Microscopic understanding of magnetic interactions in bilayer CrI3

We performed a detailed microscopic analysis of the interlayer magnetic couplings for bilayer ${\mathrm{CrI}}_{3}$. As a first step toward understanding recent experimental observations and utilizing them for device applications, we estimated the magnetic force response as well as total energy. Various van der Waals functionals unequivocally point to the ferromagnetic ground state for the low-temperature structured bilayer ${\mathrm{CrI}}_{3}$ which is further confirmed independently by magnetic force response calculations. The calculated orbital-dependent magnetic forces clearly show that the ${e}_{g}\ensuremath{-}{t}_{2g}$ interaction is the key to stabilize this ferromagnetic order. By suppressing this ferromagnetic interaction and enhancing antiferromagnetic orbital channels of ${e}_{g}\ensuremath{-}{e}_{g}$ and ${t}_{2g}\ensuremath{-}{t}_{2g}$, 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 into understanding the magnetism of multilayer ${\mathrm{CrI}}_{3}$, paving the way to utilize it for applications.