Curvature as an external field in mechanical antiferromagnets
arXiv:2208.01085 · doi:10.1103/PhysRevMaterials.6.115203
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.
arXiv comment20 pages, 12 figures
References in corpus (32)
- Local strain engineering in atomically thin MoS2
- Gauge fields in graphene
- Periodically rippled graphene: growth and spatially resolved electronic structure
- Origami Multistabilty: From Single Vertices to Metasheets
- Multiferroic Two-Dimensional Materials
- Geometric Frustration in Buckled Colloidal Monolayers
- Cycloaddition Functionalizations to Preserve or Control the Conductance of Carbon Nanotubes
- Adhesion, Stiffness and Instability in Atomically Thin MoS2 Bubbles
- Morphing of Geometric Composites via Residual Swelling
- Strain Modulated Superlattices in Graphene
- Piezoelectricity and valley Chern number in inhomogeneous hexagonal 2D crystals
- Reversal mechanism of an individual Ni nanotube simultaneously studied by torque and SQUID magnetometry
- Complex pathways and memory in compressed corrugated sheets
- Fluctuating shells under pressure
- Memory from coupled instabilities in unfolded crumpled sheets
- Snap-induced morphing: From a single bistable shell to the origin of shape bifurcation in interacting shells
- Non-Hookean statistical mechanics of clamped graphene ribbons
- Mechanical Properties of Warped Membranes
- Photoluminescence from Single-Walled MoS Nanotubes Coaxially Grown on Boron Nitride Nanotubes
- Statistical mechanics of thin spherical shells
- Two-dimensional Square Buckled Rashba Lead Chalcogenides
- Strain-induced gauge and Rashba fields in ferroelectric Rashba lead chalcogenide PbX monolayers (X = S, Se, Te)
- Buckling of thermalized elastic sheets
- Thermal buckling and symmetry breaking in thin ribbons under compression
- Buckling and metastability in membranes with dilation arrays
- A shapeable material without plastic deformation
- Thermal stiffening of clamped elastic ribbons
- STM driven transition from rippled to buckled graphene in a spin-membrane model
- Evolution of elastic moduli through a two-dimensional structural transformation
- Indentation responses of pressurized ellipsoidal and cylindrical elastic shells: Insights from shallow-shell theory
- Strain-engineered wrinkles on graphene using polymeric actuators
- Shape multistability in flexible tubular crystals through interactions of mobile dislocations