Globally correlated states and control of vortex lattices in active roller fluids

Active fluids demonstrate complex collective behavior and self-organization often resulting in the emergence of localized vortices. We report on a combined experimental and computational study of the spontaneous formation of globally correlated vortex lattices formed in active roller fluids. The vortices are comprised of active ferromagnetic rollers placed on a patterned substrate promoting localization of self-organized vortices in a lattice with square symmetry. Each individual vortex spontaneously selects its chiral state (clockwise or counterclockwise). Nevertheless, confined to a square lattice, an ensemble of interacting active vortices is capable of developing correlations between chiral states of neighboring vortices. We show that such ensembles of active vortices can spontaneously evolve towards a globally correlated state with the antiferromagnetic ordering of their vorticities. We explore the correlations between chiral states of neighboring vortex pairs in response to changes in the geometry of the confining lattice. The results are supported by numerical simulations based on phenomenological coarse grained particle dynamics coupled to shallow water Navier-Stokes hydrodynamics. We show that these ordered vortex lattices formed by magnetic rollers have the ability to self-heal the antiferromagnetic order and stabilize individual vortical states in the activity regimes beyond optimal conditions for the collective vortex states. The results provide insights into the collective behavior of active magnetic roller fluids in the presence of geometrical confinement.