Relative stability and magnetic ground state of all stacking patterns in bilayer chromium trihalides from first principles

Chromium trihalides, CrX₃ (X = Cl, Br, I), are layered magnetic materials that have recently attracted considerable attention owing to their easy exfoliability. Their monolayers are ferromagnetic, with spins lying in-plane for CrCl₃ and out-of-plane for CrBr₃ and CrI₃. This difference is reflected also in distinct interlayer interactions when layers are stacked into their bulk: antiferromagnetic for CrCl₃, while ferromagnetic for the others. Still, even multilayers of CrI₃ behave as antiferromagnets, whereas CrBr₃ remains ferromagnetic. Here, we address this controversy by studying bilayers of these materials using density functional theory. We enumerate all possible stacking patterns with the smallest unit cell and investigate their relative stability. We show that, depending on the stacking order, the magnetic ground state can be different. In particular, we recover that the bulk stacking is indeed the most stable and it is correctly ferromagnetic for CrI₃ and CrBr₃, although there exist other low-lying metastable configurations that are antiferromagnetic. Based on our findings, we speculate on how the apparent controversy could be resolved.