Complete Multipole Basis Set for Single-Centered Electron Systems
Complete Multipole Basis Set for Single-Centered Electron Systems
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DOI：
10.7566/jpsj.89.104704
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发表时间：
2020-10-15
影响因子：
1.7
通讯作者：
Hayami, Satoru
中科院分区：
文献类型：
--
作者：
Kusunose, Hiroaki;Oiwa, Rikuto;Hayami, Satoru
提供了四种多极（电、磁、磁环形和电环形）的完整系列表达式作为描述任意单中心自旋电子系统的完整基础集。还导出了计算这些多极子矩阵元素的紧凑公式。提出了一种以多极子为特征的电子状态的可视化方法。完整的基组可用于缩小相变中电子系统的候选有序参数范围、描述互相关现象的性质、分析磁有序状态下的 X 射线散射光谱等。我们通过以单极子和环形偶极子排序以及自旋轨道耦合系统中三个不同磁偶极子（轨道、自旋角动量和各向异性偶极子）之间的相互关系作为主要示例来演示完整基组的使用。
A whole series of expressions for four species of multipoles (electric, magnetic, magnetic toroidal, and electric toroidal) is provided as a complete basis set to describe arbitrary single-centered spinful electron systems. A compact formula to calculate matrix elements of these multipoles is also derived. A visualization method of an electronic state characterized in terms of multipoles is proposed. The complete basis set is useful to narrow down a candidate order parameter of electron systems in phase transition, to describe a property of cross-correlated phenomena, to analyze spectra of x-ray scattering in magnetically ordered states, and so on. We demonstrate a usage of the complete basis set by taking monopole and toroidal dipole orderings, and the mutual relationship among three distinct magnetic dipoles (orbital, spin angular momenta, and anisotropic dipole) in a spin-orbit coupled system as prime examples.