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.
Highlights
Two-dimensional (2D) magnetic materials are receiving a lot of attention, due, e.g., to the search for long-range ferromagnetism (FM),[1,2] which can facilitate various applications from sensing to data storage.[3,4] According to Mermin and Wagners theorem,[2] strong the short-range isotropic couplings are, the realization of 2D magnetism relies on magnetic anisotropy, as a result of spin–orbit coupling (SOC)
A recent theoretical work adopted the XXZ model, for which the exchange coupling is identical between the in-plane x-direction and y-direction but different along the out-of-plane zdirection, to explain the out-of-plane magnetization of CrI3.8 there is no definite proof that the XXZ model is accurate enough to describe the magnetic anisotropy of CrI3, and there is a current paucity of knowledge for the mechanism responsible for the magnetic anisotropy of CrGeTe3
Density functional theory (DFT) calculations are performed on CrI3 and CrGeTe3 monolayers to extract the components of J and A using a precise four-states method[17,18]
Summary
Two-dimensional (2D) magnetic materials are receiving a lot of attention, due, e.g., to the search for long-range ferromagnetism (FM),[1,2] which can facilitate various applications from sensing to data storage.[3,4] According to Mermin and Wagners theorem,[2] strong the short-range isotropic couplings are, the realization of 2D magnetism relies on magnetic anisotropy, as a result of spin–orbit coupling (SOC). The requirement of strong magnetic anisotropy in low-dimensional systems explains the rareness of 2D FM materials. The recent observation of FM in monolayers made of CrI3 and CrGeTe3,5–7 opens a new chapter in the field of 2D materials. The chromium in both compounds share the same valence state of Cr3+, with the 3d3 configuration and S = 32.7–10 FM arises there from the super exchange between nearest-neighbor Cr ions, that are linked by I or Te ligands through nearly 90° angles.[10,11]. The magnetic anisotropy of CrGeTe3 was determined to be consistent with the Heisenberg behavior,[2,7,12] for which the spins can freely rotate and adopt any direction in the three-dimensional space. A thorough microscopic understanding of the difference between the Ising behavior of CrI3 and the Heisenberg behavior of CrGeTe3 is highly desired
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call