  Diverse interlayer tunability of physical properties of two-dimensional
layers mostly lies in the covalent-like quasi-bonding 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
anti-ferromagnetically coupled CrI3 bilayers, we carried out first-principles
calculations for CrI3 bilayers. We found that the anti-ferromagnetic coupling
results from a new stacking order with the C2/m space group symmetry, rather
than the graphene-like one with R3 as previously believed. Moreover, we
demonstrated that the intra- and inter-layer couplings in CrI3 bilayer are
governed by two different mechanisms, namely ferromagnetic super-exchange 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 new paradigm for tuning interlayer magnetic properties
with the freedom of stacking order in two dimensional layered materials.
