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

Abstract

On the basis of the point charge model, we formulate the crystalline electronic field (CEF) Hamiltonian H CEF in the rare-earth based quasicrystal (QC) and approximant crystal (AC) with ligand ions located at pseudo 5-fold configurations by using the operator equivalent method. By setting the total angular momentum J = 7/2, the CEF in the quantum critical QC Au 51 Al 34 Yb 15 and the 1/1 AC Au 51 Al 35 Yb 14 is analyzed with consideration for the effect of Al/Au mixed sites. We find that the ratio of the valences of ligand ions x = Z Al /Z Au plays an important role in characterizing the CEF ground state. As x decreases from x = 3, the 4f wave function of the CEF ground state with the flat shape lying in the mirror plane is deformed around x ≈ 0.8 to the flat shape perpendicular to the pseudo 5-fold axis at x = 0. The formulated H CEF by J is generally applicable to rare-earth-based QCs and ACs, which is useful to analyze the CEF.