Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice

Abstract

Geometrically frustrated materials have a ground-state degeneracy that may be lifted by subtle effects, such as higher order interactions causing small energetic preferences for ordered structures. Alternatively, ordering may result from entropic differences between configurations in an effect termed order-by-disorder. Motivated by recent experiments in a frustrated colloidal system in which ordering is suspected to result from entropy, we consider in this paper, the antiferromagnetic Ising model on a deformable triangular lattice. We calculate the displacements exactly at the microscopic level, and contrary to previous studies, find a partially disordered ground state of randomly zigzagging stripes. Each such configuration is deformed differently and thus has a unique phonon spectrum with distinct entropy, thus lifting the degeneracy at finite temperature. Nonetheless, due to the free-energy barriers between the ground-state configurations, the system falls into a disordered glassy state.

Accepted to PNAS

References in corpus (22)

• Artificial "spin ice" in a geometrically frustrated lattice of nanoscale ferromagnetic islands
• Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets
• Order by distortion and string modes in pyrochlore antiferromagnet
• Spin Driven Jahn-Teller Distortion in a Pyrochlore system
• Geometric Frustration in Buckled Colloidal Monolayers
• Stacking Entropy of Hard Sphere Crystals
• Low-frequency vibrations of soft colloidal glasses
• Dynamic Phase Transition, Universality, and Finite-size Scaling in the Two-dimensional Kinetic Ising Model in an Oscillating Field
• Evidence for a dynamic phase transition in [Co/Pt]_3 magnetic multilayers
• Triangular Antiferromagnets
• Extreme sensitivity of a frustrated quantum magnet: Cs_2CuCl_4
• Density of states of colloidal glasses
• Stochastic Hysteresis and Resonance in a Kinetic Ising System
• The dynamics of thin vibrated granular layers
• Spin phonon induced colinear order and magnetization plateaus in triangular and kagome antiferromagnets. Applications to CuFeO_2
• Buckling Instabilities of a Confined Colloid Crystal Layer
• Most stable structure for hard spheres
• Magnetoelastic coupling in triangular lattice antiferromagnet CuCrS2
• Stripes, Zigzags, and Slow Dynamics in Buckled Hard Spheres
• A quest for frustration driven distortion in Y2Mo2O7
• The structure of the hard sphere solid
• Phonon Spectra, Nearest Neighbors, and Mechanical Stability of Disordered Colloidal Clusters with Attractive Interactions

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• Pseudo-Goldstone modes and dynamical gap generation from order-by-thermal-disorder
• Simulations of Frustrated Ising Hamiltonians with Quantum Approximate Optimization
• Topologically Protected Steady Cycles in an Ice-Like Mechanical Metamaterial
• Topology Restricts Quasidegeneracy in Sheared Square Colloidal Ice
• Attraction Controls the Inversion of Order by Disorder
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