# Topological crystalline antiferromagnetic state in tetragonal FeS

## TL;DR

This paper predicts a novel topological crystalline antiferromagnetic state in tetragonal FeS, combining magnetism and topology, with potential implications for antiferromagnetic spintronics.

## Contribution

It introduces the concept of a topological crystalline antiferromagnetic state and demonstrates its realization in tetragonal FeS through first-principles calculations and symmetry analysis.

## Key findings

- The state arises from band reconstruction due to pair checker-board antiferromagnetic order.
- Band-gap opening is induced by intrinsic spin-orbit coupling.
- The topological state is protected by combined symmetries and is surface-dependent.

## Abstract

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 checker-board 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 present some unique features. In contrast to strong topological insulators, the topological robustness is surface-dependent. These findings indicate that non-trivial topological states could emerge in pure antiferromagnetic materials, which sheds new light on potential applications of topological properties in fast-developing antiferromagnetic spintronics.