Self-assembly of magnetic balls: from chains to tubes.

The self-assembly of spherical magnets (magnetic balls) is addressed theoretically. Minimal energy structures are obtained by optimization procedures as well as Monte Carlo computer simulations. Three typical shapes are obtained depending on the number of constitutive magnets N. In the regime of small N, chains are stable as dimers or trimers (i.e., N = 14). The number of stacked rings is found to increase as N-2/3, leading to a tubular structure at large N. All the relevant predicted shapes are experimentally reproduced by manipulating millimetric magnets.