Multicolor groups for molecules and solids

TL;DR

This paper introduces a comprehensive multicolor group classification framework that unifies the symmetry analysis of molecules and solids, including complex magnetic states like altermagnets and p-wave magnets, surpassing traditional methods.

Contribution

The authors develop a novel multicolor group scheme that unifies the classification of all matter types, including nonmagnetic, collinear, non-collinear, and spin-orbit coupled magnets, addressing limitations of previous frameworks.

Findings

Unifies classification of magnetic and nonmagnetic materials.

Enables diagnosis of altermagnets and p-wave magnets with SOC.

Addresses misconceptions in traditional magnetic group theory.

Abstract

The local magnetic moments of atoms in a molecule or solid can be designated by different colors. Magnetic groups, or 2-color groups, or black-and-white groups have been applied in crystallography to classify different magnets. Despite its successes in the past decades, the recent advents of altermagnets and p-wave magnets raise new challenges to this long-standing framework, which urges for a new and unified one. Here we develop a multicolor group classification framework to classify all kinds of molecules and solids, including nonmagnetic materials and magnets with collinear or non-collinear magnetism, and with or without spin-orbit couplings (SOC). This new scheme can unify the classifications of matters into a single framework, including the recently identified altermagnets and p-wave magnets. Especially, altermagnetic topological matters and p-wave magnets with SOC, can also be diagnosed with multicolor groups, a task which can not be accomplished by magnetic space groups and spin space groups. Moreover, insufficiencies and misconceptions of conventional magnetic group classification can be supplemented through this new framework. Multicolor group will serve as a new stage in the symmetry classification of matters.