CrI₃ monolayer: magnetic and electronic behaviors under biaxial strain and external electric field—a first principle study

Abstract

We have studied the magnetic and electronic behaviors of CrI₃ monolayer under biaxial strain and external electric field using first principle calculation. A magnetic phase transition from ferromagnetic to antiferromagnetic state has been observed under a compressing strain of − 6%. The observed influence of biaxial strain on magnetic anisotropy energy is also surprising. Under zero strain it is as high as 0.74 meV/Cr and increases rapidly with compressing strain reaching a value of 1.53 meV/Cr under a compressing strain of − 6%. Moreover, we observe a switching of magnetic easy axis from off-plane to in-plane direction under a tensile strain of 9%. In addition, the bandgap for spin-up (${E}_{\mathrm{g}}^{\mathrm{up}})$ from − 10% compressing strain to 10% tensile strain at first increases slowly and exhibits a maximum (~ 0.60 eV) for zero strain. Then it gradually reduces to ~ 0.42 eV for 10% tensile strain. However, the bandgap for spin-down (${E}_{\mathrm{g}}^{\mathrm{down}})$ increases monotonically within the entire range and reaches maximum (~ 2.02 eV) for 10% tensile strain. On the other hand, external electric field applied along the off-plane direction (i.e., along c direction) induces significant variations in electronic as well as magnetic (especially MAE) behaviors of CrI₃ monolayer.

Graphical abstract