  We formulate and solve the equations governing the dynamics of a microscopic
artificial swimmer composed of a head and of a tail made of a thin film of
permanent magnetic material. This is a variant of the model swimmer proposed by
Dreyfus et al. in 2005, whose tail is a filament obtained from the assembly of
super-paramagnetic beads. The swimmer is actuated by an oscillating magnetic
field, and its geometry is inspired by that of sperm cells. Using values for
the geometric and material parameters that are realistic for a magnetic
multilayer, we show that the model swimmer can reach swimming speeds exceeding
one body length per second, under reasonable values of the driving magnetic
field. This provides a proof of principle for the viability of the concept. In
addition, we discuss the possibility to steer the system along curved paths.
Finally, we compare the propulsion mechanism (swimming `gait') of our swimmer
with that of sperm cells. The main difference between the two is that, contrary
to its biological template, our artificial system does not rely on the
propagation of bending waves along the tail, at least for the range of material
and geometric parameters explored in this article.
