Collective Motion and Programmable Self-Organization of Rotating Active Particles Manipulated by Magnetic Fields

Rotating magnetic microparticles are classic active matter systems dominated by competing magnetic dipolar attraction and spin-induced hydrodynamic repulsion, whose collective behaviors under programmable magnetic field remain insufficiently characterized. This work builds a two-dimensional orthogonal Helmholtz coil experimental setup to investigate the collective motion and self-organization of magnetic microparticles. For single-component assemblies, the hexatic order parameter varies non-monotonically with driving frequency and particle area fraction; an intermediate frequency range (60-80 Hz) yields optimal hexagonally ordered structures, and a full phase diagram covering clustered, ordered and disordered states is established. Binary mixtures of 200 μm and 300 μm particles display hydrodynamic driven size segregation, with the segregation parameter peaking uniformly at 60 Hz. By applying programmable Lissajous-type magnetic fields with mismatched orthogonal frequencies, we achieve tunable elliptical particle trajectories and controlled splitting of particle clusters. This study reveals the coupling mechanism between magnetic and finite Reynolds number hydrodynamic interactions and proposes a programmable method to dynamically reconfigure active microparticle swarms.