Magnetic long-range order in real icosahedral quasicrystals

Determine whether magnetic long-range order is realized in real quasicrystals, including whether the experimentally studied icosahedral quasicrystals support such order despite their aperiodic structures.

Background

The paper situates magnetic ordering in quasicrystals as a major unresolved issue because quasicrystals lack translational symmetry and therefore cannot be treated using conventional Bloch-theorem-based approaches. Although magnetic long-range order has been observed in several approximant crystals and in some rare-earth-based quasicrystals, the existence of magnetic long-range order in real quasicrystals remains unresolved in the statement quoted by the authors.

The paper subsequently studies noncollinear magnetic structures and magnetic-toroidal multipoles in Ce-based icosahedral quasicrystal clusters, but it does not experimentally establish the realization of magnetic long-range order in real quasicrystals.