  A quantum critical behavior of the magnetic susceptibility was observed in a
quasicrystal containing ytterbium. At the same time, a mixed-valence feature of
Yb ions was reported, which appears to be incompatible with the magnetic
instability. We derive the magnetic susceptibility by expressing the
quasiperiodicity as the distributed hybridization strength between Yb 4f and
conduction electrons. Assuming a wide distribution of the hybridization
strength, the most f electrons behave as renormalized paramagnetic states in
the Kondo or mixed-valence regime, but a small number of f moments remain
unscreened. As a result, the bulk magnetic susceptibility exhibits a nontrivial
power-law-like behavior, while the average f-electron occupation is that of
mixed-valence systems. This model thus resolves two contradictory properties of
Yb quasicrystals.
