Layer-locked anomalous valley Hall effect in a two-dimensional A -type tetragonal antiferromagnetic insulator

Antiferromagnetic (AFM) spintronics provides a route towards energy-efficient and ultrafast device applications. Achieving anomalous valley Hall effect (AVHE) in AFM monolayers is thus of considerable interest for both fundamental condensed-matter physics and device engineering. Here we propose a route to achieve an AVHE in A-type AFM insulator composed of vertically stacked monolayer quantum anomalous Hall insulators with strain and electric field modulations. Uniaxial strain and electric field generate valley polarization and spin splitting, respectively. Using first-principles calculations, ${\mathrm{Fe}}_{2}\mathrm{BrMgP}$ monolayer is predicted to be a prototype hosting valley-polarized quantum spin Hall insulators in which AVHE and quantum spin Hall effect are synergized in a single system. Our findings reveal a route to achieve multiple Hall effects in two-dimensional tetragonal AFM monolayers.