Equilibrium properties of assembly of interacting superparamagnetic nanoparticles

The stochastic Landau–Lifshitz equation is used to investigate the relaxation process and equilibrium magnetization of interacting assembly of superparamagnetic nanoparticles (SPMNPs) uniformly distributed in a nonmagnetic matrix. For weakly interacting assembly, the equilibrium magnetization is shown to deviate significantly from the Langevin law at moderate and large magnetic fields under the influence of their magnetic anisotropies. For dense assemblies with noticeable influence of the magneto-dipole interaction, a significant dependence of the initial susceptibility on the assembly density is revealed. The difference between the initial susceptibility and the corresponding Langevin susceptibility can serve as an indication of appreciable influence of the magneto-dipole interaction on the assembly properties. A new self-consistent approach is developed to explain the effect of mutual magneto-dipole interaction on the behavior of dense assembly of SPMNPs. The probability densities of the components of random magnetic field acting on magnetic NPs are calculated at thermodynamic equilibrium. The self-consistent probability densities of these components are found to be close to Gaussian distribution. A decreasing equilibrium assembly magnetization as a function of its density can be explained as a disorienting effect of the random magnetic field on the NPs magnetic moments.