It has recently been demonstrated that various topological states, including Dirac, Weyl, nodal-line, and triple-point semimetal phases, can emerge in antiferromagnetic (AFM) half-Heusler compounds. However, how to determine the AFM structure and to distinguish different topological phases from transport behaviors remains unknown. We show that, due to the presence of combined time-reversal and fractional translation symmetry, the recently proposed second-order nonlinear Hall effect can be used to characterize different topological phases with various AFM configurations. Guided by the symmetry analysis, we obtain expressions of the Berry curvature dipole for different AFM configurations. Based on the effective model, we explicitly calculate the Berry curvature dipole, which is found to be vanishingly small for the triple-point semimetal phase, and large in the Weyl semimetal phase. Our results not only put forward an effective method for the identification of magnetic orders and topological phases in AFM half-Heusler materials, but also suggest these materials as a versatile platform for engineering the nonlinear Hall effect.

最近已经证明，各种拓扑状态，包括狄拉克、外尔、节点线和三点半金属相，可以出现在反铁磁 (AFM) 半赫斯勒化合物中。然而，如何确定原子力显微镜结构并将不同的拓扑阶段与传输行为区分开来仍然未知。我们表明，由于存在组合的时间反转和分数平移对称性，最近提出的二阶非线性霍尔效应可用于表征具有各种 AFM 配置的不同拓扑相位。在对称性分析的指导下，我们获得了不同 AFM 配置的 Berry 曲率偶极子的表达式。基于有效模型，我们明确计算了贝里曲率偶极子，发现它对于三点半金属相非常小，在外尔半金属相中大。我们的研究结果不仅提出了一种有效的方法来识别 AFM 半赫斯勒材料中的磁级和拓扑相，而且还表明这些材料可以作为工程非线性霍尔效应的通用平台。