Topologically Protected Steady Cycles in an Ice-Like Mechanical Metamaterial

TL;DR

This paper introduces a mechanical metamaterial inspired by spin ice, demonstrating topologically protected steady cycles, controllable domain wall behaviors, and complex multistable states useful for studying material memory and glassiness.

Contribution

It presents a novel mechanical spin-ice system with tunable domain wall dynamics and topologically protected steady cycles, expanding understanding of topological excitations beyond magnetic systems.

Findings

Controlled domain wall propagation and morphology in the metamaterial.

Observation of a first-order dynamical transition with driving frequency.

Multiple topologically-distinct steady cycles induced by textured forcing.

Abstract

Competing ground states may lead to topologically constrained excitations such as domain walls or quasiparticles, which govern metastable states and their dynamics. Domain walls and more exotic topological excitations are well studied in magnetic systems such as artificial spin ice, in which nanoscale magnetic dipoles are placed on geometrically frustrated lattices, giving rise to highly degenerate ground states. We propose a mechanical spin-ice constructed from a lattice of floppy, bistable square unit cells. We compare the domain wall excitations that arise in this metamaterial to their magnetic counterparts, finding that new behaviors emerge in this overdamped mechanical system. By tuning the ratios of the internal elements of the unit cell, we control the curvature and propagation speed of internal domain walls. We change the domain wall morphology from a binary, strictly spin-like regime, to a more continuous, elastic regime. In the elastic regime, we inject, manipulate, and expel domain walls via textured forcing at the boundaries. The system exhibits dynamical hysteresis, and we find a first-order dynamical transition as a function of the driving frequency. We demonstrate a forcing protocol that produces multiple, topologically-distinct steady cycles, which are protected by the differences in their internal domain wall arrangements. These distinct steady cycles rapidly proliferate as the complexity of the applied forcing texture is increased, thus suggesting that such mechanical systems could serve as useful model systems to study multistability, glassiness, and memory in materials.