Nearly triple 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 topological features is the “triple point” where three bands become degenerate. In contrast to Weyl and Dirac nodes, triple 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 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 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 point” phase which exhibits very similar surface spectra and transport properties compared to a true triple-point 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.