| Abstract: | The symmetry of the time-independent Schrödinger equation is investigated in antiferromagnetic single crystals using the spinor representation for the electron. The one-particle Hamiltonian depends on the assumed rigid antiferromagnetic structure via the vector potential of the magnetic induction. The Pauli term and the spin-orbit term are taken into account as well as the crystal potential. It is shown how to find the Shubnikov space group relevant to the problem. A representation of the appropriate double group gives the symmetry group of the Hamiltonian. From the lattice periodicity of the Hamiltonian an analogue of the classical Bloch theorem is obtained. The symmetry group of the Hamiltonian is used to determine the symmetry properties of the energy bands. These symmetries are examined systematically for each type of Shubnikov space groups. Special attention is paid to the validity of the Kramers symmetry. In certain antiferromagnets, the energy bands are allowed by symmetry to have terms linear in k. Such a behaviour can have measurable consequences. |
