  Two-dimensional (2D) materials with intrinsic ferromagnetism provide unique
opportunity to engineer new functionalities in nano-spintronics. One such
material is CrI$_3$, showing long-range magnetic order in monolayer with the
Curie temperature ($T_c$) of 45 K. Here we study detailed evolution of magnetic
transition and magnetic critical properties in response to systematic reduction
in crystal thickness down to 50 nm. Bulk $T_c$ of 61 K is gradually suppressed
to 57 K, however, the satellite transition at $T^*$ = 45 K is observed
layer-independent at fixed magnetic field of 1 kOe. The origin of $T^*$ is
proposed to be a crossover from pinning to depinning of magnetic domain walls.
The reduction of thickness facilitates a field-driven metamagnetic transition
around 20 kOe with out-of-plane field, in contrast to the continuous changes
with in-plane field. The critical analysis around $T_c$ elucidates the
mean-field type interactions in microscale-thick CrI$_3$.
