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We compare three first-principles methods of calculating the Curietemperature in two-dimensional (2D) ferromagnetic materials (FM), modeled usingthe Heisenberg model, and propose a simple formula for estimating the Curietemperature with high accuracy that works for all common 2D lattice types.First, we study the effect of exchange anisotropy on the Curie temperaturecalculated using the Monte-Carlo (MC), the Green's function method, and therenormalized spin-wave (RNSW). We find that the Green's function overestimatesthe Curie temperature in high-anisotropy regimes compared to MC, whereas RNSWunderestimates the Curie temperature compared to the MC and the Green'sfunction. Next, we propose a closed-form formula for calculating the Curietemperature of 2D FMs, which provides an estimate of the Curie temperaturegreatly improving over the mean-field expression for magnetic materialscreening. We apply the closed-form formula to predict the Curie temperature 2Dmagnets screened from the C2DB database and discover several high Curietemperature FMs with Fe2F2 and MoI2 emerging as the most promising 2Dferromagnets. Finally, comparing to experimental results for CrI3, CrCl3, andCrBr3, we conclude that for small effective anisotropies, the Green'sfunction-based equations are preferable, while, for larger anisotropiesMC-based results are more predictive.

Computing Curie temperature of two-dimensional ferromagnets in the presence of exchange anisotropy