Intrinsic Nonlinear Hall Detection of the N\'eel Vector for Two-Dimensional Antiferromagnetic Spintronics

The respective unique merit of antiferromagnets and two-dimensional (2D) materials in spintronic applications inspire us to exploit 2D antiferromagnetic spintronics. However, the detection of the N\'eel vector in 2D antiferromagnets remains a great challenge because the measured signals usually decrease significantly in the 2D limit. Here we propose that the N\'eel vector of 2D antiferromagnets can be efficiently detected by the intrinsic nonlinear Hall (INH) effect which exhibits unexpected significant signals. As a specific example, we show that the INH conductivity of the monolayer manganese chalcogenides Mn$X$ ($X$=S, Se, Te) can reach the order of nm$\cdot$mA/V$^2$, which is orders of magnitude larger than experimental values of paradigmatic antiferromagnetic spintronic materials. The INH effect can be accurately controlled by shifting the chemical potential around the band edge, which is experimentally feasible via electric gating or charge doping. Moreover, we explicitly demonstrate its $2\pi$-periodic dependence on the N\'eel vector orientation based on an effective $k.p$ model. Our findings enable flexible design schemes and promising material platforms for spintronic memory device applications based on 2D antiferromagnets.