It is shown that the magnetic dynamics of an assembly of nanoparticles dispersed in a viscous liquid differs significantly from the behavior of the same assembly of nanoparticles immobilized in a solid matrix. For an assembly of magnetic nanoparticles in a liquid two characteristic mode for stationary magnetization oscillations are found that can be called the viscous and magnetic modes, respectively. In the viscous mode, which occurs for small amplitude of the alternating magnetic field H₀ as compared to the particle anisotropy field H_k, the particle rotates in the liquid as a whole. In a stationary motion the unit magnetization vector and the director, describing the spatial orientation of the particle, move in unison, but the phase of oscillations of these vectors is shifted relative to that of the alternating magnetic field. Therefore, for the viscous mode the energy absorption is mainly due to viscous losses associated with the particle rotation in the liquid. In the opposite regime, H₀ ≥ H_k, the director oscillates only slightly near the external magnetic field direction, whereas the unit magnetization vector sharply jumps between magnetic potential wells. Thus, a complete orientation of the assembly of nanoparticles in the liquid occurs in the alternating magnetic field of sufficient amplitude. As a result, large specific absorption rates, of the order of 1 kW/g, can be obtained for an assembly of magnetic nanoparticles in viscous liquid in the transient, H₀ ∼ 0.5H_k, and magnetic modes at moderate frequency and alternating magnetic field amplitude.

The low frequency hysteresis loops of superparamagnetic nanoparticles with uniaxial anisotropy are calculated as a function of the particle diameter, alternating magnetic field amplitude $H_0$ , frequency, and particle magnetic parameters both for oriented and nonoriented assemblies. The magnetic field frequency is assumed so high, $f>50–100\text{kHz}$ , that the mechanical rotation of a particle in surrounding medium is restricted. Thus, only the Neel–Brown magnetization relaxation process is taken into account. Pronounced dependence of the specific loss power on the particle diameter is found in the linear regime pertaining to small magnetic field amplitudes. For an oriented assembly of Co nanoparticles with optimal diameter $D\approx 6\text{nm}$ the specific power loss can be as high as 1600 W/g for typical values $H_0=200\text{Oe}$ and $f=500\text{kHz}$ . It is three times less for the corresponding nonoriented assembly. Nevertheless, using of particles with low anisotropy field, i.e., particles of soft magnetic type, seems to be preferable for the purpose of magnetic nanoparticle hyperthermia. For such an assembly the nonlinear regime can be easily accessed. Hence the hysteresis loop area increases and is comparable with its maximum possible value.