Three-dimensional Weyl hourglass networks in the nonsymmorphic half-metal Mg 2 VO 4

Fermions with hourglass dispersions have been hotly studied in a nonmagnetic system currently. However, magnetic ones have been rarely discussed because of the scarcity of excellent candidate materials. Here, promoted by first-principles and symmetry analysis, we propose the presence of novel hourglass nodal networks in a nonsymmorphic half-metal ${\mathrm{Mg}}_{2}{\mathrm{VO}}_{4}$ that is constructed by three touching hourglass nodal lines at mutually intersecting planes in the extended Brillouin zone. Unlike previous hourglass semimetals in nonmagnetic materials, the material proposed here has a ferromagnetic half-metallic state; thus, the hourglass nodal networks are fully spin polarized. We also show that the hourglass nodal networks manifest spin-polarized drumhead surface states. We demonstrate the hourglass nodal networks are enforced by nonsymmorphic symmetry, and effective models are constructed. We further show that the novel topological phase of ${\mathrm{Mg}}_{2}{\mathrm{VO}}_{4}$ is robust against lattice strain and electron correlation effects. Our work provides a good platform to investigate novel hourglass fermions from nonsymmorphic symmetries in magnetic system.