  The interplay of electric charge, spin, and orbital polarizations, coherently
driven by picosecond long oscillations of light fields in spin-orbit coupled
systems, is the foundation of emerging terahertz spintronics and orbitronics.
The essential rules for how terahertz light interacts with these systems in a
nonlinear way are still not understood. In this work, we demonstrate a
universally applicable electronic nonlinearity originating from spin-orbit
interactions in conducting materials, wherein the interplay of light-induced
spin and orbital textures manifests. We utilized terahertz harmonic generation
spectroscopy to investigate the nonlinear dynamics over picosecond timescales
in various transition metal films. We found that the terahertz harmonic
generation efficiency scales with the spin Hall conductivity in the studied
films, while the phase takes two possible values (shifted by {\pi}), depending
on the d-shell filling. These findings elucidate the fundamental mechanisms
governing non-equilibrium spin and orbital polarization dynamics at terahertz
frequencies, which is relevant for potential applications of terahertz spin-
and orbital-based devices.
