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Antiferromagnetic (AFM) spintronics provides a route towards energy-efficientand ultrafast device applications. Achieving anomalous valley Hall effect(AVHE) in AFM monolayers is thus of considerable interest for both fundamentalcondensed matter physics and device enginering. Here we propose a route toachieve AVHE in A-type AFM insulator composed of vertically-stacked monolayerquantum anomalous Hall insulator (QAHI) with strain and electric fieldmodulations. Uniaxial strain and electric field generate valley polarizationand spin splitting, respectively. Using first-principles calculations,$\mathrm{Fe_2BrMgP}$ monolayer is predicted to be a prototype A-type AFMhosting \emph{valley-polarized quantum spin Hall insulator} (VQSHI) in whichAVHE and quantum spin Hall effect (QSHE) are synergized in a single system. Ourfindings reveal a route to achieve multiple Hall effects in 2D tetragonal AFMmonolayers.

Layer-Locked Anomalous Valley Hall Effect in Two-Dimensional A-Type Tetragonal Antiferromagnetic Insulator