  Two-dimensional (2D) van der Waals (vdW) magnetic materials could be an ideal
platform for ultracompact spintronic applications. Among them, FeCl$_{2}$
monolayer in the triangular lattice is subject to a strong debate. Thus, we
critically examine its spin-orbital state, electronic structure, and magnetic
properties, using a set of delicate first-principles calculations, crystal
field level analyses, and Monte Carlo simulations. Our work reveals that
FeCl$_{2}$ monolayer is a ferromagnetic (FM) semiconductor in which the
electron correlation of the narrow Fe $3d$ bands determines the band gap of
about 1.2 eV. Note that only when the spin-orbit coupling (SOC) is properly
handled, the unique $d$$^{5\uparrow}$$l$$^\downarrow_{z+}$ electronic ground
state is achieved. Then, both the orbital and spin contributions (0.59
$\mu_{\rm B}$ plus 3.56 $\mu_{\rm B}$) to the total magnetic moment well
account for, for the first time, the experimental perpendicular moment of 4.3
$\mu_{\rm B}$/Fe. Moreover, we find that a compressive strain further
stabilizes the $d$$^{5\uparrow}$$l$$^\downarrow_{z+}$ ground state, and that
the enhanced magnetic anisotropy and exchange coupling would boost the Curie
temperature ($T_{\rm C}$) from 25 K for the pristine FeCl$_{2}$ monolayer to
69-102 K under 3$\%$-5$\%$ compressive strain. Therefore, FeCl$_{2}$ monolayer
is indeed an appealing 2D FM semiconductor.
