Crystals are characterized by a periodic arrangement of atoms and well-defined Bragg diffraction patterns with definite rotational symmetries. This notion about crystals was challenged by the discovery of quasicrystals (or QCs), materials with long-range order but a non-periodic atomic arrangement. Interest in QCs have been revived recently following the observation of non-Fermi liquid (FL) behavior and strong correlation effects associated with quasiperiodic structures.

In a recent review, researchers from Japan outlined these effects and other properties in icosahedral QCs, characterized by a diffraction pattern with five-fold symmetry. They compared the magnetic properties of QCs with two other unconventional systems, namely approximant crystals (or ACs), which show similar local structures as QCs, and heavy fermions (or HFs), periodic crystals with strong correlation effects and unusual quantum critical behavior.

In view of a recent cutting-edge experiment, the researchers compared the properties of Ytterbium (or Yb)-based QCs and ACs with HFs. They found that, at low temperatures, Yb ACs showed features similar to HFs, while QCs showed quantum critical behaviors owing to their quasiperiodicity. They also reviewed intriguing magnetic orders and textures, such as whirling structures and long-range hedgehog order, providing new aspects to the magnetism in ACs and QCs.

Furthermore, studies on strong electron correlation effect indicated that QCs and ACs exhibited critical lattice parameter anomalies, leading to quantum critical valence fluctuations that possibly caused the unusual quantum criticality and non-FL features.

The experiments further showed that the quantum criticality of QCs was robust against applications of both physical and chemical pressure, while in ACs, it appeared only at the critical pressure. Based on this observation, the researchers suggested the presence of a new state of matter in Yb QC.

This attempt to unify QCs, ACs, and HFs could mark the beginning of research into the development of novel functional materials.