Abstract
We study the microscopic origin of magnetism in suspended and dielectrically embedded CrI3 monolayer by down-folding minimal generalized Hubbard models from ab initio calculations using the constrained random phase approximation. These models are capable of describing the formation of localized magnetic moments in CrI3 and of reproducing electronic properties of direct ab initio calculations. Utilizing the magnet force theorem, we find a multi-orbital super-exchange mechanism as the origin of magnetism in CrI3 resulting from an interplay between ferro- and anti-ferromagnetic Cr-Cr d coupling channels, which is decisively affected by the ligand p orbitals. We show how environmental screening, such as resulting from encapsulation with hexagonal boron nitride, affects the Coulomb interaction in the film and how this controls its magnetic properties. Driven by a non-monotonic interplay between nearest and next-nearest neighbor exchange interactions we find the magnon dispersion and the Curie temperature to be non-trivially affected by the environmental screening.
Highlights
Ferromagnetic (FM) layered materials hold high promises for becoming one of the key ingredients in future spintronic nanodevices[1,2,3,4] based on van-der-Waals heterostructures
In contrast to the d-only model we find a density of states (DOS) which is vastly reminiscent of the full ab initio generalized gradient approximation (GGA) + U results shown in Fig. 1
By combining state-of-the-art constrained RPA (cRPA)-based ab initio down-folding with our Wannier function continuum electrostatics (WFCE) approach and the magnetic force theorem (MFT) method, we were able to study on a microscopic level how magnetism in CrI3 monolayer builds up and how it is controlled by environmental screening properties
Summary
Ferromagnetic (FM) layered materials hold high promises for becoming one of the key ingredients in future spintronic nanodevices[1,2,3,4] based on van-der-Waals heterostructures. Reported theoretical predictions to suggest, for instance, a strong dependence of the magneto-optical response on the film thickness and the spin–orbit coupling of CrI38, while recent experimental studies point towards the possibility to tune the magnetic properties of monolayer and bilayer CrI3 using electrostatic gating[9,10,11,12] These observations highlight the importance of addressing how the environment of layered magnetic systems modifies their electronic and magnetic properties via proximity, gating, or screening effects. For the case of chromium trihalides, CrX3 (X = I, Br, Cl), the nearest neighbor magnetic exchange couplings have been theoretically reported to be between 1 and 3.2 meV13–18 depending on the material and calculation scheme, which renders rigorous theoretical descriptions absolutely necessary This holds especially with respect to the Coulomb interactions in a layered material, which are enhanced due to reduced polarization in the surrounding. Any changes from environmental screening to the exchange couplings of this effective Hamiltonian can give rise to changes in the magnetic transition temperature or the magnon spectrum opening new routes towards the control and potential tailoring of magnetic properties of chromium trihalides
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