Large spontaneous valley polarization and anomalous valley Hall effect in antiferromagnetic monolayer Fe₂CF₂

Superior to ferromagnetic (FM) materials, antiferromagnetic (AFM) materials do not have any net magnetic moment and are robust to external magnetic perturbation with ultra-high dynamic speed. To achieve spontaneous valley polarization and anomalous valley Hall effect (AVHE) in AFM materials is of great significance for potential applications in spintronics and valleytronics. Here, we predict an A-type AFM monolayer Fe₂CF₂ with large spontaneous valley polarization. Monolayer Fe₂CF₂ has zero Berry curvature in momentum space but non-zero layer-locked hidden Berry curvature in real space, which provides the basic conditions for the realization of AVHE. Because Fe₂CF₂ possesses the combined symmetry ($PT$ symmetry) of spatial inversion (P) and time reversal (T) symmetry, the spin is degenerate, which prevents the AVHE. An out-of-plane external electric field can be used to produce spin splitting due to the introduction of layer-dependent electrostatic potential, and then layer-locked AVHE can be realized in Fe₂CF₂. Moreover, the spin order of spin splitting can be reversed, when the direction of electric field is reversed. It is proved that the AVHE can be achieved in Janus Fe₂CFCl without external electric field due to intrinsic built-in electric field. Our works provide an AFM monolayer with excellent properties to realize AVHE.