  We study the nonlinear dynamics of single-domain ferromagnetic nanoparticles
in a viscous liquid induced by a harmonically oscillating gradient magnetic
field in the absence and presence of a static uniform magnetic field. Under
some physically reasonable assumptions, we derive a coupled set of stiff
ordinary differential equations for the magnetization angle and particle
coordinate describing the rotational and translational motions of
nanoparticles. Analytical solutions of these equations are determined for
nanoparticles near and far from the coordinate origin, and their correctness is
confirmed numerically. We show that if a uniform magnetic field is absent, the
magnetization angle and particle coordinate of each nanoparticle are periodic
functions of time. In contrast, the presence of a uniform magnetic field makes
these functions aperiodic. In this case, we perform a detailed analysis of the
nanoparticle dynamics and predict the appearance of the drift motion (directed
transport) of nanoparticles. We calculate both analytically and numerically the
drift velocity, study its dependence on time and model parameters, analyze the
physical origin of the drift phenomenon and discuss its potential biomedical
applications.
