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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\u201380 Hz) yields optimal hexagonally ordered structures, and a full phase diagram covering clustered, ordered and disordered states is established. Binary mixtures of 200 \u03bcm and 300 \u03bcm 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.<\/jats:p>","DOI":"10.3390\/mi17091068","type":"journal-article","created":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T08:05:43Z","timestamp":1788941143000},"page":"1068","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Collective Motion and Programmable Self-Organization of Rotating Active Particles Manipulated by Magnetic Fields"],"prefix":"10.3390","volume":"17","author":[{"given":"Kailai","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Building Services Science and Engineering, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, 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X"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1038\/s42254-022-00445-3","article-title":"Topological active matter","volume":"4","author":"Shankar","year":"2022","journal-title":"Nat. Rev. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7035","DOI":"10.1038\/s41467-023-42713-5","article-title":"Non-reciprocity across scales in active mixtures","volume":"14","author":"Dinelli","year":"2023","journal-title":"Nat. Commun."},{"key":"ref_8","first-page":"e2515700","article-title":"Recent Advances in Collective Behaviors of Micro\/Nanomotor Swarms","volume":"38","author":"Sun","year":"2026","journal-title":"Adv. Mater."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1038\/s41567-024-02651-5","article-title":"Self-propulsion, flocking and chiral active phases from particles spinning at intermediate Reynolds numbers","volume":"21","author":"Chen","year":"2025","journal-title":"Nat. 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