Critical density for the stability of a 2D magnet array

Abstract

Abstract. 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.

Frequency dynamics of a chain of magnetized rotors: dumbbell model vs Landau–Lifshitz equation

“…Similarly, the dynamics of two oscillating magnets with different moments of inertia has also been studied, reporting either fluctuation around a stable fixed point or stochastic reversals between stable fixed points [33]. In systems with more than two magnets, it has been shown that a 2D hexagonal array can self-organize by repulsive forces, but has a structural collapse after surpassing a critical density [34]. The macroscopic frustration in a system with competition between the dipolar interactions and the external field also has been studied [35].…”