Assembly of magnetic spheres in strong homogeneous magnetic field

The assembly in two dimensions of spherical magnets in strong magnetic field is addressed theoretically. It is shown that the attraction and assembly of parallel magnetic chains is the result of a delicate interplay of dipole-dipole interactions and short ranged excluded volume correlations. Minimal energy structures are obtained by numerical optimization procedure as well as analytical considerations. For a small number of constitutive magnets Ntot≤26, a straight chain is found to be the ground state. In the regime of larger Ntot≥27, the magnets form two touching chains with equally long tails at both ends. We succeed to identify the transition from two to three touching chains at Ntot=129. Overall, this study sheds light on the mechanisms of the recently experimentally observed ribbon formation of superparamagnetic colloids via lateral aggregation of magnetic chains in magnetic field (Darras et al., 2016).