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Crystal Field Rotational Invariants: A New Light on the Crystal Field Effects
Physica Status Solidi (B) - Basic Solid State Physics ( IF 1.6 ) Pub Date : 2020-04-17 , DOI: 10.1002/pssb.202000064
Maciej Mulak 1 , Jacek Mulak 2
Affiliation  

Two types of rotational invariants related to the crystal field (CF) Hamiltonian parameters are exploited: three multipolar CF strengths S k = 2 2 , S k = 4 2 , and S k = 6 2 of the second order and nine invariants v 3 ( k 1 k 2 k 3 ) of the third order. They determine correspondingly the next generation of the CF invariants, i.e., the second and the third CF splitting moments of any electronic state | J . The analytical formulas are assembled for the third CF splitting moment in the case of higher symmetry, 24 out of 32 central ion point symmetry groups. Due to the multipolar additivity of the second CF splitting moment, its formula is irrespective of the central ion point symmetry. Comparing the calculated CF splitting moments with the experimental ones is a valuable source of independent relationships among the involved B k q CF parameters. The second CF splitting moments allow to preparameterize the CF Hamiltonian based on the S 2 2 , S 4 2 , and S 6 2 invariants. This reveals the actual multipolar structure of H CF . While only two independent second moments are available, a method to obtain the possible variation ranges of the multipolar S k 2 is given. In addition, the CF invariants provide an insight into the total CF splitting variation ranges under various unimodular H CF s .

中文翻译:

晶体场旋转不变量:晶体场效应的新光

利用了两种与晶体场(CF)哈密顿参数有关的旋转不变量:三个多极CF强度 小号 ķ = 2 2 小号 ķ = 4 2 小号 ķ = 6 2 二阶和九个不变式 v 3 ķ 1个 ķ 2 ķ 3 三阶。它们相应地确定下一代CF不变量,即任何电子状态的第二和第三CF分裂矩 | Ĵ 。在较高对称性的情况下,对于32个中心离子点对称性组中的24个,将为第三次CF分裂矩组装分析公式。由于第二CF分裂矩的多极加和性,其公式与中心离子点对称性无关。将计算出的CF分裂矩与实验值进行比较,是所涉及的独立关系的宝贵来源 ķ q CF参数。第二个CF分裂矩允许根据CF系数预先设定CF哈密顿量 小号 2 2 小号 4 2 小号 6 2 不变量 这揭示了实际的多极结构 H 碳纤维 。虽然只有两个独立的第二矩可用,但是一种获得多极可能变化范围的方法 小号 ķ 2 给出。此外,CF不变量提供了对各种单模量下总CF分裂变化范围的了解。 H 碳纤维 s
更新日期:2020-04-17
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