single crystals*

Two-dimensional (2D) materials with intrinsic ferromagnetism provide unique opportunity to engineer new functionalities in nano-spintronics. One such material is CrI₃, 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 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 a three-dimensional (3D) long-range magnetic coupling in bulk CrI₃, then mean-field type interactions in microscale-thick flake, and evolves into 2D Ising-like ferromagnetism in monolayer.