  Detailed calculations of the specific absorption rate (SAR) of a dilute
assembly of iron oxide nanoparticles with effective uniaxial anisotropy
dispersed in a liquid are performed depending on the particle diameters, the
alternating (ac) magnetic field amplitude and the liquid viscosity. For small
and moderate ac magnetic field amplitudes H0 with respect to particle
anisotropy field Hk the SAR of the assembly as a function of the particle
diameter passes through a characteristic maximum and then reaches a plateau,
whereas for sufficiently large amplitudes, H0 ~ Hk, the SAR increases
monotonically as a function of particle diameter. This difference is a
consequence of realization of viscous and magnetic oscillation modes for
particle unit magnetization vector and director for moderate and sufficiently
large H0 values, respectively. It is found that the SAR of the assembly changes
inversely with the viscosity only in a viscous mode, for nanoparticles of
sufficiently large diameters. In the developed magnetic mode the SAR of the
assembly is practically independent of the viscosity, since in this case the
nanoparticle director only weakly oscillates around the ac magnetic field
direction. At moderate amplitudes of the ac magnetic field the SAR values of
the assembly in the liquid and in the solid matrix are found to be close,
except of the range of large particle diameters and sufficiently low viscosity.
However, at large field amplitudes the SAR of randomly oriented assembly of
nanoparticles in a solid matrix is approximately two times less than that in a
liquid, because a significant fraction of nanoparticles of the assembly in the
solid matrix is not optimally oriented with respect to the ac magnetic field
direction. The conditions for the validity of the linear response theory have
been clarified by comparison with the numerical simulation data.
