Interaction Effects in Assembly of Magnetic Nanoparticles

A specific absorption rate of a dilute assembly of various random clusters of iron oxide nanoparticles in alternating magnetic field has been calculated using Landau–Lifshitz stochastic equation. This approach simultaneously takes into account both the presence of thermal fluctuations of the nanoparticle magnetic moments and magneto-dipole interaction between the nanoparticles of the clusters. It is shown that for usual 3D clusters, the intensity of the magneto-dipole interaction is determined mainly by the cluster packing density η = N (p) V/V (cl), where N (p) is the average number of the particles in the cluster, V is the nanoparticle volume, and V (cl) is the cluster volume. The area of the low frequency hysteresis loop and the assembly-specific absorption rate have been found to be considerably reduced when the packing density of the clusters increases in the range of 0.005 ≤ η < 0.4. The dependence of the specific absorption rate on the mean nanoparticle diameter is retained with an increase of η, but becomes less pronounced. For fractal clusters of nanoparticles, which arise in biological media, in addition to a considerable reduction of the absorption rate, the absorption maximum is shifted to smaller particle diameters. It is found also that the specific absorption rate of fractal clusters increases appreciably with an increase of the thickness of nonmagnetic shells at the nanoparticle surfaces.