Interlayer magnetic interactions in $\pi/3$-twisted bilayer CrI$_3$

The interlayer magnetic interaction in bilayer CrI$_3$ plays a crucial role for its device applications. In this work, we studied the interlayer magnetic interaction in $\pi/3$-twisted bilayer CrI$_3$ using first-principles calculations. Our calculations show that the interlayer coupling can be ferromagnetic or antiferromagnetic depending crucially on lateral shift. The strongest antiferromagnetic interlayer interaction appears in the $\bar{A}A$-stacking. The magnetic force theory calculations demonstrate that such an antiferromagnetic interaction is dominanted by the $e_g$-$e_g$ channel. Particularly, the interlayer antiferromagnetic interaction is very sensitive to external pressure. This highly tunable interlayer interaction makes $\pi/3$-twisted bilayer CrI$_3$ a potential building block for magnetic field effect transistors and pressure sensors.