Interplay between Kitaev interaction and single ion anisotropy in ferromagnetic CrI$_3$ and CrGeTe$_3$ monolayers

TL;DR

This study uses first-principles calculations to analyze magnetic anisotropy in CrI3 and CrGeTe3 monolayers, revealing that Kitaev interactions and single ion anisotropy, driven by spin-orbit coupling of heavy ligands, explain their distinct magnetic behaviors.

Contribution

It uncovers the microscopic origin of magnetic anisotropy differences in CrI3 and CrGeTe3, highlighting the role of Kitaev interactions and ligand spin-orbit coupling.

Findings

Kitaev-type anisotropic exchange in both materials

Interplay between Kitaev interaction and SIA explains magnetic differences

Spin-orbit coupling of heavy ligands induces key magnetic interactions

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 3d magnetic Cr ions.