Curvature as an external field in mechanical antiferromagnets

TL;DR

This paper explores how curvature acts as an external field influencing phase transitions in mechanical antiferromagnets, enabling control over their magnetic-like ordering through geometric design.

Contribution

It introduces a theoretical and simulation-based framework showing how curvature can tune phase behavior in puckered crystalline membranes with bistable units.

Findings

Curvature induces a radius-dependent effective field affecting spin alignment.

The effective field scales inversely with the radius of curvature.

Simulations confirm curvature's role in stabilizing or disrupting ordered phases.

Abstract

A puckered sheet is a freestanding crystalline membrane with an embedded array of bistable buckled units. Recent work has shown that the bistable units behave like spins in a two-dimensional compressible Ising antiferromagnet with, however, a coupling to flexural phonons. At finite temperature, this purely mechanical system displays Ising-like phase transitions, which drive anomalous thermal expansion. Here, we show that geometry can be used to control phase behavior: curvature produces a radius-dependent "external field" that encourages alignment between neighboring "spins," disrupting the ordered checkerboard ground state of antialigned neighbors. The effective field strength scales as the inverse of the radius of curvature. We identify this effective field theoretically with both a discrete real space model and a nonlinear continuum elastic model. We then present molecular dynamics simulations of puckered sheets in cylindrical geometries at zero and finite temperature, probing the influence of curvature on the stability of configurations and phase transitions. Our work demonstrates how curvature and temperature can be used to design and operate a responsive and tunable metamaterial at either the macroscale or nanoscale.