Three dimensional dynamics of ferromagnetic swimmer

It is shown that a flexible ferromagnetic filament self-propels perpendicularly to the AC magnetic field during a limited period of time due to the instability of the planar motion with respect to three dimensional perturbations. The transition from the oscillating U-like shapes to the oscillating S-like shapes is characterized by the calculated Wr number. ►A ferromagnetic filament self-propels perpendicularly to the AC field. ►During the self-propulsion cycle the filament moves both forward and backward. ►The self-propulsion stops due to the three dimensional instability. ►The mechanism of the self-propulsion is similar to that used by some microorganisms.