Perturbation-induced Magnetic Phase Transition in Bilayer Phosphorene

In the present paper, we theoretically study the impacts of “dilute” charged impurity, perpendicular electric field, and the Zeeman magnetic field on the magnetic phase of Bernal bilayer phosphorene (BLP) along both armchair (AC) and zigzag (ZZ) directions. In so doing, we use the tight-binding Hamiltonian model, the Born approximation, and the Green's function approach. Overall, originating from the inherent anisotropic property of phosphorene, we found that the value of susceptibility along the ZZ direction is larger than the AC direction. Also, dilute charged impurity infected BLP suffers from an antiferromagnetic–paramagnetic–ferromagnetic magnetic phase transition depending on the impurity concentration, whereas the susceptibility increases with impurity scattering potential and converges at strong enough potentials. In addition, our results show that applying a perpendicular electric field leads to an antiferromagnetic–paramagnetic–ferromagnetic transition as well. On the other hand, it is observed that the susceptibility fluctuates around a critical Zeeman magnetic field. These findings provide basic information for future experimental researches and spintronic applications of impurity-infected BLP in the presence of electric and magnetic fields.