Effects of Electron Correlation and Geometrical Frustration on Magnetism of Icosahedral Quasicrystals and Approximants - An Attempt to Bridge the Gap between Quasicrystals and Heavy Fermions

Icosahedral quasicrystals (QCs), which are long-range ordered materials featuring a symmetry incompatible with translational invariance, have received a revived interest since the observation of their non-Fermi liquid (FL) behaviors, owing to an interest in the strong correlation effects developing in quasiperiodic structures. Herein, we review the progress in our understanding of magnetism in QCs, with an emphasis on the comparison with approximant crystals (ACs) and heavy fermions (HFs). ACs are solids that possess similar local structures (clusters) as QCs but form a periodic array of clusters, and HFs are periodic crystals showing a strong electron correlation effect (e.g., the Kondo effect) and unconventional quantum criticality. Topics discussed in this review lie at the crossroads of two fundamental enterprises (i.e., QCs and HFs) in condensed matter physics. Therefore, the fundamentals of QC structures and the basic notions of HF physics are introduced for readers who are unfamiliar with either QCs or HFs. According to a recent cutting-edge experiment, the mean valence of Yb exhibits instability at a critical lattice parameter, independently of whether the global structure is quasiperiodic or periodic. In contrast, the QC and AC exhibit a difference in the emergence of divergence in their magnetic susceptibility under pressure, which is considered to be an effect of the quasiperiodic structure on physical properties. Using these results, we reveal novel structure???property relationships (e.g., the interrelation between quasiperiodicity and quantum critical behavior) and discuss how the quantum criticality results from quantum critical valence fluctuations. We further discuss the possible presence of the quantum critical phase, a new state of matter, in the QC. In addition, an overview of the local moment magnetism of ACs is given with a focus on geometrical-frustration effects. Throughout the review, we attempt to develop a unified view on the magnetism of these intriguing materials.