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Diamond-structure materials have been extensively studied for decades, whichform the foundation for most semiconductors and their modern day electronicdevices. Here, we discover a e$_g$-orbital ($d_{z^2}$,$d_{x^2-y^2}$ ) modelwithin the diamond lattice (e$_g$-diamond model) that hosts novel topologicalstates. 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 ofdegenerate states (i.e., e$_g$-orbital and diamond-sublattice degeneracies). Wedemonstrate materials realization of this model in the well-known spinelcompounds (AB$_2$X$_4$), where the tetrahedron-site cations (A) form thediamond sub-lattice. An ideal half metal with one metallic spin channel formedby well-isolated and half-filled e$_g$-diamond bands, accompanied by a largespin 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 isfurther considered. Our discovery greatly enriches the physics of diamondstructure and spinel compounds, opening a door to their application inspintronics.

Magnetic Weyl semimetals with diamond structure realized in spinel compounds