  We calculate the Curie temperature of layered ferromagnets, chromium
tri-iodide (CrI3), chromium tri-bromide (CrBr3), chromium germanium
tri-telluride (CrGeTe3), and the Neel temperature of a layered anti-ferromagnet
iron di-chloride (FeCl2), using first-principles density functional theory
calculations and Monte-Carlo simulations. We develop a computational method to
model the magnetic interactions in layered magnetic materials and calculate
their critical temperature. We provide a unified method to obtain the magnetic
exchange parameters (J) for an effective Heisenberg Hamiltonian from
first-principles, taking into account both the magnetic ansiotropy as well as
the out-of-plane interactions. We obtain the magnetic phase change behavior, in
particular the critical temperature, from the susceptibility and the
specific-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 the
interlayer interaction in bulk CrI3 with R3 stacking is significantly stronger
than the C2/m stacking, in line with experimental observations. We show that
the strong interlayer interaction in R3 CrI results in a competition between
the in-plane and the out-of-plane magnetic easy axis. Finally, we calculate the
Neel temperature of FeCl2 to be 47 +- 8 K, and show that the magnetic phase
transition in FeCl2 occurs in two steps with a high-temperature intralayer
ferromagnetic phase transition, and a low-temperature interlayer
anti-ferromagnetic phase transition.
