  The magnetic properties of two-dimensional VI3 bilayer are the focus of our
first-principles analysis, highlighting the role of trigonal crystal-field
effects and carried out in comparison with the CrI3 prototypical case, where
the effects are absent. In VI3 bilayers, the empty a1g state - consistent with
the observed trigonal distortion - is found to play a crucial role in both
stabilizing the insulating state and in determining the inter-layer magnetic
interaction. Indeed, an analysis based on maximally localized Wannier functions
allows to evaluate the interlayer exchange interactions in two different VI3
stackings (labelled AB and AB'), to interpret the results in terms of
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
AB' stacking can be switched from antiferromagnetic to ferromagnetic,
suggesting VI3 bilayer as an appealing candidate for electric-field-driven
miniaturized spintronic devices.
