{'fraction_non_alphanumeric': 0.016791044776119403, 'fraction_numerical': 0.0, 'mean_word_length': 6.25, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Ordering of sedimenting paramagnetic colloids in a monolayer.

Sedimentation enables self-assembly of colloidal particles into crystalline structures, as needed for catalysis or photonics applications. Here we combine experiments, theory, and simulations to investigate the equilibrium structure of a colloidal monolayer with tunable interparticle repulsion via an applied external magnetic field. Experimental observations of the equilibrium structure are in excellent agreement with density functional theory. Within a (zero-temperature) local density approximation, we derive a simple analytical expression that quantitatively captures the inhomogeneous ordering ranging from solid to liquidlike states. Monte Carlo simulations corroborate these findings and explore an even wider range of sedimentation conditions, thus providing a global view of the sedimentation-mediated ordering in colloidal monolayers with tunable long-ranged interparticle repulsions. Our findings shed further light on the classical sedimentation problem in colloidal science and related areas.