Topological crystalline antiferromagnetic state in tetragonal FeS

Integration between magnetism and topology is an exotic phenomenon in condensed-matter physics. Here, we propose an exotic phase named topological crystalline antiferromagnetic state, in which antiferromagnetism intrinsically integrates with nontrivial topology, and we suggest such a state can be realized in tetragonal FeS. A combination of first-principles calculations and symmetry analyses shows that the topological crystalline antiferromagnetic state arises from band reconstruction induced by pair checkerboard antiferromagnetic order together with band-gap opening induced by intrinsic spin-orbit coupling in tetragonal FeS. The topological crystalline antiferromagnetic state is protected by the product of fractional translation symmetry, mirror symmetry, and time-reversal symmetry, and presents some unique features. In contrast to strong topological insulators, the topological robustness is surface dependent. These findings indicate that nontrivial topological states could emerge in pure antiferromagnetic materials, which sheds new light on potential applications of topological properties in fast-developing antiferromagnetic spintronics.