Antiferromagnetically ordered Dirac semimetal in Hubbard model with spin-orbit coupling

We examine the possible existence of Dirac semimetal with magnetic order in a two-dimensional system with a nonsymmorphic symmetry by using the Hartree-Fock mean-field theory within the Hubbard model. We locate the region in the second-neighbor spin-orbit coupling vs Hubbard interaction phase diagram, where such a state is stabilized. The edge states for the ribbons along two orthogonal directions concerning the orientation of in-plane magnetic moments are obtained. Finally, the effect of the in-plane magnetic field, which results in the stabilization of the Weyl semimetallic state, and the nature of the edge states corresponding to the Weyl semimetallic state for ribbon geometries are also explored.