# Hall coefficient signals orbital differentiation in the Hund's metal Sr$_2$RuO$_4$

## TL;DR

This paper explains the non-monotonic temperature dependence of the Hall coefficient in Sr$_2$RuO$_4$, linking it to orbital differentiation and scattering crossovers, supported by theoretical calculations.

## Contribution

It reveals the connection between Hall coefficient sign changes and orbital differentiation in Hund's metals through combined Boltzmann and dynamical mean-field theory.

## Key findings

- Hall coefficient shows two sign reversals with temperature.
- Sign changes correspond to crossovers in scattering regimes.
- Orbital differentiation influences transport properties in Hund's metals.

## Abstract

The Hall coefficient $R_H$ of Sr$_2$RuO$_4$ exhibits a non-monotonic temperature dependence with two sign reversals. We show that this puzzling behavior is the signature of two crossovers which are key to the physics of this material. The increase of $R_H$ and the first sign change upon cooling are associated with a crossover into a regime of coherent quasiparticles with strong orbital differentiation of the inelastic scattering rates. The eventual decrease and the second sign change at lower temperature is driven by the crossover from inelastic to impurity-dominated scattering. This qualitative picture is supported by quantitative calculations of $R_H(T)$ using Boltzmann transport theory in combination with dynamical mean-field theory, taking into account the effect of spin-orbit coupling. Our insights shed new light on the temperature dependence of the Hall coefficient in materials with strong orbital differentiation, as observed in Hund's metals.