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In addition to spintronics another motivation for exploring ferromagnetic two-dimensional materials is for biomedical applications such as magnetic labeling and hyperthermia treatment of tumors. Unfortunately, the widely studied Mn-containing monolayer is not biocompatible, although it is ferromagnetic. Here using first principles calculations combined with Monte Carlo simulations based on the Ising model, we systematically study a class of 2D ferromagnetic monolayers CrX3 (X = Cl, Br, I). The feasibility of exfoliation from their layered bulk phase is confirmed by the small cleavage energy and high in-plane stiffness. Spin-polarized calculations, combined with self-consistently determined Hubbard U that accounts for strong correlation energy, demonstrate that CrX3 (X = Cl, Br, I) monolayers are ferromagnetic and that Cr is trivalent and carries a magnetic moment of 3 μB; the resulting Cr3+ ions are biocompatible …