Antiferromagnetic Topological Semimetals in Three Dimensions*

We study three-dimensional topological semimetals with magnetic ordering and strong spin-orbit interaction. Such topological semimetals include Dirac semimetals (DSMs) and nodal line semimetals (NLSMs). Two distinct classes of magnetic NLSMs are proposed. The first class is band-inversion NLSM where the accidental line node is induced by band inversion and locally protected by glide mirror plane and the combined time-reversal and inversion symmetries. This can be viewed as a trivial stacking of the two-dimensional antiferromagnetic Dirac semimetals. The second class is essential NLSM where the nodal features are filling enforced by specific magnetic symmetry group. Similar classification also applies to magnetic DSMs. Concrete tight-binding models for magnetic NLSMs and DSMs which belong to these two different classes are also provided.