Recently it has been shown experimentally that the superconducting state of ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$ exhibits Bogoliubov Fermi surfaces for $x>0.17$. These Bogoliubov Fermi surfaces appear together with broken time-reversal symmetry and surprisingly demonstrate nematic behavior in a structurally tetragonal phase. Here, through a comprehensive analysis that deduces the structure of Bogoliubov Fermi surfaces from all symmetry-allowed types of translation invariant broken time-reversal symmetry, we find that the origin of nematic Bogoliubov Fermi surfaces is due to magnetic toroidal order that belongs to an $E_u$ irreducible representation of the $D_{4h}$ point group. We further show that this magnetic toroidal order appears as a consequence of either static Néel antiferromagnetic order or due to the formation of a spontaneous pair density wave superconducting order. Finally, we reveal that independent of the presence of Bogoliubov Fermi surfaces, supercurrents will induce Néel magnetic order in many Fe-based superconductors.

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• Antiferromagnetism
• Superconductivity
• Iron-based superconductors