Stacking-dependent magnetic ordering in bilayer ScI$_{2}$

Abstract: Stacking-dependent magnetism in two-dimensional van der Waals materials offers an effective route for controlling magnetic order without chemical modification. Here, we present a combined first-principles and finite-temperature study of magnetic ordering in bilayer ScI${2}$ with different stacking configurations. Using density functional theory with Hubbard-U corrections, we investigate the structural, electronic, and magnetic properties of monolayer and bilayer ScI${2}$ in $AA$, $AB$, and $BA$ stackings. The electronic structure exhibits a spin-polarized ground state dominated by Sc-$d$ states near the Fermi level. Mapping total energies onto an effective Heisenberg spin Hamiltonian reveals strong intralayer ferromagnetic exchange that is largely insensitive to stacking, while the inter-layer exchange depends strongly on stacking geometry, favoring ferromagnetic coupling for $AA$ and $BA$ stackings and antiferromagnetic coupling for the $AB$ stacking. Spin-orbit coupling calculations show that both monolayer and bilayer ScI${2}$ possess a robust out-of-plane magnetic easy axis. Finite-temperature Monte Carlo simulations indicate that all bilayer configurations sustain magnetic ordering at and above room temperature, with ordering temperatures in the range $360-375$ K, as confirmed by Binder cumulant analysis and finite-size scaling. These results demonstrate that stacking geometry enables control of the magnetic ground state in bilayer ScI${2}$ without significantly affecting its thermal stability.