Anisotropic magnetic interactions in CrI₃

CrI₃ is famous among van-der-Waals materials because it displays ferromagnetism in the bulk form, and also in the monolayer form, with an only slightly reduced Curie temperature. Since Heisenberg and XY models do not allow long-range ordering in 2D, it was initially assumed that the magnetic Hamiltonian in CrI₃ is of the Ising symmetry. However, it was later shown that it is not the single-site anisotropy, but exchange interaction anisotropy (driven by the spin-orbit coupling on I) that ensures the high Curie temperature. It was assumed, however, without any theoretical justification, that this interaction is of the simplest, pseudo-Ising, form, namely S^z S^z, z being the global hexagonal axis. In this talk, we will present first principle calculations showing that not only this pseudo-Ising interaction is present in the system, but all three nearest-neighbor anisotropic terms allowed by symmetry (S^xS^x-S^yS^y and S^xS^z-S^zS^x), plus proper rotations for two other bonds)are of similar order.