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-1 arXiv:1811.05413v1 [cond-mat.mtrl-sci] 13 Nov 2018 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.

Magnetism and magneto-optical effects in bulk and few-layer CrI3: a theoretical GGA + U study

“…This appears to be somewhat surprising since the 3d transition metals such as Cr usually have small SOC. The large MAEs could be attributed to two factors, namely, the 2D and quasi-2D structures of these materials and also the large SOC of the heavy ligand ion (I) [49]. As a result, these CrI 3 multilayers could have valuable applications in high density data storage devices.…”

Topological spin texture in Janus monolayers of the chromium trihalides Cr(I, X)3

“…The ferromagnetic monolayer CrI 3 crystalizes in honeycomb lattice made of edge-sharing octahedra. Its ferromagnetic order is stabilized by an out-of-plane anisotropy 11 , which arises from single ion anisotropy (SIA) andKitaev-type exchange coupling that both result from the SOC of its heavy ligands 13,14 . However, the ingredient DMI is absent between the most strongly coupled first nearest neighbor (1st NN) Cr-Cr pairs, because the inversion center between the two Cr atoms prevents its existence 15 .…”

“…Kitaev-type exchange coupling that both result from the SOC of its heavy ligands 13,14 . However, the ingredient DMI is absent between the most strongly coupled first nearest neighbor (1st NN) Cr-Cr pairs, because the inversion center between the two Cr atoms prevents its existence 15 .…”

Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2

“…We chose here to study CrSiTe 3 (CST) and CrGeTe 3 (CGT) under compressive strain because, as we will see, their J coefficient is rather sensitive to such strain. CST has the same structure than CGT, and exhibits a similar Heisenberg behavior than CGT but with an additional slightly favoring out-of-plane anisotropy [25,26] (note that properties of CST, including the nature of its FM state, can be well explained by Eq (2) as well [15]).…”