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 CrI 3 and CrGeTe 3 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 CrI 3 versus Heisenberg behavior for CrGeTe 3. 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 CrI 3 and CrGeTe 3 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 CrI 3 and CrGeTe 3. Finally, both the Kitaev interaction and SIA are further found to be induced by spin–orbit coupling of the heavy ligands (I of CrI 3 or Te of CrGeTe 3) rather than the commonly believed 3 d magnetic Cr ions.