Design of two-dimensional half-metals with large spin gaps

Two-dimensional (2D) half-metals exhibit promising potential in magnetic nanodevices. However, the discovery of 2D half-metals is still based on a case-by-case evaluation. Here, we propose a general rule to design two-dimensional transition-metal-based half-metals with large spin gaps, namely to find the materials that have a Hund's-rule splitting of the $d$ orbitals and a deep anion $p$-orbital energy level that minimizes the d-p interactions. On the basis of DFT calculations for 54 transition-metal compounds $M{X}_{2}$ ($M=3d$ block transition metal; X = VIA-VIIA elements) with a distorted tetrahedral crystal field, we found that all the ferromagnetic compounds exhibit half-metallicity. We attribute the half-metallicity to Hund's rule splitting of partially filled $d$ orbitals of M cations with a weak d-p orbital hybridization. The chlorides exhibit a spin gap larger than 4 eV, because of the deep Cl $p$-orbital energy level (\ensuremath{-}8.4 eV). We validate this rule in transition-metal trichlorides ${M\mathrm{Cl}}_{3}$ ($M=3d$ block transition metal). Using this rule, we predict that ferromagnetic monolayer MCl and ${M}_{3}{\mathrm{Cl}}_{8}$ ($M=3d$ block transition metal) are half-metals with large band gaps. This work enriches the variety of 2D half-metals and could lead to novel magnetic nanodevices.