Bethe-Slater-curve-like behavior and interlayer spin-exchange coupling mechanisms in two-dimensional magnetic bilayers

Layered magnets have recently received tremendous attention, however spin-exchange coupling mechanism across their interlayer regions is yet to be revealed. Here, we report a Bethe-Slater-curve (BSC)-like behavior in nine transition metal dichalcogenide bilayers ($M{X}_{2}$, $M=\mathrm{V}$, Cr, Mn; $X=\mathrm{S}$, Se, Te) and established interlayer spin-exchange coupling mechanisms at their van der Waals gaps using first-principle calculations. The BSC-like behavior offers a distance-dependent interlayer antiferromagnetic (AFM) to ferromagnetic (FM) transition. This phenomenon is explained with the spin-exchange coupling mechanisms established using bilayer $\mathrm{CrS}{\mathrm{e}}_{2}$ as a prototype in this work. The Se ${p}_{\mathrm{z}}$ wave functions from two adjacent interfacial Se sublayers overlap at the interlayer region. The spin alignment of the region determines interlayer magnetic coupling. At a shorter interlayer distance, Pauli repulsion at the overlapped region dominates and thus favors antiparallel oriented spins leading to interlayer AFM. For a longer distance, kinetic-energy gain of polarized electrons across the bilayer balances the Pauli repulsion and the bilayer thus prefers an interlayer FM state. In light of this, the AFM-FM transition is a result of competition between Pauli and Coulomb repulsions and kinetic-energy gain. All these results open a route to tune interlayer magnetism and the revealed spin-exchange coupling mechanisms are paramount additions to those previously established ones.