  Most of solid-state spin physics arising from spin-orbit coupling, from
fundamental phenomena to industrial applications, relies on symmetry-protected
degeneracies. So does the Zeeman spin-orbit coupling, expected to manifest
itself in a wide range of antiferromagnetic conductors. Yet, experimental proof
of this phenomenon has been lacking. Here, we demonstrate that the N\'eel state
of the layered organic superconductor $\kappa$-(BETS)$_2$FeBr$_4$ shows no spin
modulation of the Shubnikov-de Haas oscillations, contrary to its paramagnetic
state. This is unambiguous evidence for the spin degeneracy of Landau levels, a
direct manifestation of the Zeeman spin-orbit coupling. Likewise, we show that
spin modulation is absent in electron-doped Nd$_{1.85}$Ce$_{0.15}$CuO$_4$,
which evidences the presence of N\'eel order in this cuprate superconductor
even at optimal doping. Obtained on two very different materials, our results
demonstrate the generic character of the Zeeman spin-orbit coupling.
