Multifield tunable valley splitting and anomalous valley Hall effect in two-dimensional antiferromagnetic MnBr

Compared to the ferromagnetic materials that realize the anomalous valley Hall effect by breaking time-reversal symmetry and spin-orbit coupling, the antiferromagnetic materials with joint spatial inversion and time-reversal $(PT)$ symmetry are rarely reported to achieve the anomalous valley Hall effect. Here, we predict that the antiferromagnetic monolayer MnBr possesses spontaneous valley polarization. The valley splitting of the valence band maximum is 21.55 meV at $K$ and ${K}^{\ensuremath{'}}$ points, which originates from $\mathrm{Mn}\text{\ensuremath{-}}{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital by analyzing the effective Hamiltonian. Importantly, monolayer MnBr has zero Berry curvature in the entire momentum space but nonzero spin-layer locked Berry curvature, which offers the condition for the anomalous valley Hall effect. In addition, the magnitude of valley splitting can be signally tuned by the strain, magnetization rotation, electric field, and built-in electric field. The electric field and built-in electric field induce spin splitting due to breaking the $P$ symmetry. Therefore, the spin-layer locked anomalous valley Hall effect can be observed in MnBr. More remarkably, the ferroelectric substrate ${\mathrm{Sc}}_{2}{\mathrm{CO}}_{2}$ can tune monolayer MnBr to realize the transition from metal to valley polarization semiconductor. Our findings not only extend the implementation of the anomalous valley Hall effect, but also provide a platform for designing low-power and nonvolatile valleytronics devices.