TY - JOUR

T1 - Complete multipole basis set for single-centered electron systems

AU - Kusunose, Hiroaki

AU - Oiwa, Rikuto

AU - Hayami, Satoru

N1 - Funding Information:
Acknowledgments We would like to thank Yuichi Yamasaki, Hironori Nakao, and Hiroshi Amitsuka for fruitful discussions on XMCD spectra. This work was supported by JSPS KAKENHI Grants Numbers JP15H05885, JP18H04296 (J-Physics), JP18K13488, JP19K03752, JP19H01834, and JP20J21838.

PY - 2020/9/16

Y1 - 2020/9/16

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85092281147&partnerID=8YFLogxK

U2 - 10.7566/JPSJ.89.104704

DO - 10.7566/JPSJ.89.104704

M3 - Article

AN - SCOPUS:85092281147

VL - 89

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 10

M1 - 104704

ER -