  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.
