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We applied the generalized Bloch theorem to verify the ground state (moststable state) in monolayer metal diiodides 1T-XI$_{2}$ (X: Fe, Co, and Ni), afamily of metal dihalides, using the first-principles calculations. The groundstate, which can be ferromagnetic, antiferromagnetic, or spiral state, wasspecified by a wavevector in the primitive unit cell. While the ground state ofFeI$_{2}$ is ferromagnetic, the spiral state becomes the ground state forCoI$_{2}$ and NiI$_{2}$. Since the multiferroic behavior in the metal dihalidecan be preserved by the spiral structure, we believe that CoI$_{2}$ andNiI$_{2}$ are promising multiferroic materials in the most stable state. Whenthe lattice parameter increases, we also show that the ground state ofNiI$_{2}$ changes to a ferromagnetic state while others still keep theirinitial ground states. For the last discussion, we revealed the phasetransition manipulated by hole-electron doping due to the spin-spin competitionbetween the ferromagnetic superexchange and the antiferromagnetic directexchange. These results convince us that metal diiodides have many benefits forfuture spintronic devices.

Controlling phase transition in monolayer metal diiodides XI$_{2}$ (X: Fe, Co, and Ni) by carrier doping