Fig. 8: Schematic illustration of the nodal-line structure along the K-H symmetry line for spin a perpendicular to orbital S⊥L and b parallel to orbital S||L.

The thick arrows indicate the opposite orbital momenta L along z. The opening of spin-orbit gap makes the nodal line behave as 1D vortex line and generates Berry flux in the momentum space as illustrated by the thinner red arrows. c Anomalous Hall angle \({\mathrm{\Theta }}_{AH} = \sigma _{xy}^A/\sigma _{xx}\) and anomalous Hall factor \({\mathrm{S}}_H = \sigma _{xy}^A/M\) of Fe_3−xGeTe₂ and metallic taken at low temperature (T ≪ Tc) ferromagnets. (adapted from ref. ¹⁹ with permission, copyright Springer Nature 2018).