  We show that the three commonly employed approaches that define the same
intrinsic linear anomalous Hall response actually lead to different results for
intrinsic nonlinear transport. The difference arises from an intrinsic
anomalous distribution. It originates from scattering, but its value is
completely independent of scattering, because it represents the local
equilibration of electron wave packets with field corrected energy. As a
manifestation, we find that under ac driving, the intrinsic contributions in
rectified component and in double-frequency component exhibit distinct
frequency dependence, which can be probed in experiment. Using first-principles
calculations, we estimate the signals that can be probed in antiferromagnetic
CuMnAs.
