Nuclear magnetic resonance reveals ‘forbidden’ symmetries in quasicrystals and related metallic alloys with giant unit cells

We report on measurements of angular dependences of the selectively excited NMR intensity in a decagonal AlNiCo quasicrystal, icosahedral AlPdMn quasicrystal and orthorhombic ξ′-AlPdMn single crystal with approximately 258 atoms in the unit cell. In all three cases, we found 10-fold rotation patterns, in agreement with structural properties of the investigated samples. However, in the orthorhombic ξ′-AlPdMn complex metallic alloy, a non-perfect 10-fold symmetry was observed, which is a consequence of periodicity that strictly forbids non-crystallographic rotational symmetries. These measurements represent a starting point for testing structural models of quasicrystals and related metallic alloys with giant unit cells by means of NMR.