Critical density for the stability of a 2D magnet array

Confining a given number of magnets with vertically aligned moments on a non-magnetic surface creates a 2D magnet array, self-organized by repulsive forces in a hexagonal crystal-like network. Increasing areal density leads to a dramatic collapse of the structure where magnets finally stick together. We study the origin of this collapse and its critical density both experimentally, by either increasing the number of magnets or reducing the area, and theoretically, by using a dipole model. We suggest the collapse occurs when magnetic forces or torques created by irregularities overcome gravity. Transition from torque-driven to force-induced mechanism is observed when the critical density increases.