On the basis of the point charge model, we formulate the crystalline electronic field (CEF) Hamiltonian H_CEF in 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 Au₅₁Al₃₄Yb₁₅ and the 1/1 AC Au₅₁Al₃₅Yb₁₄ 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.

中文翻译：

---

稀土基准晶体及其附近的晶体电场：量子临界Au-Al-Yb准晶体及其附近的分析

在点电荷模型的基础上，我们通过使用算符，在配体离子位于伪5倍构型的稀土基准晶体（QC）和近似晶体（AC）中制定了晶体电场（CEF）的哈密顿H _CEF等效方法。通过设置总角动量J = 7/2，考虑了Al / Au混合位点的影响，对量子临界QC Au ₅₁ Al ₃₄ Yb ₁₅和1/1 AC Au ₅₁ Al ₃₅ Yb _14中的CEF进行了分析。 。我们发现配体离子的化合价比x = Z _Al / Z _Au在表征CEF基态方面起着重要作用。作为X减小从X = 3，用扁平形状趴在镜平面上的CEF基态的4F波函数变形围绕X在≈0.8到平坦形状垂直于伪5倍轴X = 0。配制ħ _CEF通过Ĵ一般适用于基于稀土的QC和AC，来分析CEF这是有用的。