Multipole classification in 122 magnetic point groups for unified understanding of multiferroic responses and transport phenomena

TL;DR

This paper classifies all multipoles in 122 magnetic point groups to connect microscopic degrees of freedom with macroscopic responses, aiding the discovery of multiferroic materials.

Contribution

It provides a comprehensive group-theoretical classification of multipoles in all magnetic point groups, linking them to physical responses and material design.

Findings

Classified multipoles in all 122 magnetic point groups.

Identified multipoles relevant for various physical responses.

Provided insights into microscopic origins of cross-correlated phenomena.

Abstract

Mutual interplay between the electronic degrees of freedom in solids, such as charge, spin, orbital, sublattice, and bond degrees of freedom, is a source of cross-correlated phenomena with unconventional electronic ordered states. Such degrees of freedom can be described by four types of multipoles (electric, magnetic, magnetic toroidal, and electric toroidal) in a unified way, which enable us to tightly connect the microscopic degrees of freedom with macroscopic physical responses in a transparent manner. We complete a classification of the multipoles in all 122 magnetic point groups based on the group theory. The classification is useful to identify potentially active multipoles not only in ordinary ferromagnetic and antiferromagnetic orderings but also in exotic orderings breaking time-reversal symmetry, e.g., a loop-current state. Moreover, the classification gives an insight into the microscopic origin of the cross-correlated responses and quantum transports. By analyzing response functions up to the second order, we summarize the indispensable multipole moments for various responses, such as the linear magnetoelectric, piezoelectric, and elastic responses, and the nonlinear conductivity and Nernst coefficient. Our results highly promote a further discovery of functional multiferroic materials, guided by the bottom-up material design based on the symmetry-adapted multipoles.