  Two-dimensional (2D) half-metallic materials are of great interest for their
promising applications in spintronics. Although numerous of 2D half-metals have
been proposed theoretically, rarely of them can be synthesized experimentally.
Here, exemplified by monolayer FeCl2, we show three mechanisms in such quantum
magnets that would cause the metal-insulator transition by using
first-principles calculations. In particular, half-metallicity, especially that
protected by symmetry-induced degeneracies, predicted by the previous
theoretical simulations could be destroyed by electron correlation, spin-orbit
coupling and further structural distortions to lower the total energy. Our work
reveals the fragility of the symmetry-protected half-metals upon various
competing energy-lowering mechanisms, which should be taken into account for
theoretically predicting and designing quantum mateirals with exotic
functionalities.
