Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs

The nonlinear Hall effect is mostly studied as a Berry curvature dipole effect in nonmagnetic materials, which depends linearly on the relaxation time. On the other hand, in magnetic materials, an intrinsic nonlinear Hall effect can exist, which does not depend on the relaxation time. Here we show that the intrinsic nonlinear Hall effect can be observed in an antiferromagnetic metal: tetragonal CuMnAs, and the corresponding conductivity can reach the order of mA/V$^2$ based on density functional theory calculations. The dependence on the chemical potential of such nonlinear Hall conductivity can be qualitatively explained by a tilted massive Dirac model. Moreover, we demonstrate its strong temperature-dependence and briefly discuss its competition with the second order Drude conductivity. Finally, a complete survey of magnetic point groups are presented, providing guidelines for finding candidate materials with the intrinsic nonlinear Hall effect.