Symmetry of electron states in antiferromagnets

The symmetry of the electron states in an antiferromagnetically ordered crystal is investigated. The elements of the two-value corepresentation apparatus for the magnetic groups are used in a form that corresponds to the models and methods of the microscopic theories. The symmetry restriction on the quasiparticle spectra, on their interaction with the magnetic field h, and on the interband matrix elements are found. The spin-orbit effects are considered. It is shown that a field h perpendicular to the antiferromagnetic ordering vector n does not split the twofold degeneracy of the states at the boundary of the magnetic Brillouin zone but shifts the spectrum extrema away from the boundary. The results are illustrated for the case of a two-dimensional system corresponding to the CuO2 plane in weakly doped high-temperature superconductors. The general conclusions are applicable to itinerant antiferromagnets, including quasi-one-dimensional compounds with a spin density wave