Emerging two-dimensional magnetism in nonmagnetic electrides Hf2X (X=S, Se, Te

Recent experimental discoveries of two-dimensional (2D) magnets have triggered intense research activities to search for atomically thin magnetic systems. Using first-principles calculations, we predict the emergence of 2D magnetism in the monolayers (MLs), few layers, and surfaces of nonmagnetic layered electrides ${\mathrm{Hf}}_{2}X$ $(X=\text{S}, \mathrm{Se}, \mathrm{Te})$ consisting of three-atom-thick $\mathrm{Hf}\text{\ensuremath{-}}X\text{\ensuremath{-}}\mathrm{Hf}$ stacks. It is revealed that each bulk ${\mathrm{Hf}}_{2}X$ hosts a quantum state of Dirac nodal lines with a high density of states arising from $\mathrm{Hf}\text{\ensuremath{-}}5d$ cationic and interlayer anionic electrons around $\ensuremath{-}0.9 \mathrm{eV}$ below the Fermi level ${E}_{F}$. However, for the MLs, few layers, and surfaces of ${\mathrm{Hf}}_{2}X$, such hybridized states are shifted toward ${E}_{F}$ to generate van Hove singularities, leading to a Stoner instability. The resulting surface ferromagnetism gives rise to strongly spin-polarized topological surface states at ${\mathrm{Hf}}_{2}X(001)$, demonstrating that anionic electrons, 2D magnetism, and band topology are entangled with each other. Our findings will open different perspectives for the discovery of 2D magnets via exploiting surface effects in nonmagnetic layered electrides.