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

In this paper, I analyze the symmetries and degeneracies of electron eigenstates in a commensurate collinear antiferromagnet. In a magnetic field transverse to the staggered magnetization, a hidden antiunitary symmetry protects double degeneracy of the Bloch eigenstates at a special set of momenta. In addition to this Kramers degeneracy subset, the manifold of momenta, labeling the doubly degenerate Bloch states in the Brillouin zone, may also contain an accidental degeneracy subset that is not protected by symmetry and that may change shape under perturbation. These degeneracies give rise to a substantial momentum dependence of the transverse g-factor in the Zeeman coupling, turning the latter into a spin-orbit interaction. I discuss a number of materials, where Zeeman spin-orbit coupling is likely to be present, and outline the simplest properties and experimental consequences of this interaction, that may be relevant to systems from chromium to borocarbides, cuprates, hexaborides, iron pnictides, as well as organic and heavy fermion conductors.