Emergent antiferromagnetism and Mott proximity in BaF electride bilayer

Bilayer stacking provides a powerful route to engineer quantum phases in two-dimensional materials. We investigate a bilayer system constructed from monolayers of the BaF electride---a prototypical magnetrene---and find a pronounced tendency toward antiferromagnetic (AFM) ordering driven by interlayer confinement of interstitial anionic electrons. Using first-principles calculations and dynamical mean-field theory (DMFT), we show that the bilayer is dynamically stable and that our density functional theory calculations indicate an AFM-G configuration as the lowest among the collinear magnetic orders examined, with spin density highly localized between the layers. Constructing cavity-centered Wannier functions yields an effective low-energy Hamiltonian for the correlated interstitial subspace. DMFT calculations show that increasing electronic correlations triggers spectral weight transfer to Hubbard bands, leading to quasiparticle suppression and the opening of a correlation-induced gap. Long-lived local moments emerging within the interlayer subspace, signaled by the progressive flattening of $\ensuremath{\chi}(\ensuremath{\tau})$ with $U$, naturally favor AFM ordering. Our findings establish bilayer electrides as a tunable platform for creating and controlling correlated magnetic states via confinement in a van der Waals gap.