Interplay between Kitaev Interaction and Single Ion Anisotropy in Ferromagnetic CrI₃ and CrGeTe₃ Monolayers

First-principles calculations are performed and analyzed to develop a rather simple Hamiltonian, in order to investigate the magnetic anisotropy of the recently discovered ferromagnetic monolayers made of CrI3 and CrGeTe3. The anisotropic exchange coupling in these two systems is surprisingly determined to be of Kitaev-type, which broadens the candidate materials that may realize quantum spin liquid states. Moreover, the interplay between this Kitaev interaction and single ion anisotropy (SIA) is found to naturally explain the Ising behavior of CrI3 versus the Heisenberg behavior of CrGeTe3, as well as other observed phenomena in other related 2D systems. Finally, both the Kitaev interaction and SIA are further found to be induced by the spin-orbit coupling of the heavy ligands (I of CrI3 or Te of CrGeTe3) rather than the 3d magnetic Cr ion.