Dynamics of magnetic self-propelled particles in a harmonic trap

Artificial active particles provide a powerful platform to investigate non-equilibrium collective behavior. Here, we use Hexbugs equipped with embedded magnetic dipoles as macroscopic realizations of magnetic self-propelled particles (MSPPs) to study active matter under confinement. By combining experiments and simulations, we analyze their dynamics within a parabolic domain modeled as a symmetric external harmonic potential. We uncover a rich landscape of metastable and dynamically evolving configurations, including climbing chains, polarized orbiting clusters, and rotating ring-like states, arising from the competition between dipolar interactions, confinement, and activity. While orbiting states are recovered at the single-particle level, we show that self-alignment alone does not determine the collective dynamics, which instead emerge from magnetic interactions. We demonstrate that the number of particles and the relative strength of magnetic interactions and harmonic confinement control the structure and stability of these states. Our experimental observations are quantitatively reproduced by a minimal model of disk-like magnetic active Brownian particles with inertial translational dynamics and overdamped orientation. These results provide a unified framework for understanding structure formation and dynamical states in confined active systems with dipolar interactions.