  We applied the generalized Bloch theorem to verify the ground state (most
stable state) in monolayer metal diiodides 1T-XI$_{2}$ (X: Fe, Co, and Ni), a
family of metal dihalides, using the first-principles calculations. The ground
state, which can be ferromagnetic, antiferromagnetic, or spiral state, was
specified by a wavevector in the primitive unit cell. While the ground state of
FeI$_{2}$ is ferromagnetic, the spiral state becomes the ground state for
CoI$_{2}$ and NiI$_{2}$. Since the multiferroic behavior in the metal dihalide
can be preserved by the spiral structure, we believe that CoI$_{2}$ and
NiI$_{2}$ are promising multiferroic materials in the most stable state. When
the lattice parameter increases, we also show that the ground state of
NiI$_{2}$ changes to a ferromagnetic state while others still keep their
initial ground states. For the last discussion, we revealed the phase
transition manipulated by hole-electron doping due to the spin-spin competition
between the ferromagnetic superexchange and the antiferromagnetic direct
exchange. These results convince us that metal diiodides have many benefits for
future spintronic devices.
