Interlayer Magnetic Exchange Mechanism of Bilayer Transition‐Metal Trihalides.

Layer‐ and stacking‐dependent interlayer magnetism observed in bilayer CrI3${\rm CrI}_3$ has attracted a lot of attention recently. Although considerable efforts have been made, the interlayer exchange mechanism still lacks a clear physical picture. In this paper, orbital overlap‐dependent super‐super‐exchange (SSE) interactions are proposed to understand the interlayer magnetism of bilayer MX3${\rm MX}_3$ (M = Cr, Fe, and Mo; X = Cl, Br, and I) with different stacking orders. The detailed atom‐ and orbital‐resolved magnetic exchange couplings are evaluated to reveal the underlying mechanism. The results suggest that the interlayer magnetic ground state of all FeX3${\rm FeX}_3$ bilayers are antiferromagnetism (AFM) due to the t2g3eg2$t_{2g}^{3}e_{g}^{2}$ electronic configuration of Fe3+${\rm Fe}^{3+}$ cation. While CrX3${\rm CrX}_3$ and MoX3${\rm MoX}_3$ are found to possess stacking‐dependent interlayer magnetism due to the competition between AFM and ferromagnetism (FM), the dominant interlayer AFM exchange couplings are the eg−eg$e_{g}-e_{g}$ and t2g−t2g$t_{2g}-t_{2g}$ for CrX3${\rm CrX}_3$ and MoX3${\rm MoX}_3$, respectively, indicating different underlying mechanisms. These distinct interlayer magnetism can be consistently understood by the number and strength of SSE paths, which can be determined by the rule based on the orbital overlap of mediating anions. Moreover, the atom‐ and orbital‐resolved magnetic exchange couplings are also evaluated in detail, which are in good agreement with the above qualitative mechanism. This work provides detailed information and insight for understanding the stacking‐dependent interlayer magnetism, which is beneficial for the application of 2D magnetic materials. [ABSTRACT FROM AUTHOR]