Interplay between interlayer exchange and stacking in CrI3 bilayers

We address the interplay between stacking and interlayer exchange for ferromagnetically ordered CrI3, both for bilayers and bulk. Whereas bulk CrI3 is ferromagnetic, both magneto-optical and transport experiments show that interlayer exchange for CrI3 bilayers is antiferromagnetic. Bulk CrI3 is known to assume two crystal structures, rhombohedral and monoclinic, that differ mostly in the stacking between monolayers. Below 210-220 K, bulk CrI3 orders in a rhombohedral phase. Our density functional theory calculations show a very strong dependence of interlayer exchange and stacking. Specifically, the ground states of both bulk and freestanding CrI3 bilayers are ferromagnetic for the rhombohedral phase. In contrast, the energy difference between both configurations is more than one order of magnitude smaller for the monoclinic phase, and eventually becomes antiferromagnetic when either positive strain or on-site Hubbard interactions (U >= 3) are considered. We also explore the interplay between interlayer hybridization and stacking, using a Wannier basis, and between interlayer hybridization and relative magnetic alignment for CrI3 bilayers, that helps to account for the very large tunnel magnetoresistance observed in recent experiments.