  The combination of antiferromagnetic (AFM) spintronics and anomalous valley
Hall effect (AVHE) is of great significance for potential applications in
valleytronics. Here, we propose a design principle for achieving AVHE in A-type
hexagonal AFM monolayer. The design principle involves the introduction of
layer-dependent electrostatic potential caused by out-of-plane external
electric field, which can break the combined symmetry ($PT$ symmetry) of
spatial inversion ($P$) and time reversal ($T$), producing spin splitting. The
spin order of spin splitting can be reversed by regulating the direction of
electric field. Based on first-principles calculations, the design principle
can be verified in AFM $\mathrm{Cr_2CH_2}$. The layer-locked hidden Berry
curvature can give rise to layer-Hall effect, including valley layer-spin Hall
effect and layer-locked AVHE. Our works provide an experimentally feasible way
to realize AVHE in AFM monolayer.
