# Scaling parameters in anomalous and nonlinear Hall effects depend on temperature

## TL;DR

This paper reveals that the scaling parameters in anomalous and nonlinear Hall effects are temperature-dependent due to electron-phonon scattering, challenging the traditional view of fixed scaling relations.

## Contribution

It uncovers the temperature dependence of Hall effect scaling parameters caused by electron-phonon interactions and proposes experimental methods to observe this phenomenon.

## Key findings

- Electron-phonon scattering induces apparent temperature dependence of scaling parameters.
- The phenomenon is also present in nonlinear Hall effects in nonmagnetic materials.
- The results may help identify side-jump contributions in Hall effects.

## Abstract

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.