Diverse interlayer tunability of physical properties of two-dimensional layers mostly lies in the covalent-like quasibonding that is significant in electronic structures but rather weak for energetics. Such characteristics result in various stacking orders that are energetically comparable but may significantly differ in terms of electronic structures, e.g., magnetism. Inspired by several recent experiments showing interlayer antiferromagnetically coupled ${\mathrm{CrI}}_3$ bilayers, we carried out first-principles calculations for ${\mathrm{CrI}}_3$ bilayers. We found that the antiferromagnetic coupling results from a different stacking order with the $C2/m$ space group symmetry, rather than the graphene-like one with $R\overline{3}$ as previously believed. Moreover, we demonstrated that the intra- and interlayer couplings in ${\mathrm{CrI}}_3$ bilayer are governed by two different mechanisms, namely ferromagnetic superexchange and direct-exchange interactions, which are largely decoupled because of their significant difference in strength at the strong- and weak-interaction limits. This allows the much weaker interlayer magnetic coupling to be more feasibly tuned by stacking orders solely. Given the fact that interlayer magnetic properties can be altered by changing crystal structure with different stacking orders, our work opens a paradigm for tuning interlayer magnetic properties with the freedom of stacking order in two-dimensional layered materials.

• Received 10 July 2018
• Revised 13 March 2019

DOI:https://doi.org/10.1103/PhysRevB.99.144401