Kramers degeneracy in a magnetic field and Zeeman spin-orbit coupling in antiferromagnetic conductors

In this Letter, I study the magnetic response of electron wave functions in a commensurate collinear antiferromagnet. I show that, at a special set of momenta, hidden antiunitary symmetry protects Kramers degeneracy of Bloch eigenstates against a magnetic field, pointing transversely to staggered magnetization. Hence, a substantial momentum dependence of the transverse g-factor in the Zeeman term, turning the latter into a spin-orbit coupling that may be present in materials from chromium to borocarbides, cuprates, pnictides, as well as organic and heavy fermion conductors.