Classification of atomic-scale multipoles under crystallographic point groups and application to linear response tensors

Satoru Hayami, Megumi Yatsushiro, Yuki Yanagi, Hiroaki Kusunose

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)

Abstract

Four types of atomic-scale multipoles (electric, magnetic, magnetic toroidal, and electric toroidal multipoles) give a complete set to describe arbitrary degrees of freedom for coupled charge, spin, and orbital of electrons. We here present a systematic classification of these multipole degrees of freedom towards the application in condensed matter physics. Starting from the multipole description under the rotation group in real space, we generalize the concept of multipoles in momentum space with the spin degree of freedom. We show how multipoles affect the electronic band structure and linear responses, such as the magnetoelectric effect, magnetocurrent (magnetogyrotropic) effect, spin conductivity, piezoelectric effect, and so on. Moreover, we exhibit a complete table to represent the active multipoles under 32 crystallographic point groups. Our comprehensive and systematic analyses will give a foundation to identify enigmatic electronic order parameters and a guide to evaluate peculiar cross-correlated phenomena in condensed matter physics from the microscopic point of view.

Original languageEnglish
Article number165110
JournalPhysical Review B
Volume98
Issue number16
DOIs
Publication statusPublished - 2018 Oct 8

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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