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Emergent magnetic ordering and topological frustration in quasicrystal artificial spin ices

Artificial spin ices (ASIs) are nanoscale geometrically engineered arrays of magnetic bars or islands that display magnetic frustration and provide a fertile system for modeling and testing many complex statistical mechanics theories and emergent phenomena. Aperiodic ASIs display spatially varying magnetic frustration as a result of the aperiodicity. We have explored the magnetization reversal of quasicrystalline ASIs (QC-ASIs) patterned on P2 and P3 Penrose tilings, using a statistical graph-theory approach that enables quantitative comparison between the two tilings. Our approach offers insight into the QC-ASIs. We show that the P2 tiling leads to enhanced topological frustration compared to the P3 tiling, and we elucidate the emergence of local antiferromagnetic ordering as well as disordered states in these ferromagnetic aperiodic lattices. Our method enables quantitative exploration of frustration behavior on any periodic or aperiodic lattice, thereby opening pathways to study collective behavior in various topologically frustrated systems.