Quasicrystals are metallic alloys that possess long-range, aperiodic structures with diffraction symmetries forbidden to conventional crystals. Since the discovery of quasicrystals by Schechtman et al. in 1984, there has been considerable progress in resolving their geometric structure. For example, it is well known that the golden ratio of mathematics and art occurs over and over again in their crystal structure. However, the characteristic properties of the electronic states--whether they are extended as in periodic crystals or localized as in amorphous materials--are still unresolved. Here we report the first observation of quantum (T = 0) critical phenomena of the Au-Al-Yb quasicrystal--the magnetic susceptibility and the electronic specific heat coefficient arising from strongly correlated 4f electrons of the Yb atoms diverge as T→0. Furthermore, we observe that this quantum critical phenomenon is robust against hydrostatic pressure. By contrast, there is no such divergence in a crystalline approximant, a phase whose composition is close to that of the quasicrystal and whose unit cell has atomic decorations (that is, icosahedral clusters of atoms) that look like the quasicrystal. These results clearly indicate that the quantum criticality is associated with the unique electronic state of the quasicrystal, that is, a spatially confined critical state. Finally we discuss the possibility that there is a general law underlying the conventional crystals and the quasicrystals.

Quantum criticality has been considered to be specific to crystalline materials such as heavy Tsai-type quasicrystal and that both possess no localized magnetic moment. We suggest that the Au-Al-Yb system is located near the border of the divalent and trivalent states of the Yb ion; we also discuss a possible origin of the disappearance of magnetism, associated with the valence change, by the substitution of the constituent elements.

We report the emergence of bulk superconductivity in Au64.0Ge22.0Yb14.0 and Au63.5Ge20.5Yb16.0 below 0.68 and 0.36 K, respectively. This is the first observation of superconductivity in Tsai-type crystalline approximants of quasicrystals. The Tsai-type cluster center is occupied by Au and Ge ions in the former approximant, and by an Yb ion in the latter. For magnetism, the latter system shows a larger magnetization than the former. To explain this observation, we propose a model that the cluster-center Yb ion is magnetic. The relationship between the magnetism and the superconductivity is also discussed.

We report on ac magnetic susceptibility measurements under pressure of the Au-Al-Yb alloy, a crystalline approximant to the icosahedral quasicrystal that shows unconventional quantum criticality. In describing the susceptibility as χ(T ) −1 − χ(0) −1 ∝ T γ , we find that χ(0) −1 decreases with increasing pressure and vanishes to zero at the critical pressure P c ' 2 GPa, with γ (' 0:5) unchanged. We suggest that this quantum criticality emerges owing to critical valence fluctuations. Above P c , the approximant undergoes a magnetic transition at T ' 100 mK. These results are contrasted with the fact that, in the quasicrystal, the quantum criticality is robust against the application of pressure. The applicability of the so-called T=H scaling to the approximant is also discussed.

A P-type icosahedral quasicrystal with a six-dimensional lattice parameter a6D = 7.411 Å is formed as an equilibrium phase in AuAlTm alloy, of which composition was analyzed to be Au46Al38Tm16 by electron probe microanalysis. This quasicrystal is observed as a predominant phase in both as-cast and Au49Al34Tm17 alloys annealed at 910• C, and as one of main phases in the alloy slowly cooled from 1020A 1/1 approximant, Au48Al38Tm14, is also formed near the composition of the quasicrystal. This is a body-centered cubic structure (space group: Im3) with a lattice parameter a = 14.458 Å that is an isostructure to the recently reported 1/1Tsai-type approximant in AuAlYb. This approximant is characterized by disorderly arranged four AuAl atoms centered at the Tsai-type cluster, presence of atoms at 8c site, and chemical ordering of Au and Al at sites forming a partial triacontahedron.