Excitation caging in a vertex-frustrated quasiperiodic Einstein artificial spin ice
Abstract
Naturally occurring bulk quasicrystals are rare, and magnetic instances are rarer still, with chemical constraints typically permitting the synthesis of approximants rather than true quasicrystalline magnets. Here, we present an artificial spin ice based on a recently discovered Einstein lattice, the Hat tiling, which is built from the first known shape - the hat - that tiles the plane only aperiodically. The Einstein artificial spin ice has long-range structural order with no translational symmetry, and low-connectivity vertices with well-defined local ground states and excitations. Together, these properties provide a model two-dimensional quasicrystalline magnet, with magnetic correlations that we probe with magnetic force microscopy and parallel-tempered Monte Carlo simulations. We identify a two-stage partial ordering process, driven by the competition between two possible positions for magnetic excitations. This competition is resolved in the ground-state manifold, where exactly one magnetic excitation is caged on each antihat, yet the manifold remains macroscopically degenerate. This yields an unusual type of medium-range order, where the underlying quasiperiodic long-range order is randomly modulated by a strictly constrained disorder. Our findings establish the Einstein artificial spin ice as a blueprint for understanding quasicrystalline magnetism, demonstrating how quasiperiodic monotile geometries can be exploited to engineer unconventional magnetic phases with no direct equivalent in periodic systems.
Related
- Multi-flux Aharonov-Bohm caging with tunable couplings
- Dyonic black holes in Lorentz-violating gravity with a background Kalb-Ramond field: Quasiperiodic oscillations and radiative properties
- Magnon superlattices around skyrmions in frustrated magnets
- Vortex order in magnetic frustrated GeNi2O4 and GeCo2O4 spinels
- Smooth perturbation theory and generic Cantor spectrum for multi-dimensional monotone quasiperiodic operators
BibTeX
@misc{wang2026excitation,
title = {{Excitation caging in a vertex-frustrated quasiperiodic Einstein artificial spin ice}},
author = {Tianyue Wang and F. Museur and G. Macauley and J. Colbois and L. Berchialla and F. Flicker and P. Derlet and L. Heyderman},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04854},
eprint = {2609.04854},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05776184v1},
}
RIS
TY - UNPB
TI - Excitation caging in a vertex-frustrated quasiperiodic Einstein artificial spin ice
AU - Tianyue Wang
AU - F. Museur
AU - G. Macauley
AU - J. Colbois
AU - L. Berchialla
AU - F. Flicker
AU - P. Derlet
AU - L. Heyderman
PY - 2026
DA - 2026/09/04
PB - HAL
DO - 10.48550/arxiv.2609.04854
UR - https://hal.science/hal-05776184v1
AB - Naturally occurring bulk quasicrystals are rare, and magnetic instances are rarer still, with chemical constraints typically permitting the synthesis of approximants rather than true quasicrystalline magnets. Here, we present an artificial spin ice based on a recently discovered Einstein lattice, the Hat tiling, which is built from the first known shape - the hat - that tiles the plane only aperiodically. The Einstein artificial spin ice has long-range structural order with no translational symmetry, and low-connectivity vertices with well-defined local ground states and excitations. Together, these properties provide a model two-dimensional quasicrystalline magnet, with magnetic correlations that we probe with magnetic force microscopy and parallel-tempered Monte Carlo simulations. We identify a two-stage partial ordering process, driven by the competition between two possible positions for magnetic excitations. This competition is resolved in the ground-state manifold, where exactly one magnetic excitation is caged on each antihat, yet the manifold remains macroscopically degenerate. This yields an unusual type of medium-range order, where the underlying quasiperiodic long-range order is randomly modulated by a strictly constrained disorder. Our findings establish the Einstein artificial spin ice as a blueprint for understanding quasicrystalline magnetism, demonstrating how quasiperiodic monotile geometries can be exploited to engineer unconventional magnetic phases with no direct equivalent in periodic systems.
ER -