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

We compare three first-principles methods of calculating the Curie\ntemperature in two-dimensional (2D) ferromagnetic materials (FM), modeled using\nthe Heisenberg model, and propose a simple formula for estimating the Curie\ntemperature with high accuracy that works for all common 2D lattice types.\nFirst, we study the effect of exchange anisotropy on the Curie temperature\ncalculated using the Monte-Carlo (MC), the Green's function method, and the\nrenormalized spin-wave (RNSW). We find that the Green's function overestimates\nthe Curie temperature in high-anisotropy regimes compared to MC, whereas RNSW\nunderestimates the Curie temperature compared to the MC and the Green's\nfunction. Next, we propose a closed-form formula for calculating the Curie\ntemperature of 2D FMs, which provides an estimate of the Curie temperature\ngreatly improving over the mean-field expression for magnetic material\nscreening. We apply the closed-form formula to predict the Curie temperature 2D\nmagnets screened from the C2DB database and discover several high Curie\ntemperature FMs with Fe2F2 and MoI2 emerging as the most promising 2D\nferromagnets. Finally, comparing to experimental results for CrI3, CrCl3, and\nCrBr3, we conclude that for small effective anisotropies, the Green's\nfunction-based equations are preferable, while, for larger anisotropies\nMC-based results are more predictive.\n