Orbitally-resolved ferromagnetism of monolayer CrI₃

Abstract

Few-layer CrI 3 is the most known example among two-dimensional (2D) ferromagnets, which have attracted growing interest in recent years. Despite considerable efforts and progress in understanding the properties of 2D magnets both from theory and experiment, the mechanism behind the formation of in-plane magnetic ordering in chromium halides is still under debate. Here, we propose a microscopic orbitally-resolved description of ferromagnetism in monolayer CrI 3 . Starting from first-principles calculations, we construct a low-energy model for the isotropic Heisenberg exchange interactions. We find that there are two competing contributions to the long-range magnetic ordering in CrI 3 : (i) Antiferromagnetic Anderson's superexchange between half-filled t 2g orbitals of Cr atoms; and (ii) Ferromagnetic exchange governed by the Kugel-Khomskii mechanism, involving the transitions between half-filled t 2g and empty e g orbitals. Using numerical calculations, we estimate the exchange interactions in momentum-space, which allows us to restore the spin-wave spectrum, as well as estimate the Curie temperature. Contrary to the nearest-neighbor effective models, our calculations suggest the presence of sharp resonances in the spin-wave spectrum at 5-7 meV, depending on the vertical bias voltage. Our estimation of the Curie temperature in monolayer CrI 3 yields 55-65 K, which is in good agreement with experimental data.

Electron correlation effects on exchange interactions and spin excitations in 2D van der Waals materials

“…By far, except for a few studies 23,38,39 using the magnetic force theorem (MFT) 40 , most of the theoretical investigations of the magnetic interactions in m2Dv are based on mapping the total energies of various collinear spin configurations into the Heisenberg model (referred to hereafter as the energy-mapping method), often employed with DFT + U. However, the applicability and accuracy of such an approach in CrI 3 are not clear.…”

Relativistic exchange interactions in CrX3 ( X=Cl , Br, I) monolayers

“…Regarding single-layer CrI 3 , the agreement with Ref. [48] is less good, but the structural optimization was done using different functionals in these two works, which makes it difficult to compare. Nonetheless, there is one substantial qualitative difference related to the effect of Hubbard U .…”

“…As was pointed out in Refs. [45,48], theJ 1 coupling consists of two competing terms originating from e g -and t 2g -like orbitals. Following Ref.…”

“…Kashin et al [48] have analyzed the magnetic interactions in monolayered CrI 3 , using similar methods as in Ref. [45].…”

“…References [45,48] neglect the effect of spin-orbit coupling, which only allowed them to address isotropic (Heisenberg) exchange interactions. In this work we do the natural next step and provide a complete first-principles description of the relativistic magnetic interactions in CrX 3 systems.…”