Mechanism of carrier doping induced magnetic phase transitions in two-dimensional materials

Electrically tuning long-range magnetic orders has been realized in two-dimensional (2D) semiconductors via electrostatic doping. On the other hand, the observations are highly diverse: the transition can be realized by either electrons or holes or both depending on specific materials. Moreover, doped carriers seem to always favor the ferromagnetic (FM) ground state. The mechanism behind those diverse observations remains uncovered. Combining first-principles simulations, we analyze the spin superexchange paths of the correlated d/f orbitals around band edges and assign 2D magnetic semiconductors into three types by their projected density of states (PDOS). We find that each type of PDOS corresponds to a specific carrier-driven magnetic phase transition and the critical doping density and type of carriers can be quantitatively obtained by calculating the superexchange coupling strength. The model results are in good agreement with first-principles calculations and available measurements. After understanding the mechanism, we can design heterostructures to realize the FM to antiferromagnetic transition. This model is helpful to understand diverse measurements and expand the degrees of freedom to control long-range magnetic orders in 2D semiconductors.