Tunable dynamics of flexible magnetic microcrosses: synchronous rotation, breathing and out-of-plane arm overtaking.

We combine colloidal self-assembly and soft-lithography techniques to realize flexible magnetic microcrosses that can be manipulated via external, time dependent magnetic fields. The crosses are characterized by a central domain connected via four flexible arms. When subjected to an in-plane, rotating magnetic field, the crosses transit from a synchronous to an asynchronous spinning motion where their average rotation decreases with the driving frequency. In the asynchronous regime and at low field amplitudes, the crosses display a breathing mode, characterized by relative oscillations between the arms, while remaining localized in the two dimensional plane. In contrast, for high field amplitudes, we observe an arm overtaking regime where two opposite filaments surpass the remaining ones forcing the cross to perform a three-dimensional gyroscopic-like rotation. Using slender body theory and balancing the effect of magnetic and elastic interactions, we recover the experimental findings and show that the overtaking regime occurs due to different arm magnetizations. Our engineered microscopic colloidal rotors characterized by multiple flexible filaments may find potential applications for precise lab-on-a-chip operations or as stirrers dispersed within microfluidic or biological channels.