Bernal Stacking and Symmetry-Inequivalent Antiferromagnetism in MSi$_2$N$_4$ Heterobilayers

TL;DR

This work tackles how Bernal-like stacking affects magnetism in H-phase MA$_2$Z$_4$ bilayers (M = Mn, Fe; A = Si; Z = N). It combines DFT+$U$+$J$ with spin–orbit coupling to quantify intra- and interlayer exchange interactions, then builds a bilayer Heisenberg model and solves it via exact diagonalization to reveal a nonperturbative interlayer exchange that competes with intralayer couplings. The results show that stacking registry and exchange hierarchy jointly determine the magnetic ground state and low-energy spectrum, enabling domain selection and spin-texture control in these noncentrosymmetric vdW magnets. The findings establish MA$_2$Z$_4$ bilayers as a versatile platform for antiferromagnetic spintronics, with potential implications for spin valves, tunable magnetism, and spin–orbit–coupled phenomena in low dimensions.

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 and bilayers 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 bilayer 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$\bar{6}$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 bilayer Hamiltonian reveals the magnetic ground state and low-lying excitation spectrum, showing that the interlayer exchange is not merely perturbative but competes directly with intralayer interactions in stabilizing the observed spin configurations. These results establish Bernal-stacked MA$_2$Z$_4$ bilayers as a platform in which stacking geometry and exchange hierarchy jointly govern magnetic reconstruction, offering a controlled pathway toward domain selection and spin-texture engineering in low-dimensional van der Waals materials.

Figures (6)

• Figure 1: Side-view of the 2x2 BLs system showing the stacking a) H3, b) T4, c) Top where grey dashed lines point out high-symmetric interactions TM-N’s. Structural sections d) display their top-view above, excluding silicons and non-interfacial nitrogens, separately. Pcells are labeled in green.
• Figure 2: PES in the 1x1 BLs, where $d$ is the interlayer distance.
• Figure 3: Spin isosurfaces for MSN and FSN in a 2$\times$2 periodic arrangement. Blue and red lobes represent the accumulation of spin-up and spin-down probability densities, respectively, for each spin channel.
• Figure 4: Representative model of nearest ($J_a$, exchange), next ($J_d$, double-exchange), and third ($J_{2a}$, super-exchange)-second-nearest neighbors intralayer terms for AFM/FM alignments: MSN and FSN in 2x2 periodicity.
• Figure 5: (a) Low-lying many-body spectrum of the MnSi$_2$N$_4$/FeSi$_2$N$_4$ bilayer Heisenberg model with toroidal boundary conditions, using intralayer and interlayer exchange parameters extracted from DFT. (b) Cross-layer spin--spin correlation matrix $\langle S^{z,\mathrm{top}}_i S^{z,\mathrm{bot}}_j\rangle_{\mathrm{GS}}$. Red (blue) denotes ferromagnetic (antiferromagnetic) correlations between site $i$ in the top layer and site $j$ in the bottom layer. The alternating pattern among interior sites is consistent with the G2- and G3-type interlayer antiferromagnetic configurations shown in Fig. \ref{['fig:AFMordersvdWHS6']}.