Interplay between interlayer exchange and stacking in CrI$_3$ bilayers

D. Soriano, C. Cardoso, J. Fernández-Rossier

Published 2018-07-01Version 1

We address the interplay between stacking and interlayer exchange in bilayers of ferromagnetically ordered CrI$_3$. Whereas bulk CrI$_3$ is ferromagnetic, both magneto-optical and transport experiments show that interlayer exchange for CrI$_3$ bilayers is antiferromagnetic. Bulk CrI$_3$ has two crystal structures, rhombohedral and monoclinic, that differ mostly in the stacking between monolayers. Below 220 Kelvin, bulk CrI$_3$ orders in a rhombohedral phase. Our density functional calculations, at two different levels of approximation, show that interlayer coupling for free-standing CrI$_3$ bilayers is ferromagnetic for the rhombohedral phase. In contrast, the interlayer coupling is smaller for the monoclinic phase and, when calculated with electron calculations including spin-orbit coupling, antiferromagnetic (-1.7 meV per unit cell). Calculations carried out at the same level of approximation give ferromagnetic interlayer exchange (11.5 meV per unit cell) for the rhombohedral structure. We attribute this to the enhancement of interlayer hybridization in the monoclinic case, computed projecting the plane-wave Hamiltonian into a Wannier basis. Interlayer hybridization promotes antiferromagnetic superexchange, that competes with other superexchange pathways that favour ferromagnetic interlayer coupling.