Doping- and strain-tuned high Curie temperature half-metallicity and quantum anomalous Hall effect in monolayer NiAl2S4 with non-Dirac and Dirac states

Two-dimensional magnetic materials with tunable electronic and magnetic properties are promising for designing spintronics devices. Here we study, using first-principles calculations, the electronic, magnetic, and topological properties of monolayer ${\mathrm{NiAl}}_{2}{\mathrm{S}}_{4}$. Monolayer ${\mathrm{NiAl}}_{2}{\mathrm{S}}_{4}$ is in the noncollinear ${120}^{0}$-antiferromagnetic $({120}^{0}\text{\ensuremath{-}}\mathrm{AFM})$ state and is an indirect band gap semiconductor. Although the ${120}^{0}$-AFM state in monolayer ${\mathrm{NiAl}}_{2}{\mathrm{S}}_{4}$ is robust against strain, its magnetic structure can be tuned effectively by carrier doping. Remarkably, monolayer ${\mathrm{NiAl}}_{2}{\mathrm{S}}_{4}$ can be tuned into a high Curie temperature $({T}_{C})$ half-metallic state by hole doping. The ${T}_{C}$ of ferromagnetic monolayer ${\mathrm{NiAl}}_{2}{\mathrm{S}}_{4}$ increases with hole-doping concentration and can be increased up to room temperature. For the hole-doped monolayer ${\mathrm{NiAl}}_{2}{\mathrm{S}}_{4}$ with the half-metallic state, before the spin-orbit coupling (SOC) is included, the two spin-up bands around the Fermi level are simultaneously degenerate at the $\mathrm{\ensuremath{\Gamma}}$ point (dominated by S ${p}_{x}/{p}_{y}$ states) and $\mathrm{K}/{\mathrm{K}}^{\ensuremath{'}}$ points (dominated by S ${p}_{z}$ state) with quadratic non-Dirac and linear Dirac band dispersions, respectively. When the SOC is included, topologically nontrivial gaps with Chern number $C=1$ will be opened, respectively, around the non-Dirac $\mathrm{\ensuremath{\Gamma}}$ point and Dirac $\mathrm{K}/{\mathrm{K}}^{\ensuremath{'}}$ points. More interestingly, the quantum anomalous Hall (QAH) effect with high Chern number $C=2$ can be achieved in the tensile-strained monolayer ${\mathrm{NiAl}}_{2}{\mathrm{S}}_{4}$ with 1.0 hole-doped per unit cell. The obtained high Chern number of $C=2$ results from the constructive coupling effect between the topological nontrivial non-Dirac and Dirac states, which is analyzed through a schematic depiction. Our results show that monolayer ${\mathrm{NiAl}}_{2}{\mathrm{S}}_{4}$ is a promising candidate for the exploration of high ${T}_{C}$ spintronics devices and high Chern number QAH effect.