Topological gapless phases in nonsymmorphic antiferromagnets

We investigate the nature of the electronic states in a variety of nonsymmorphic collinear antiferromagnets with glide reflection symmetry, a combination of mirror and half-lattice translation. In particular, the study refers to a class of systems with two-band itinerant electrons that are spin-orbit coupled and interacting with a magnetic background having a zigzag pattern. We describe the symmetry properties of the model system by focusing on the role of nonsymmorphic transformations arising from the antiferromagnetic structure of the spin ordering. Gapless phases with Dirac points having different types of symmetry-protection as well as electronic structures with triple and quadruple band-crossing points are obtained. A glide semimetal is shown to be converted into a gapless phase with Dirac points protected by inversion and time-inversion symmetry combination. Interestingly, we find a relation between the states in the glide sectors that provides a general mechanism to get multiple band touching points. The split of the multiple Fermi points drives the transition from a point node to a line node semimetal or to a metal with nontrivial winding around the Fermi pockets and an electronic structure that is tied to the presence of glide symmetric Dirac points. Besides a new perspective of ordered states in complex materials, our findings indicate relevant paths to topological gapless phases and edge states in a wide class of magnetic systems.