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

Scaling parameters in anomalous and nonlinear Hall effects depend on temperature