  Two-dimensional chromium ditelluride (CrTe2) is a promising ferromagnetic
layered material that exhibits long-range ferromagnetic ordering in the
monolayer limit. The formation energies of the different possible structural
phases (1T, 1H, 2H) calculated from density functional theory (DFT) show that
the 1T phase is the ground state, and the energetic transition barriers between
the phases, calculated by the nudged elastic band method, are large, on the
order of 0.5 eV. The self-consistent Hubbard $U$ correction parameters are
calculated for all the phases of CrTe$_2$. The calculated magnetic moment of
1T-CrTe$_2$ with $\geq 2$ layers lies in the plane, whereas the magnetic moment
of a monolayer is out-of-plane. Band filling and tensile bi-axial strain cause
the magnetic moment of a monolayer to switch from out-of-plane to in-plane, and
compressive bi-axial strain in a bilayer causes the magnetic moment to switch
from in-plane to out-of-plane. The magnetic anisotropy is shown to originate
from the large spin orbit coupling (SOC) of the Te atoms and the anisotropy of
the exchange coupling constants $J_{xy}$ and $J_z$ in an XXZ type Hamiltonian.
Renormalized spin wave theory using experimental values for the magnetic
anisotropy energy and Curie temperatures provides a range of values for the
nearest neighbor exchange coupling.
