Electric-field tuning of the magnetic properties of bilayer VI3 : A first-principles study

The magnetic properties of the two-dimensional ${\mathrm{VI}}_{3}$ bilayer are the focus of our first-principles analysis, highlighting the role of ${t}_{2g}$ orbital splitting and carried out in comparison with the ${\mathrm{CrI}}_{3}$ prototypical case, where the splitting is negligible. In ${\mathrm{VI}}_{3}$ bilayers, the empty ${a}_{1g}$ state is found to play a crucial role in both stabilizing the insulating state and in determining the interlayer magnetic interaction. Indeed, an analysis based on maximally localized Wannier functions allows one to evaluate the interlayer exchange interactions in two different ${\mathrm{VI}}_{3}$ stackings (labeled AB and ${\mathrm{AB}}^{\ensuremath{'}}$), to interpret the results in terms of the virtual-hopping mechanism, and to highlight the strongest hopping channels underlying the magnetic interlayer coupling. Upon application of electric fields perpendicular to the slab, we find that the magnetic ground state in the ${\mathrm{AB}}^{\ensuremath{'}}$ stacking can be switched from antiferromagnetic to ferromagnetic, suggesting the ${\mathrm{VI}}_{3}$ bilayer as an appealing candidate for electric-field-driven miniaturized spintronic devices.