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We have developed a tunable colloidal system and a corresponding simulationmodel for studying the phase behavior of particles assembling under theinfluence of long-range magnetic interactions. A monolayer of paramagneticparticles is subjected to a spatially uniform magnetic field with a staticperpendicular component and rapidly rotating in-plane component. The sign andstrength of the interactions vary with the tilt angle $\theta$ of the rotatingmagnetic field. For a purely in-plane field, $\theta=90^{\circ}$, interactionsare attractive and the experimental results agree well with both equilibriumand out-of-equilibrium predictions based on a two-body interaction model. Fortilt angles $50^{\circ}\lesssim \theta\lesssim 55^{\circ}$, the two-bodyinteraction gives a short-range attractive and long-range repulsive (SALR)interaction, which predicts the formation of equilibrium microphases. Inexperiments, however, a different type of assembly is observed. Inclusion ofthree-body (and higher-order) terms in the model does not resolve thediscrepancy. We thus further characterize the anomalous behavior by measuringthe time-dependent cluster size distribution.

Phase diagram and aggregation dynamics of a monolayer of paramagnetic colloids