Phase diagram and aggregation dynamics of a monolayer of paramagnetic colloids

We have developed a tunable colloidal system and a corresponding theoretical model for studying the phase behavior of particles assembling under the influence of long-range magnetic interactions. A monolayer of paramagnetic particles is subjected to a spatially uniform magnetic field with a static perpendicular component and a rapidly rotating in-plane component. The sign and strength of the interactions vary with the tilt angle θ of the rotating magnetic field. For a purely in-plane field, θ=90^{∘}, interactions are attractive and the experimental results agree well with both equilibrium and out-of-equilibrium predictions based on a two-body interaction model. For tilt angles 50^{∘}≲θ≲55^{∘}, the two-body interaction gives a short-range attractive and long-range repulsive interaction, which predicts the formation of equilibrium microphases. In experiments, however, a different type of assembly is observed. Inclusion of three-body (and higher-order) terms in the model does not resolve the discrepancy. We further characterize the anomalous regime by measuring the time-dependent cluster size distribution.