Creating and Controlling Weyl Fermions, Nexus Points, and Nodal Lines in the Magnetic Anti-perovskite Eu${}_3$PbO

Anti-perovskite materials A${}_3$EO, where A denotes an alkaline earth metal, while E stands for Pb or Sn, exhibit low-energy electronic properties that are described by three-dimensional Dirac fermions, which are gapped out by spin-orbit coupling. If A is replaced by the rare-earth element europium then magnetic order is expected due to the electron spin moment as confirmed by magnetization measurements. Neutron diffraction leads us to the conclusion that different magnetic phases appear. We studied the effect of magnetism on the electronic properties of Eu${}_3$PbO. From DFT calculations the resulting splitting has been extracted and implemented into a tight-binding model to capture the physics close to the Fermi energy. We present the creation of Weyl points, Nexus points, and nodal lines and give their topological invariants. For the different magnetic phases we derived the respective surface states and anomalous Hall responses.