2020/07/31 by Hiroaki Kusunose, Rikuto Oiwa, Satoru Hayami · 1 citation
Materials Science · Physics and Astronomy · #Basis (linear algebra) #Basis set #Dipole #Electron #Magnetic dipole #Magnetic monopole #Magnetism in coordination complexes #Multipole expansion #Organic and Molecular Conductors Research #Physics of Superconductivity and Magnetism #Series (stratigraphy) #Toroid #cond-mat.str-el
paper · pdf · doi:10.7566/jpsj.89.104704
published as J. Phys. Soc. Jpn.,89, 104704 (2020) · 10 pages, 4 figures, 3 tables, plus 27 pages supplemental materials (some corrections are made)
openalex created_date 2020/07/23 · arxiv created 2020/09/10 · openalex publication_date 2020/09/16 · arxiv updated 2020/09/17 · openalex updated_date 2026/08/05
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 state, 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.