  Diamond-structure materials have been extensively studied for decades, which
form the foundation for most semiconductors and their modern day electronic
devices. Here, we discover a e$_g$-orbital ($d_{z^2}$,$d_{x^2-y^2}$ ) model
within the diamond lattice (e$_g$-diamond model) that hosts novel topological
states. Specifically, the e$_g$-diamond model yields a 3D nodal cage (3D-NC),
which is characterized by a $d$-$d$ band inversion protected by two types of
degenerate states (i.e., e$_g$-orbital and diamond-sublattice degeneracies). We
demonstrate materials realization of this model in the well-known spinel
compounds (AB$_2$X$_4$), where the tetrahedron-site cations (A) form the
diamond sub-lattice. An ideal half metal with one metallic spin channel formed
by well-isolated and half-filled e$_g$-diamond bands, accompanied by a large
spin gap (4.36 eV) is discovered in one 4-2 spinel compound (VMg$_2$O$_4$),
which becomes a magnetic Weyl semimetal when spin-orbit coupling effect is
further considered. Our discovery greatly enriches the physics of diamond
structure and spinel compounds, opening a door to their application in
spintronics.
