Temperature Dependence of Scaling Parameters in Anomalous and Nonlinear Hall Effects

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 the scaling parameters when the longitudinal resistivity is tuned through temperature. An experimental approach is proposed to observe this temperature-dependence. We further show that this phenomenon also exists in the nonlinear Hall effect and helps identify experimentally the presence of the side-jump contribution alongside the Berry-curvature dipole.