  We study the effect of an elliptically polarized magnetic field on a system
of non-interacting, single-domain ferromagnetic nanoparticles characterized by
a uniform distribution of easy axis directions. Our main goal is to determine
the average magnetization of this system and the power loss in it. In order to
calculate these quantities analytically, we develop a general perturbation
theory for the Landau-Lifshitz-Gilbert (LLG) equation and find its steady-state
solution for small magnetic field amplitudes. On this basis, we derive the
second-order expressions for the average magnetization and power loss,
investigate their dependence on the magnetic field frequency, and analyze the
role of subharmonic resonances resulting from the nonlinear nature of the LLG
equation. For arbitrary amplitudes, the frequency dependence of these
quantities is obtained from the numerical solution of this equation. The impact
of transitions between different regimes of regular and chaotic dynamics of
magnetization, which can be induced in nanoparticles by changing the magnetic
field frequency, is examined in detail.
