  In the study of the anomalous Hall effect, the scaling relations between the
anomalous Hall and longitudinal resistivities play the central role. The
scaling parameters by definition are fixed as the scaling variable
(longitudinal resistivity) changes. Contrary to this paradigm, we unveil that
the electron-phonon scattering can result in apparent temperature-dependence of
scaling parameters when the longitudinal resistivity is tuned through
temperature. An experimental approach is proposed to observe this hitherto
unexpected temperature-dependence. We further show that this phenomenon also
exists in the nonlinear Hall effect in nonmagnetic inversion-breaking materials
and may help identify experimentally the presence of the side-jump contribution
besides the Berry-curvature dipole.
