Unified Theory of Atomic-Group-Based Magnetism in Carbon Allotropes

Traditional carbon allotropes, such as graphene, diamond, nanotubes, and fullerenes, are typically nonmagnetic. However, recent experimental observations of intrinsic magnetism challenge conventional theories. The microscopic origin, exchange interactions, and design strategies for magnetic carbon structures, particularly three-dimensional (3D) allotropes, remain elusive. Here, combining first-principles calculations with hybrid orbital analysis, we establish a unified framework showing that magnetism arises from symmetry breaking of unhybridized 2p orbitals within atomic groups exhibiting bent sp-sp²or trigonal pyramidal sp²-sp³hybridizations. Distinct from conventional atomic-centered magnetism theories, our atomic-group-based paradigm systematically predicts magnetic carbon allotropes from zero-dimensional to 3D systems. We further propose a general design strategy and predict a family of metastable two-dimensional and 3D phases displaying intrinsic itinerant ferromagnetism or antiferromagnetism. These findings lay the groundwork for a p-block magnetism theory and open avenues for spintronic and quantum material design.