Magnetic Anisotropy in Spin-3/2 with Heavy Ligand in Honeycomb Mott Insulators: Application to CrI₃

Ferromagnetism in the two-dimensional CrI₃ has generated a lot of excitement, and it was recently proposed that the spin-orbit coupling in Iodine may generate bond-dependent spin interactions leading to magnetic anisotropy. Here we derive a microscopic spin model of S=3/2 on transition metals surrounded by heavy ligands in honeycomb Mott insulators using a strong-coupling perturbation theory. For ideal octahedra we find the Heisenberg and Kitaev interactions, which favor the magnetic moment along the cubic axis via quantum fluctuations. When a slight distortion of the octahedra is present together with the spin-orbit coupling, three additional terms, the off-diagonal symmetric interactions Γ and Γ', and on-site Ising interactions arise. They result in the magnetic anisotropy that pins the moment perpendicular to the honeycomb plane. Applications to single layer CrI₃ are discussed. [1]

[1] arXiv:2009.04475