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

TL;DR

The study demonstrates that bilayer ScI$_2$ exhibits stacking-dependent interlayer magnetic exchange, enabling a switch between ferromagnetic and antiferromagnetic coupling through lateral registry changes, while intralayer ferromagnetism and strong out-of-plane anisotropy remain robust. Using DFT+$U$ to quantify exchange constants and MAE, and classical Monte Carlo simulations to assess finite-temperature behavior, the authors show ordering temperatures around $T_c \approx 360$--$375$ K for all stackings, with AB stacking favoring AFM interlayer alignment and AA/BA stackings favoring FM. The results reveal that stacking geometry can control the magnetic ground state without compromising thermal stability, offering a route to tunable magnetism in 2D van der Waals materials for spintronic applications. The combination of a large intralayer exchange scale and stacking-tunable interlayer exchange suggests a general design principle for stacking-engineered magnetism in layered transition-metal halides and related systems, with experimental validation and external-stimulus tuning as promising future directions.

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.

Figures (4)

• Figure 1: (a) Top view of monolayer ScI$_2$. Side view of bilayer ScI$_2$ showing three distinct stacking configurations: (b)BA, (c) AA, and (d)AB. Scandium and iodine atoms are represented in violet and grey, respectively.
• Figure 2: Electronic structure of monolayer ScI$_2$. (a) Spin-polarized band structure along high-symmetry directions of the Brillouin zone. (b) Spin-polarized density of states showing contributions from Sc-$d$ and I-$p$ orbitals. (c) Spin-polarized density of states projected on the five $d$ orbitals of Sc. The Fermi level $\left( E_F\right)$ is set to zero of the energy axis.
• Figure 3: Stacking-dependent electronic structure of bilayer ScI$_2$. (a) Projected density of states for the AA-stacked bilayer, highlighting Sc-$d$ and I-$p$ orbital contributions. (b) Spin-polarized band structures for AA, AB, and BA stacking configurations. Orange (grey) bands present the majority (minority) spin channel. The Fermi level is set to zero of the energy axis.
• Figure 4: Finite-size scaling analysis of the magnetic transition temperature in bilayer ScI$_2$. Panels (a)–(c) show the temperature dependence of the Binder cumulant $U_L$ for different system sizes for the AA, AB, and BA stacking configurations, respectively. Panels (d)–(f) display the corresponding Binder cumulant crossings used to extract finite-size estimates of the transition temperature. The Monte Carlo simulations shown in panels (a)–(f) were performed on lattices with a linear dimension of $L = 100$. Panels (g)–(h) present the weighted linear extrapolation of the critical temperature $T_c$ as a function of $1/L$, where the intercept yields the transition temperature in the thermodynamic limit.