  We performed the detailed microscopic analysis of the inter-layer magnetic
couplings for bilayer CrI$_3$. As the first step toward understanding the
recent experimental observations and utilizing them for device applications, we
estimated magnetic force response as well as total energy. Various van der
Waals functionals equivocally point to the ferromagnetic ground state for the
low-temperature structured bilayer CrI$_3$ which is further confirmed
independently by magnetic force response calculations. The calculated
orbital-dependent magnetic forces clearly show that $e_g$-$t_{2g}$ interaction
is the key to stabilize this ferromagnetic order. By suppressing this
ferromagnetic interaction and enhancing antiferromagnetic orbital channels of
$e_g$-$e_g$ and $t_{2g}$-$t_{2g}$, one can realize the desirable
antiferromagnetic order. We showed that high-temperature monoclinic stacking
can be the case. Our results provide unique information and insight to
understand the magnetism of multi-layer CrI$_3$ paving the way to utilize it
for applications.
