A combined first principles study of the structural, magnetic, and phonon properties of monolayer CrI₃

The first magnetic 2D material discovered, monolayer (ML) CrI₃, is particularly fascinating due to its ground state ferromagnetism. However, because ML materials are difficult to probe experimentally, much remains unresolved about ML CrI₃'s structural, electronic, and magnetic properties. Here, we leverage Density Functional Theory (DFT) and high-accuracy Diffusion Monte Carlo (DMC) simulations to predict lattice parameters, magnetic moments, and spin-phonon and spin-lattice coupling of ML CrI₃. We exploit a recently developed surrogate Hessian DMC line search technique to determine CrI₃'s ML geometry with DMC accuracy, yielding lattice parameters in good agreement with recently published STM measurements-an accomplishment given the ∼10% variability in previous DFT-derived estimates depending upon the functional. Strikingly, we find that previous DFT predictions of ML CrI₃'s magnetic spin moments are correct on average across a unit cell but miss critical local spatial fluctuations in the spin density revealed by more accurate DMC. DMC predicts that magnetic moments in ML CrI₃ are 3.62 μ_B per chromium and -0.145 μ_B per iodine, both larger than previous DFT predictions. The large disparate moments together with the large spin-orbit coupling of CrI₃'s I-p orbital suggest a ligand superexchange-dominated magnetic anisotropy in ML CrI₃, corroborating recent observations of magnons in its 2D limit. We also find that ML CrI₃ exhibits a substantial spin-phonon coupling of ∼3.32 cm^-1. Our work, thus, establishes many of ML CrI₃'s key properties, while also continuing to demonstrate the pivotal role that DMC can assume in the study of magnetic and other 2D materials.