Heesch Weyl Fermions in inadmissible chiral antiferromagnets

Symmetry plays a vital role in determining the topological properties of a material. Recently, the topological nature of the Kramers degeneracy at time-reversal-invariant momenta (TRIMs) as the Kramers Weyl node was revealed for the nonmagnetic chiral crystals. However, it remains obscure whether Weyl nodes can be also pinned at points of symmetry in magnetic materials where the time-reversal symmetry is spontaneously broken. In this work, we point out the existence of a new type of Weyl fermions in the inadmissible chiral antiferromagnets that are stabilized and pinned at points of symmetry by the Heesch group, which we call the Heesch Weyl fermions (HWFs). The origin of HWFs is fundamentally different from that of Kramers Weyl fermions, as the emergence of the former does not rely on any anti-unitary symmetry A that satisfies A$^2$ = −1. Through group theory analysis, we classify all the magnetic little co-groups of momenta where Heesch Weyl nodes are enforced and pinned by symmetry. With the guidance of the classification and first-principles calculation, the antiferromagnetic (AFM) perovskite YMnO3 is identified as a candidate host of the AFM-order-induced HWFs. Novel properties of the HWF, such as its axial moving under strain and therefore the potential realization of Weyl braiding, are also explored.