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We present a comprehensive study on the electronic and magnetic properties ofthe EuCl$_3$ monolayer using first-principles calculations. By taking intoaccount the spin-orbit coupling (SOC) and the Hubbard effects, we elucidate theinfluence of these interactions on the structural properties of EuCl$_3$monolayer. Comparing the lattice parameters obtained with the PBE+SOC andPBE+SOC+Hubbard effects reveals an increase in the lattice parameters whenincluding the Hubbard effect. In the absence of the Hubbard interaction, themagnetic ground state of the EuCl$_3$ monolayer exhibits a preference for aferromagnetic (FM) configuration as determined by the PBE+SOC calculations.However, the introduction of the Hubbard parameter leads to a shift in themagnetic ground state preference towards an antiferromagnetic (AFM) N\'{e}elstate. Based on the calculated energy values, Monte Carlo simulations arecarried out to determine the N\'{e}el temperature $(T_N)$. Our simulationsyield a N\'{e}el temperature of \SI{390}{\kelvin} for the EuCl$_3$ monolayer,indicating the temperature at which the transition from a paramagnetic phase toan antiferromagnetic phase occurs. These results highlight the importance ofincorporating the SOC and the Hubbard effect in accurately describing theelectronic and magnetic properties of the EuCl$_3$ monolayer. Our resultscontribute to a deeper understanding of the fundamental physics underlying thebehavior of this intriguing two-dimensional material and provide insights intoits potential applications in spintronics and magnetic devices.

Emergent Antiferromagnetic Behavior in EuCl$_3$ Monolayer: A Comprehensive First-Principles Study Including Hubbard-SOC Interplay