Antiferromagnetism caused by excess electrons and multiple topological electronic states in the electride Ba4Al5·e−

Electrides are a hot research topic due to their special electronic distribution. Recently, the coupling effects among electrides, magnetism, and topological electronic states have attracted considerable attention in condensed-matter physics. Here, based on first-principles calculations, we report an electride phase, namely, ${\mathrm{Ba}}_{4}{\mathrm{Al}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{e}^{\ensuremath{-}}$, with combing antiferromagnetic magnetism and multiple types of nontrivial band crossings locating near the Fermi level. The electride feature in ${\mathrm{Ba}}_{4}{\mathrm{Al}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{e}^{\ensuremath{-}}$ has been evidenced by electron contribution calculations and symmetry analysis. The material is found to show an antiferromagnetic ground state. Especially, the magnetism in the system is provided by the excess electrons in the crystal cavity, which is fundamentally different from the orbital-composed one in traditional magnetic materials. In addition, near the Fermi level ($\ensuremath{-}0.3$ to 0.3 eV) the material shows several regions of band crossings, which are mainly contributed by excess electrons. These band crossings form different topological states, ranging from the zero-dimensional nodal point to the one-dimensional nodal line and two-dimensional nodal surface. The protection mechanism, the effective model, the surface states, and the impacts of spin-orbital coupling on the topological states are systematically discussed. In addition, ${\mathrm{Ba}}_{4}{\mathrm{Al}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{e}^{\ensuremath{-}}$ has a very low work function and good catalysis on the [001] surface. Our work provides an excellent candidate for studying the potential entanglement of electride states, magnetism, and nontrivial band topology.