The family of atomically thin magnets holds great promise for a number of prospective applications in magneto-optoelectronics, with CrI$_3$ arguably being its most prototypical member. However, the formation of defects in this system remains unexplored to date. Here, we investigate native point defects in monolayer CrI$_3$ by means of first-principles calculations. We consider a large set of intrinsic impurities and address their atomic structure, thermodynamic stability, diffusion and aggregation tendencies as well as local magnetic moments. Under thermodynamic equilibrium, the most stable defects are found to be either Cr or I atomic vacancies along with their complexes, depending on the chemical potential conditions. These defects are predicted to be quite mobile at room temperature and to exhibit a strong tendency to agglomerate. In addition, our calculations indicate that the defect-induced deviation from the nominal stoichiometry largely impacts the local magnetic moments, thereby suggesting a marked interplay between magnetism and disorder in CrI$_3$. Overall, this work portrays a comprehensive picture of intrinsic point defects in monolayer CrI$_3$ from a theoretical perspective.
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