Progress of theories and experiments of the quantum valence criticality is overviewed focusing on recent discoveries of direct evidence of quantum critical point of valence transitions in periodic crystal $\alpha$-YbAl$_{ 1-x}$Fe$_x$B$_4$ at $x=0.014$ and quasicrystal Yb$_{ 15}$(Al$_{ 1-x} $Ga$_{ x}$)$_{ 34}$(Au$_{ 1-y}$Cu$_{ y}$)$_{ 51}$ at $x=y=0$. The common quantum criticality as well as $T/B$ scaling behavior in the magnetization observed in the periodic crystal $\beta$-YbAlB$_4$ and quasicrystal Yb$_{ 15}$Al$_{ 34}$Au$_{ 51}$ is shown to be explained from the theory of critical Yb-valence fluctuations starting from the Hamiltonians for describing the low-energy electronic states in both systems.
Categories: cond-mat.str-el cond-mat.mtrl-sci