  Recently, three different magnetic states were observed experimentally in
trilayer CrI3 under pressure,including ferromagnetic (FM)-upupup, FM-downupdown
and FM-upupdown. To reveal the nature of the observed three magnetic states, we
studied the magnetic properties of four possible stacking structures in
trilayer CrI3: I (rhombohedral), II (monoclinic), III (hexagonal) and IV
(triclinic). We find that all four stacking structures possess the FM-upupup
ground state. After applying a few strains, the FM-downupdown becomes the
ground state in II and III structures, and the FM-upupdown is preferred in IV
structure, while the FM-upupup persists in I structure. Our results unveil that
the three magnetic states observed in trilayer CrI3 may correspond to different
stacking structures with small tensile strains, which can well interpret the
experimentally obtained pressure dependent interlayer coupling and Curie
temperature. Our present study paves a way to design the magnetic multilayers
with required magnetic states by tuning stacking and strain.
