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 interlayer 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.