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, observations are highly diverse: transition can be by either electrons or holes both depending on specific materials. Moreover, doped carriers seem to always favor ferromagnetic (FM) ground state. The mechanism behind those diverse remains uncovered. Combining first-principles simulations, we analyze spin superexchange paths of correlated d/f orbitals around band edges and assign 2D into three types their projected density states (PDOS). We find that each type PDOS corresponds a carrier-driven phase critical doping quantitatively obtained calculating coupling strength. model results good agreements with calculations available measurements. After understanding mechanism, design heterostructures realize FM antiferromagnetic transition, which not before. This is helpful understand measurements expand degrees freedom control semiconductors.