Role of Electronic Correlations on Exchange Interactions and Curie Temperature in Monolayer CrI3.

We investigate the magnetic properties of monolayer CrI3 by combining first-principles density functional theory calculations with an effective spin model and finite-temperature statistical analysis. The electronic structure is computed within the DFT+U framework, including spin-orbit coupling, allowing us to assess the role of electronic correlations on the structural, electronic, and magnetic properties of the system. Magnetic exchange interactions are extracted using the Green's-function-based Liechtenstein formalism and mapped onto an effective isotropic Heisenberg Hamiltonian. Our results show that the on-site Coulomb interaction U strongly influences the Cr-I bond geometry and the ligand-mediated superexchange pathways, leading to a nonmonotonic dependence of the dominant nearest-neighbor exchange interaction on U. This behavior places monolayer CrI3 in an intermediate-correlation regime, where electronic localization and hybridization compete to determine the strength of ferromagnetic coupling. Finite-temperature magnetic properties are investigated using the cluster mean-field theory, which partially incorporates short-range magnetic correlations beyond conventional mean-field approaches. The calculated effective Curie temperature within the cluster mean-field (CMF) framework exhibits a pronounced maximum at intermediate values of U, yielding values of the same order of magnitude as experimental measurements for monolayer CrI3. However, this temperature should be interpreted as an effective energy scale associated with the onset of short-range magnetic correlations within the CMF approximation, rather than a true thermodynamic transition temperature. These results indicate that the dominant energy scale governing magnetic ordering is primarily controlled by isotropic exchange interactions and short-range correlations. Thus, our results show that a minimal Heisenberg model parametrized from first principles, combined with the CMF theory, supplies a well-grounded and computationally efficient framework to describe the magnetic properties of two-dimensional van der Waals magnets.