Environmental Screening and Ligand-Field Effects to Magnetism in CrI$_3$ Monolayer

Abstract

We present a detailed study on the microscopic origin of magnetism in suspended and dielectrically embedded CrI3 monolayer. To this end, we down-fold two distinct minimal generalized Hubbard models with different orbital basis sets from ab initio calculations using the constrained random phase approximation. Within mean-field approximation, we show that these models are capable of describing the formation of localized magnetic moments in CrI3 and of reproducing electronic properties of full ab initio calculations. We utilize the magnet force theorem to study microscopic magnetic exchange channels between the different orbital manifolds. We find a multi-orbital superexchange mechanism as the origin of magnetism in CrI3 resulting from a detailed interplay between effective ferro-and anti-ferromagnetic Cr-Cr d coupling channels, which is decisively affected by the ligand (I) p orbitals. We show how environmental screening such as resulting from encapsulation with hexagonal boron nitride (hBN) of the CrI3 monolayer affects the Coulomb interaction in the film and how this successively controls its magnetic properties. Driven by a non-monotonic interplay between nearest and next-nearest neighbour exchange interactions we find the magnon dispersion and the Curie temperature to be non-trivially affected by the environmental dielectric screening.

Electronic structure of rhombohedral CrX3 (X=Br, Cl, I)

“…6, the incoherent part of the GGA + DMFT spectral function and the experimental spectrum of CrBr 3 bulk crystal agree in many aspects, especially as for the splitting of the first two peaks. This validates the choice of the Coulomb parameter values used in our calculations [31], contrasting with values assumed in previous studies [17,20,21,28,30,48,49]. However, while good FIG.…”

“…However, before delving into the MO electronic structure reconstruction of CrX 3 bulk crystals, we recall here that the on-site Coulomb interaction parameter is reported to be in the range between 1.0 eV [21] and 4.1 eV [30] for CrI 3 crystals. Thus, given the uncertainty in the precise estimation of U for this layered system [17,20,21,30,44,48] and analogs [49,50] if not mentioned otherwise, we use the U values considered in our earlier GGA + DMFT study [31], i.e., U t 2g 1 = 2.75 eV and U t 2g 2 = U e g 2 = 4.0 eV, and fixed J H = 0.85 eV [20], where good theory-experiment agreement has been found within the paramagnetic phase of CrI 3 bulk crystal.…”

Electronic Structure of Chromium Trihalides beyond Density Functional Theory

“…2,[14][15][16][17][18][19][20][21][22] CrX 3 is a two-dimensional FM insulator with FM originating from the Cr-X-Cr superexchange interaction. 13,[23][24][25] Six Cr 3+ ions form a honeycomb structure with D 3d point group symmetry and each Cr is surrounded by six X in an octahedral geometry (see Fig. 1).…”