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 Hk, 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 ≥ Hk, 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 ∼ 0.5Hk, and magnetic modes at moderate frequency and alternating magnetic field amplitude.

The hysteresis losses of a dense assembly of magnetite nanoparticles with an average diameter D = 25 nm are measured in the frequency range f = 10 – 200 kHz for magnetic field amplitudes up to H0 = 400 Oe. The low frequency hysteresis loops of the assembly are obtained by means of integration of the electro-motive force signal arising in a small pick-up coil wrapped around a sample which contains 1 – 5 mg of a magnetite powder. It is proved experimentally that the specific absorption rate diminishes approximately 4.5 times when the sample aspect ratio decreases from 11.4 to 1. Theoretical estimate shows that experimentally measured hysteresis loops can be approximately described only by taking into account appreciable contributions of magnetic nanoparticles of both very small, D < 10 – 12 nm, and rather large, D > 30 nm, diameters. Thus the wide particle size distribution has to be assumed

A set of equations describing the motion of a free magnetic nanoparticle in an external magnetic field in a vacuum, or in a medium with negligibly small friction forces is postulated. The conservation of the total particle momentum, i.e. the sum of the mechanical and the total spin momentum of the nanoparticle is taken into account explicitly. It is shown that for the motion of a nanoparticle in uniform magnetic field there are three different modes of precession of the unit magnetization vector and the director that is parallel the particle easy anisotropy axis. These modes differ significantly in the precession frequency. For the high-frequency mode the director points approximately along the external magnetic field, whereas the frequency and the characteristic relaxation time of the precession of the unit magnetization vector are close to the corresponding values for conventional ferromagnetic resonance. On the other hand, for the low-frequency modes the unit magnetization vector and the director are nearly parallel and rotate in unison around the external magnetic field. The characteristic relaxation time for the low-frequency modes is remarkably long. This means that in a rare assembly of magnetic nanoparticles there is a possibility of additional resonant absorption of the energy of alternating magnetic field at a frequency that is much smaller compared to conventional ferromagnetic resonance frequency. The scattering of a beam of magnetic nanoparticles in a vacuum in a non-uniform external magnetic field is also considered taking into account the precession of the unit magnetization vector and director.

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