  The magnetic ground state is crucial for the applications of the
two-dimension magnets as it decides fundamental magnetic properties of the
material, such as magnetic order, magnetic transition temperature, and
low-energy excitation of the spin waves. However, the simulations for magnetism
of local-electron systems are challenging due to the existence of metastable
states. In this study, occupation matrix control (OMC) and density functional
theory plus Hubbard $U$ calculations are applied to investigate the magnetic
ground state of monolayer CeI$_{2}$. Following the predicted ferrimagnetic (FM)
order, the FM ground state and the FM metastable states are identified and
found to have different values of the magnetic parameters. Based on the
calculated magnetic parameters of the FM ground state, the Curie temperature is
estimated to be $128$ K for monolayer CeI$_{2}$. When spin-orbit coupling (SOC)
is considered,the FM ground state is further confirmed to contain both
off-plane and in-plane components of magnetization. SOC is shown to be
essential for reasonably describing not only magnetic anisotropy but also local
electronic orbital state of monolayer CeI$_{2}$.
