  We study the deterministic dynamics of single-domain ferromagnetic
nanoparticles in a viscous liquid induced by the joint action of the gradient
and uniform magnetic fields. It is assumed that the gradient field depends on
time harmonically and the uniform field has two components, perpendicular and
parallel to the gradient one. We also assume that the anisotropy magnetic field
is so strong that the nanoparticle magnetization lies along the anisotropy
axis, i.e., the magnetization vector is "frozen" into the particle body. With
these assumptions and neglecting inertial effects we derive the torque and
force balance equations that describe the rotational and translational motions
of particles. We reduce these equations to a set of two coupled equations for
the magnetization angle and particle coordinate, solve them numerically in a
wide range of the system parameters and analyze the role of the parallel
component of the uniform magnetic field. It is shown, in particular, that
nanoparticles perform only periodic rotational and translational motions if the
perpendicular component of the uniform magnetic field is absent. In contrast,
the nanoparticle dynamics in the presence of this component becomes
non-periodic, resulting in the drift motion (directed transport) of
nanoparticles. By analyzing the short and long-time dependencies of the
magnetization angle and particle coordinate we show that the increase in the
parallel component of the uniform magnetic field decreases both the particle
displacement for a fixed time and its average drift velocity on each period of
the gradient magnetic field.
