Sub-THz momentum drag and violation of Matthiessen's rule in an ultraclean ferromagnetic SrRuO$_3$ metallic thin film

Phys. Rev. Lett. 125, 217401 (2020) SrRuO$_3$, a ferromagnet with an approximately 160\,K Curie temperature, exhibits a $T^2$ dependent dc resistivity below $\approx$ 30 K. Nevertheless, previous optical studies in the infrared and terahertz range show non-Drude dynamics at low temperatures which seem to contradict a Fermi-liquid picture with long-lived quasiparticles. In this work, we measure the low-frequency THz range response of thin films with residual resistivity ratios, $\rho_{300K}/ \rho_{4K} \approx$ 74. Such low disorder samples allow an unprecedented look at the effects of electron-electron interactions on low-frequency transport. At temperatures below 30 K, we found both a very sharp zero-frequency mode which has a width narrower than $k_BT/\hbar$ as well as a broader zero frequency Lorentzian that has at least an order of magnitude larger scattering rate. Both features have temperature dependencies consistent with a Fermi-liquid with the wider feature explicitly showing a T$^2$ scaling. Such two -Drude transport sheds light on previous reports of the violation of Mathielssen's rule and extreme sensitivity to disorder in metallic ruthenates. We consider a number of possibilities for the origin of the two feature optical conductivity including multiband effects that arise from momentum conserving interband scattering and the approximate conservation of a pseudo-momentum that arises from quasi-1D Fermi surfaces.