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<p>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 advent of altermagnets and p-wave magnets raises new challenges to this long-standing framework, which calls for a new and unified one. Here we develop a multicolor group classification framework to classify nonmagnetic materials and magnets with collinear or non-collinear magnetism, and with or without spin-orbit coupling (SOC), including the recently identified altermagnets and p-wave magnets. Especially, altermagnetic topological matter with SOC and p-wave magnets can also be diagnosed with multicolor groups, a task which cannot 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 matter.</p>

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Multicolor groups for molecules and solids

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月29日

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  • Hai-Yang Ma,
  • Shihao Zhang,
  • Hu Xu,
  • Shengbai Zhang,
  • Jin-Feng Jia

摘要

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 advent of altermagnets and p-wave magnets raises new challenges to this long-standing framework, which calls for a new and unified one. Here we develop a multicolor group classification framework to classify nonmagnetic materials and magnets with collinear or non-collinear magnetism, and with or without spin-orbit coupling (SOC), including the recently identified altermagnets and p-wave magnets. Especially, altermagnetic topological matter with SOC and p-wave magnets can also be diagnosed with multicolor groups, a task which cannot 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 matter.