Complete Multipole Basis Set for Single-Centered Electron Systems
Abstract
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.
Cite
@article{arxiv.2007.08039,
title = {Complete Multipole Basis Set for Single-Centered Electron Systems},
author = {Hiroaki Kusunose and Rikuto Oiwa and Satoru Hayami},
journal= {arXiv preprint arXiv:2007.08039},
year = {2020}
}
Comments
10 pages, 4 figures, 3 tables, plus 27 pages supplemental materials (some corrections are made)