Crystalline Electronic Field in Rare-Earth Based Quasicrystal and Approximant: Analysis of Quantum Critical Au–Al–Yb Quasicrystal and Approximant

On the basis of point charge model, we formulate crystalline electronic field (CEF) Hamiltonian HCEF in rare-earth based quasicrystal (QC) and approximant crystal (AC) with ligand ions located at pseudo 5-fold configurations by using operator equivalent method. By setting total angular momentum J = 7/2, CEF quantum critical QC Au51Al34Yb15 1/1 AC Au51Al35Yb14 is analyzed consideration for effect Al/Au mixed sites. We find that ratio valences x ZAl/ZAu plays an important role characterizing ground state. As decreases from 3, 4f wave function state flat shape lying mirror plane deformed around ≈ 0.8 to perpendicular axis 0. The formulated generally applicable rare-earth-based QCs ACs, which useful analyze CEF.