Group-theoretical classification of multipole order: emergent responses and candidate materials

TL;DR

This paper develops a group-theoretical framework to classify multipole orders in solids, revealing dualities and electromagnetic responses, and identifies over 110 candidate materials with emergent properties.

Contribution

It introduces a novel classification theory for multipole order in solids, linking symmetry properties to electromagnetic responses and predicting candidate materials.

Findings

Revealed duality between real space and momentum space in odd-parity multipole order.

Clarified electromagnetic responses such as magnetoelectric and Edelstein effects in these states.

Identified over 110 candidate materials exhibiting odd-parity multipole order.

Abstract

The multipole moment is an established concept of electrons in solids. Entanglement of spin, orbital, and sublattice degrees of freedom is described by the multipole moment, and spontaneous multipole order is a ubiquitous phenomenon in strongly correlated electron systems. In this paper, we present group-theoretical classification theory of multipole order in solids. Intriguing duality between the real space and momentum space properties is revealed for odd-parity multipole order which spontaneously breaks inversion symmetry. Electromagnetic responses in odd-parity multipole states are clarified on the basis of the classification theory. A direct relation between the multipole moment and the magnetoelectric effect, Edelstein effect, magnetopiezoelectric effect, and dichromatic electron transport is demonstrated. More than 110 odd-parity magnetic multipole materials are identified by the group-theoretical analysis. Combining the list of materials with the classification tables of multipole order, we predict emergent responses of the candidate materials.