Deciphering the origin of spin current in spintronic terahertz emitters and its imprint on their electromagnetic radiation via time-dependent density functional theory

Spin current flowing between femtosecond laser pulse (fsLP)-driven ferromagnetic metal and adjacent normal metal (NM) hosting strong spin-orbit coupling is invariably invoked to explain terahertz (THz) radiation believed to be emitted solely by NM layer. Despite being such a central concept, the microscopic origin of interlayer spin current remains vague. Here, we employ recently developed [A. Kefayati {\em et al.}, Phys. Rev. Lett. {\bf 133}, 136704 (2024)] time-dependent density functional theory plus Jefimenko equations approach to extract spin current between Co and NM=Pt or NM=W layer where Co is driven by fsLP responsible for its demagnetization, i.e., shrinking of its magnetization vector, $M^y(t)/M^y(t=0)<1$. By comparing time dependence of spin current with those of other relevant quantities, we find that: ({\em i}) spin current is generated by demagnetization dynamics because it {\em follows} closely $dM^y/dt$, thus it is an example of quantum pumping phenomenon that cannot be captured by phenomenological notions (such as ``spin voltage'') and related semiclassical transport theories; ({\em ii}) time dependence of pumped spin current {\em does not follow} closely that of charge current emerging within NM layer via spin-to-charge conversion mechanisms; ({\em iii}) THz emission can be governed by {\em both} charge current (i.e., its time derivative entering the Jefimenko equations) within Co layer or NM layer, but in different times frames. We also unravel a special case of NM=W where spin-to-charge conversion by the inverse spin Hall effect and its contribution to THz emission is suppressed, despite large spin Hall angle of W, because of localization of excited electrons onto the outer unfilled $d$-orbitals of W.