Anisotropic RKKY interaction and modulation with mechanical strain in phosphorene

Abstract

We investigate the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between two magnetic impurities placed on a phosphorene surface based on the tight-binding model. It is found that the RKKY interaction exhibits strong anisotropy along different lattice directions and is sensitive to the deformed direction. The RKKY interaction is largest for impurities distributed in the armchair direction while the strain effect is strongest for the deformation exerted along the zigzag direction. Applied linear strain can increase the RKKY magnitude nonlinearly, and observably prolong the decay rate from the exponent to the $1/{R}^{2}$ law with the impurity distance. Most interestingly, near the strain-induced closing point of the bandgap, we find that the RKKY interaction is no longer simply ferromagnetic or antiferromagnetic, but presents oscillatory behavior, exhibiting the transition from ferromagnetism to antiferromagnetism. This originates from the combination effect of negative energy in the conduction band due to modification of the Fermi surface and the narrowing bandgap, and importantly both of them are reached simultaneously just by tuning the strain. Therefore, the strain effect proves to be an alternative approach to engineering impurity interactions in phosphorene materials.

Keywords

• phosphorene
• RKKY interaction
• impurity effect