Windmilling clusters of active quadrupoles

Active matter has thrived in recent years, driven both by the insight that it underlies fundamental processes in nature, and by its vast potential for applications. This allows for innovation both inspired by experimental observations, and by construction of novel systems with desired properties. In this paper, we develop a novel system in the search for a new kind of pattern formation: microstructural motifs with orthogonal alignment. Taking a simple active Brownian particle (ABP) model applied to dumbbell-shaped particles, we add a quadrupolar interaction by positioning two antiparallel magnetic dipolar moments on each particle. We find that the phase behavior is determined by the competition between active motion and the orthogonal alignment favored by quadrupolar attraction. By varying these quantities, we are able to tune both the internal structure of the aggregates, and find a surprising stability of triangular aggregates, to the point of clusters of size $N=3$ being strongly overrepresented. Although none of the component particles are chiral, the resulting structures spin in a random, fixed direction due to combination of the polarity of the active motion. This results in an ensemble of windmilling (randomly spinning in a circular motion) aggregates with windmill-like shape (due to the three- or four core component dumbbells). Ultimately, this simple model shows an interesting range of microstructural motifs, with great potential for experimental implementations.