Magnetic properties of monolayer, multilayer, and bulk CrTe$_2$

We investigate magnetic properties of CrTe$_2$ within the density functional theory (DFT) approach in ferromagnetic phase and combination of DFT and dynamical mean field theory (DFT+DMFT) approach in paramagnetic phase. We show that few layer CrTe$_2$ possesses well formed local magnetic moments. In the single layer CrTe$_2$ we find antiferromagnetic exchange with 120\degree antiferromagnetic structure most preferable. In the bilayer and trilayer systems electronic correlations in DFT+DMFT approach yield ferromagnetic exchange interaction within each layer, but the interaction between the layers is antiferromagnetic, such that alternation of the direction of magnetization of the layers is expected. In bulk CrTe$_2$ we find the tendency to ferromagnetic order at low temperature, but with increase of temperature antiferromagnetic correlations between the layers dominate. Determination of the critical number of layers at which the interlayer antiferromagnetic order changes to the ferromagnetic one, requires consideration of the non-local Coulomb interactions.