期刊
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
卷 89, 期 10, 页码 -出版社
PHYSICAL SOC JAPAN
DOI: 10.7566/JPSJ.89.104704
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资金
- JSPS KAKENHI [JP15H05885, JP18H04296, JP18K13488, JP19K03752, JP19H01834, JP20J21838]
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.
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