Hall number sign changes in Sr₂RuO₄ reveal coherent-to-incoherent and elastic-to-inelastic crossovers

The 4d transition metal oxide Sr₂RuO₄ exhibits an unusual temperature dependence of its Hall number with two sign reversals: it is negative at low temperature below 30K (Fermi liquid temperature), turns positive, reaches a maximum and turns negative again at ~120K. We show that this non-monotonic behavior is due to the strong temperature-dependence of the ratio of inelastic scattering rates between the xy and xz/yz orbitals. This ratio becomes remarkably large upon cooling into the Fermi liquid regime, but is overshadowed at lower temperatures by impurity scattering. Another pivotal factor to account for the full temperature dependence is the spin-orbit coupling, as it impacts the topography of the Fermi surface sheets and strongly mixes their orbital character. By considering all these effects, we are able to reveal the significance of both sign changes: the one at 30K is a direct consequence of the crossover from elastic to inelastic scattering, while the higher-T one is associated with the coherence-to-incoherence crossover due to electronic correlations. These qualitative conclusions are supported by quantitative calculations using a Boltzmann transport theory in combination with dynamical mean-field theory, taking into account the electronic structure of the material.