Spin-to-charge-current conversion in altermagnetic candidate RuO$_2$ probed by terahertz emission spectroscopy

Using the THz emission spectroscopy, we investigate ultrafast spin-to-charge current conversion in epitaxial thin films of the altermagnetic candidate RuO$_2$. We perform a quantitative analysis of competing effects that can contribute to the measured anisotropic THz emission. These include the anisotropic inverse spin splitter and spin Hall effects in RuO$_2$, the anisotropic conductivity of RuO$_2$, and the birefringence of the TiO$_2$ substrate. We observe that the leading contribution to the measured signals comes from the anisotropic inverse spin Hall effect, with an average spin-Hall angle of $2.4\times 10^{-3}$ at room temperature. In comparison, a possible contribution from the altermagnetic inverse spin-splitter effect is found to be approximately $2-4\times 10^{-4}$. Our work stresses the importance of carefully disentangling spin-dependent phenomena that can be generated by the unconventional altermagnetic order, from the effects of the relativistic spin-orbit coupling.