Excitation caging in a vertex-frustrated quasiperiodic Einstein artificial spin ice

RESUMO

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.