Orbital-tailored interstitial magnetism: From electrides to magnetrides

Electrides provide a unique opportunity to study electron localization and emergent magnetism in systems where the Fermi surface is formed by interstitial electronic states. This work introduces ``magnetrides'' as electrides where nonatomic electrons develop correlated magnetic order while maintaining a spatially and electronically distinct subsystem from atomic states---a paradigm enabling pristine electron spin systems. This concept is realized in novel monolayer XF $(X=\mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba})$ electrenes, with BaF emerging as a prototypical example of ``magnetrene'' through its intrinsic interstitial moments, absent in the isoelectronic CaF and SrF. First-principles calculations trace this behavior to strain-tunable competition between cation $s$, $p$, and $d$ orbital contributions that shape the electride molecular orbital's topology at the Fermi level. The resulting system combines metallicity, robust in-plane ferromagnetism, strongly correlated localization $(U=2.9\phantom{\rule{0.28em}{0ex}}\mathrm{eV})$ confirmed by DMFT, and orbital-controlled magnetic transitions, establishing 2D magnetrenes as a versatile platform for designing nonatomic magnetic quantum phases.