Zeeman spin-orbit coupling and magnetic quantum oscillations in antiferromagnetic conductors

We find that the N\'eel state of the layered organic conductor $\kappa$-(BETS)$_2$FeBr$_4$ shows no spin modulation of the Shubnikov-de Haas oscillations, contrary to the paramagnetic state of the same material. This is evidence of spin degeneracy of Landau levels -- a direct manifestation of the generic Zeeman spin-orbit coupling, predicted for antiferromagnetic conductors. Likewise, we find no spin modulation in the angle dependence of the slow Shubnikov-de Haas oscillations in the optimally electron-doped cuprate Nd$_{2-x}$Ce$_x$CuO$_4$. This points to the presence of N\'eel order in this superconductor even at optimal doping.