Na₂C monolayer : A novel 2p Dirac half-metal with multiple symmetry-protected Dirac cones

A Dirac half-metal material, which has a gapped band structure in one spin channel but Dirac cones in the other, combines two intriguing properties of 100% spin polarization and massless Dirac fermions and has recently started to attract increasing attention. In this work, using first-principles calculations we predict that the disodium carbide (Na₂C) monolayer is an intrinsic 2p Dirac half-metal material with 12 fully spin-polarized and symmetry-protected Dirac cones, and a slightly gapped (53 meV) spin-polarized nodal line coexisting in one spin channel, leaving the other spin channel insulated with a gap of 1.9 eV. There are two kinds of Dirac cones in Na₂C, protected by different crystalline symmetries, both of which are robust against biaxial strains (±5%) and spin-orbit coupling effects, with Fermi velocities of up to 5.2 × 10⁵ m s^-1. Ferromagnetism is mainly contributed to by the unpaired 2p electrons in the carbon, with a Curie temperature estimated to be 382 K, and the origin of the 2p magnetism could be explained by the superexchange mechanism between C^2- anions with the Na⁺ cation as a bridge. Our results not only indicate a promising candidate for high-speed spintronic devices, but also reveal the hidden mechanism of the origin of symmetric protection and ferromagnetic exchange interactions in a Dirac semi-metal, which would provide a feasible strategy for the design of Dirac materials.