Bernal stacking and symmetry-inequivalent antiferromagnetism in MSi ₂ N ₄ heterobilayers

Abstract Layered MA {}₂ Z {}₄ compounds, structural relatives of MoS {}₂ discovered in 2020, exhibit rich magnetic behavior arising from reduced dimensionality, noncentrosymmetric lattice symmetries, and stacking-dependent exchange interactions. Here, we investigate Bernal-like stackings in H-phase MA {}₂ Z 4 (M = Mn and Fe; A = Si; Z = N) monolayers (MLs) and bilayers (BLs) by combining first-principles spin-dependent relaxation energies with a localized-spin Heisenberg description. From density-functional calculations, we extract the dominant intralayer exchange couplings up to third-nearest neighbors and the leading interlayer exchanges up to second-nearest neighbors, enabling construction of an effective BL spin Hamiltonian. We first analyze interface-driven proximity effects within a ferromagnetic reference configuration, demonstrating how recovery of AB-type stacking and spin alignment—while varying only the transition-metal species—provides a route for selectively tuning magnetic order and symmetry breaking within the P \overset{¯}{6} m2 space group. Building on this microscopic understanding of the bonding environment, we then examine antiferromagnetic ordering tendencies in the coupled layers. Exact diagonalization of the resulting BL Hamiltonian reveals that the interlayer exchange is not merely perturbative but competes directly with intralayer Goodenough–Kanamori–Anderson-driven interactions. Crucially, atomistic spin dynamics simulations demonstrate a dimensional crossover: while isolated MLs suffer thermal collapse at cryogenic temperatures ( {T}_N≈2 – 175 K) due to Mermin–Wagner restrictions, the robust van der Waals interlayer exchange ( J⟨ij⟩≈+5.46 meV) explicitly stabilizes the heterobilayer, elevating the Néel temperature to 210 K. These results establish Bernal-stacked MA {}₂ Z {}₄ BLs as a platform in which stacking geometry, exchange hierarchy, and thermodynamic proximity govern the resulting magnetic ordering landscape.