  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 the 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 non-linear
Hall effect.
