Nearly triple nodal point topological phase in half-metallic GdN

Recent developments in topological semimetals open a way to realize relativistic dispersions in condensed-matter systems. One recently studied type of topological feature is the ``triple nodal point'' where three bands become degenerate. In contrast to Weyl and Dirac nodes, triple nodal points, which are protected by a rotational symmetry, have nodal lines attached, so that a characterization in terms of a chirality is not possible. Previous studies of triple nodal points considered nonmagnetic systems, although an artificial Zeeman splitting was used to probe the topological nature. Here instead we treat a ferromagnetic material, half-metallic GdN, where the splitting of the triple nodal points comes from the spin-orbit coupling. The size of the splitting ranges from 15 to 150 meV depending on the magnetization orientation, enabling a transition between a Weyl-point phase and a ``nearly triple nodal point'' phase that exhibits very similar surface spectra and transport properties compared with a true triple-node system. The rich topological surface states, manipulable via the orientation of the magnetization, make half-metallic GdN a promising platform for future investigations and applications.