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Spontaneous order in ensembles of rotating magnetic droplets

Ensembles of elongated magnetic droplets in a rotating field are studied experimentally. In a given range of field strength and frequency the droplets form rotating structures with a triangular order - rotating crystals. A model is developed to describe ensembles of several droplets, taking into account the hydrodynamic interactions between the rotating droplets in the presence of a solid wall below the rotating ensemble. A good agreement with the experimentally observed periodic dynamics for an ensemble of four droplets is obtained. During the rotation, the tips of the elongated magnetic droplets approach close to one another. An expression is derived that gives the magnetic interaction between such droplets by taking into account the coulombian forces between magnetic charges on the droplet tips.