  Ferromagnetism in the two-dimensional CrI$_3$ has generated a lot of
excitement, and it was recently proposed that the spin-orbit coupling (SOC) in
Iodine may generate bond-dependent spin interactions leading to magnetic
anisotropy. Here we derive a microscopic spin model of S=3/2 on transition
metals surrounded by heavy ligands in honeycomb Mott insulators using a
strong-coupling perturbation theory. For ideal octahedra we find Heisenberg and
Kitaev interactions, which favor the magnetic moment along the cubic axis via
quantum fluctuations. When a slight trigonal distortion of the octahedra is
present together with the SOC, three additional interactions arise, comprised
of the off-diagonal symmetric $\Gamma$ and $\Gamma^\prime$, and single-ion
anisotropy. The resulting magnetic anisotropy pins the moment perpendicular to
the honeycomb plane as observed in a single-layer of CrI$_3$, suggesting the
significance of SOC and trigonal distortion in understanding magnetism of two
dimensional Mott insulators. Comparison to the spin-orbit coupled $J_{\rm
eff}$= 1/2 and S=1 models is also presented.
