  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 magneto-
dipole interaction is determined mainly by the cluster packing density eta =
Np*V/Vcl, where Np is the average number of the particles in the cluster, V is
the nanoparticle volume, and Vcl 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 < eta < 0.4. The dependence of the specific
absorption rate on the mean nanoparticle diameter is retained with increase of
eta, but becomes less pronounced. For fractal clusters of nanoparticles, which
arise in biological media, in addition to 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 increase of the thickness of nonmagnetic
shells at the nanoparticle surfaces.
