Anomalous Hall effect in A-type antiferromagnetic bilayers

Altermagnetism (AM) is a recently proposed compensated magnetic state that exhibits the characteristics previously thought to be absent in conventional collinear antiferromagnets (AFMs), including the nonrelativistic spin splitting and a possible anomalous Hall effect (AHE). In two-dimensional (2D) A-type AFM bilayers with intralayer ferromagnetic and interlayer AFM coupling, interlayer operations serve as effective strategies to expand the family of 2D AM candidates. In this work, we systematically investigate the symmetry conditions enabling the AHE in collinear A-type AFM bilayers. We demonstrate that the in-plane N\'eel vector can induce finite anomalous Hall conductivity (AHC) in both twisted and mirror-stacked A-type AFM bilayers. However, spin splitting only exists in twisted bilayers and is absent in mirror-stacked ones. We further calculate the AHC in ${\mathrm{VS}}_{2}$ bilayers as a prototype and analyze the correlation between the direction of in-plane N\'eel vector and the AHC.