  We investigated the ground state of monolayer 1T-XCl$_{2}$ (X: Fe, Co, and
Ni) using the generalized Bloch theorem, which can generate ferromagnetic,
spiral, and antiferromagnetic states. Each state was represented by a unique
spiral vector that arranges the magnetic moment of magnetic atom in the
primitive unit cell. We found the ferromagnetic ground state for the FeCl$_{2}$
and NiCl$_{2}$ while the spiral ground state appears for the CoCl$_{2}$. We
also showed that the ground state depends sensitively on the lattice constant.
When the hole-electron doping was taken into account, we found the phase
transition, which involves the ferromagnetic, spiral, and antiferromagnetic
states, for all the systems. Since the spin-spin interaction in the monolayer
metal dichlorides is influenced by the competition between the direct exchange
and the superexchange, we justify that the carrier concentration determines
which interaction should dominate.
