Interplay between Kitaev interaction and single ion anisotropy in ferromagnetic CrI3 and CrGeTe3 monolayers

Abstract

Magnetic anisotropy is crucially important for the stabilization of two-dimensional (2D) magnetism, which is rare in nature but highly desirable in spintronics and for advancing fundamental knowledge. Recent works on CrI3 and CrGeTe3 monolayers not only led to observations of the long-time-sought 2D ferromagnetism, but also revealed distinct magnetic anisotropy in the two systems, namely Ising behavior for CrI3 versus Heisenberg behavior for CrGeTe3. Such magnetic difference strongly contrasts with structural and electronic similarities of these two materials, and understanding it at a microscopic scale should be of large benefits. Here, first-principles calculations are performed and analyzed to develop a simple Hamiltonian, to investigate magnetic anisotropy of CrI3 and CrGeTe3 monolayers. The anisotropic exchange coupling in both systems is surprisingly determined to be of Kitaev-type. Moreover, the interplay between this Kitaev interaction and single ion anisotropy (SIA) is found to naturally explain the different magnetic behaviors of CrI3 and CrGeTe3. Finally, both the Kitaev interaction and SIA are further found to be induced by spin–orbit coupling of the heavy ligands (I of CrI3 or Te of CrGeTe3) rather than the commonly believed 3d magnetic Cr ions.