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

We compare three first-principles methods of calculating the Curie temperature in two-dimensional (2D) ferromagnetic materials (FM), modeled using the Heisenberg model, and derive a simple formula for estimating the Curie temperature with high accuracy that works for all common 2D lattice types. First, we study the effect of exchange anisotropy on the Curie temperature calculated using three-dimensional Monte-Carlo (MC), the Green function method, and the renormalized spin-wave (RNSW). We find that the Green function overestimates the Curie temperature in high-anisotropy regimes compared to MC, whereas, RNSW underestimates the Curie temperature compared to the MC and the Green function. Next, we propose a closed-form formula for calculating the Curie temperature of 2D FMs using each method, which takes only the nearest neighbor anisotropy, the lattice type, and the exchange interaction strength as an input. We apply the closed-form formula to predict the Curie temperature 2D magnets screened from the C2DB database and discover several high Curie temperature FMs with Fe2F2 and MoI2 emerging as the most promising 2D ferromagnets. Finally, comparing to experimental results for CrI3, CrCl3, and CrBr3, we conclude that for small effective anisotropies, the Green function-based equations are preferable, while, for larger anisotropies MC-based results are more predictive.