Observation of the anomalous Hall effect in a layered polar semiconductor

Progress in magnetoelectric materials is hindered by apparently contradictory requirements for time-reversal symmetry broken and polar ferroelectric electronic structure in common ferromagnets and antiferromagnets. Alternative routes could be provided by recent discoveries of a time-reversal symmetry breaking anomalous Hall effect in noncollinear magnets and altermagnets, but hitherto reported bulk materials are not polar. Here, we report the observation of a spontaneous anomalous Hall effect in doped AgCrSe$_2$, a layered polar semiconductor with an antiferromagnetic coupling between Cr spins in adjacent layers. The anomalous Hall resistivity 3 $\mu\Omega$ cm is comparable to the largest observed in compensated magnetic systems to date, and is rapidly switched off when the angle of an applied magnetic field is rotated to $\sim 80^{\circ}$ from the crystalline $c$-axis. Our ionic gating experiments show that the anomalous Hall conductivity magnitude can be enhanced by modulating the $p$-type carrier density. We also present theoretical results that suggest the anomalous Hall effect is driven by Berry curvature due to noncollinear antiferromagnetic correlations among Cr spins, which are consistent with the previously suggested magnetic ordering in AgCrSe$_2$. Our results open the possibility to study the interplay of magnetic and ferroelectric-like responses in this fascinating class of materials.