Intrinsic excitations and a proposed ground state in an Ammann-Beenker artificial spin ice

Abstract

Artificial spin ices built on quasiperiodic geometries remain under-explored. Here we investigate an ASI based on the octagonal Ammann-Beenker tiling, whose six vertex types present local environments inaccessible in periodic lattices. Combining Monte Carlo simulations of dipolar-coupled macrospins with micromagnetic calculations of individual vertex energies, we find that vertex types freeze in an order set not by coordination number, but by quasi-degenerate levels at five-island vertices and their local environment. Excitations in the low energy state are correspondingly localised to specific, geometrically determined sites. Using twice-inflated substitution rules as an energetic backbone, we propose an analytical ground state combining a long-range ordered fixed spin network with a sparse set of degenerate regions.