Theoretical design of graphene-C₂N₁ composites exhibiting intrinsic magnetic, superhard, and lightweight properties

Combining magnetic, superhard, and lightweight properties in a single material system remains largely elusive, primarily due to the conflicting nature of these properties. Here, we designed a series of such systems <i>via</i> stacking synthesized lightweight nanosheets of graphene and C₂N₁ in different sequences. First-principles calculations demonstrate that most of the designed systems successfully combine superhardness, magnetism, and low mass density. Specifically, all these systems demonstrate superhard characteristics with Vickers hardness ranging from 51.8 to 69.1 GPa. The magnetic ordering is governed by the distribution of three-fold carbon atoms surrounding the holes in C₂N₁ nanosheet, which is influenced by the stacking sequence of the precursor nanosheets. C₆N_1ABC, C₁₀N_1AA, and C₁₀N_1ABC possess antiferromagnetic ground states with magnetic moments of approximatively 0.26, 0.33, and 0.31<i>μ</i>_B on each magnetic C atoms, respectively, while C₆N_1AA is nonmagnetic. The magnetism in these systems arises from the disruption of the Kekulé valence structures. The intralayer magnetic ordering is attributed to the indirect exchange interaction <i>via</i> nonmagnetic carbon atoms, while the interlayer magnetic ordering is determined by direct exchange interaction. Notably, all systems exhibit both dynamic and mechanical stability, implying that their stability is independent of the stacking sequence. Electronic calculations unveil that all these systems behave as indirect band gap semiconductors. The three antiferromagnetic systems have similar band gaps of 0.80, 0.98, and 1.00 eV, respectively. This study presents a promising approach for designing functional materials that simultaneously possess magnetic, superhard, and lightweight characteristics, applicable in energy conservation, spintronics, and other fields.