Reprogrammable self-assembly of magnetic lattices in two dimensions

Simple local interactions can cause primitive building blocks to self-assemble into complex and functional patterns; however, even for a small number of blocks, there exist a vast number of plausible and stable configurations with varying degrees of order. The ability to dynamically shift between multistable patterns (i.e., reprogram the self-assembly) entails navigating an intractable search space, which remains a challenge. In this paper, we engineer the self-assembly of macroscopic magnetic particles to create metamaterials with dynamically reversible emergent phases. We use a boundary composed of magnetic hinges to confine free-floating magnetic disks into different stable assemblies. We exploit the nondestructive nature of the magnetic boundaries to create reprogrammable two-dimensional metamaterials that morph from crystalline to quasicrystalline to disordered assembly using the same number of disks and the same boundary. Furthermore, we explore their utility in controlling the propagation of sound waves in an effectively undamped medium with rich nonlinearities. Our findings can broaden the horizon of metamaterials, enabling functional and tunable devices.