Columnar dipolar clusters defying gravity

A striking and highly versatile feature of magnetic (nano)particles is their ability to be manipulated at will at a distance by external fields. In this paper, the influence of gravity on the self-assembly of dipolar particles near a surface in the presence of a strong vertical magnetic field is investigated theoretically. A rich ground-state phase diagram stems from the effects of the number of particles N and gravity. Two distinct regimes are discovered for the gravity-mediated breakup of a standing chain. When N is small, there is a chain fragmentation (with two widely separated repulsive chain fragments) above a critical value for the gravity, whereas for higher chains, ribbonization (with two cohesive chain fragments) sets in. In both scenarios, simple algebraic decays for the transition gravity as a function of N are analytically predicted and accurately corroborate the exact numerical results. Further intricate chain fragmentations and internal ribbon transformations operate upon further increasing the gravity until all N constitutive particles lie on the surface. Our findings shed additional light on various recent experiments and computer simulations on magnetic colloids and granular media.