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We calculate the Curie temperature of layered ferromagnets, chromiumtri-iodide (CrI3), chromium tri-bromide (CrBr3), chromium germaniumtri-telluride (CrGeTe3), and the Neel temperature of a layered anti-ferromagnetiron di-chloride (FeCl2), using first-principles density functional theorycalculations and Monte-Carlo simulations. We develop a computational method tomodel the magnetic interactions in layered magnetic materials and calculatetheir critical temperature. We provide a unified method to obtain the magneticexchange parameters (J) for an effective Heisenberg Hamiltonian fromfirst-principles, taking into account both the magnetic ansiotropy as well asthe out-of-plane interactions. We obtain the magnetic phase change behavior, inparticular the critical temperature, from the susceptibility and thespecific-heat, calculated using the three-dimensional Monte-Carlo (Metropolis)algorithm. The calculated Curie temperatures for ferromagnetic materials (CrI3,CrBr3 and CrGeTe3), match very well with experimental values. We show that theinterlayer interaction in bulk CrI3 with R3 stacking is significantly strongerthan the C2/m stacking, in line with experimental observations. We show thatthe strong interlayer interaction in R3 CrI results in a competition betweenthe in-plane and the out-of-plane magnetic easy axis. Finally, we calculate theNeel temperature of FeCl2 to be 47 +- 8 K, and show that the magnetic phasetransition in FeCl2 occurs in two steps with a high-temperature intralayerferromagnetic phase transition, and a low-temperature interlayeranti-ferromagnetic phase transition.

Critical behavior of ferromagnets CrI3, CrBr3, CrGeTe3, and anti-ferromagnet FeCl2: a detailed first-principles study