by the single relaxation time, magnetic relaxation in those ensembles is characterized by two different relaxation times. and that the rate of relaxation decreases with Lime.