Type-III Weyl semi-half-metal in an ultralight monolayer Li 2 N

The interplay between magnetic ordering and band topology has emerged as a fertile ground for discovering novel quantum states with profound implications for fundamental physics and next-generation electronics. Here, we theoretically predict a different type-III Weyl semi-half-metal (SHM) state in monolayer ${\mathrm{Li}}₂\mathrm{N}$, uniquely combining magnetic half-metallicity and type-III Weyl semimetal characteristics. First-principles calculations reveal a fully spin polarized and critically tilted Weyl cone around the Fermi level in monolayer ${\mathrm{Li}}₂\mathrm{N}$, driven by $p$-orbital ferromagnetism. This arises from the symmetry-protected band crossing between a partially flat valence band and a highly dispersive conduction band, leading to type-III Weyl fermions with strong transport anisotropy. A low-energy $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ Hamiltonian is constructed and corresponding nontrivial edge states are uncovered to capture the topological nature of ${\mathrm{Li}}₂\mathrm{N}$. Notably, this Weyl SHM phase remains robust under biaxial strain ranging from $\ensuremath{-}2%$ to $4%$, with an ideal type-III Weyl fermion emerging alongside a linelike ergodic surface emerging at $3.7%$ strain, offering a promising platform for exploring correlated electronic phenomena. Our results establish ${\mathrm{Li}}₂\mathrm{N}$ as a viable candidate for realizing exotic type-III Weyl SHM states and open an avenue for exploring the intricate interplay among magnetism, topology, and flat-band physics.