  Electrical control of magnetism has great potential for low-power spintronics
applications and the newly discovered two-dimensional van-der-Waals magnetic
materials are promising systems for this type of applications. In fact, it has
been recently shown experimentally that upon electrostatic doping by electrons
bilayer CrI3 undergoes an antiferromagnetic-ferromagnetic (AFM-FM) phase
transition, even in the absence of magnetic field. Doping by holes, on the
other hand, does not induce the same transition in the experiment, which points
to an intrinsic asymmetry in the hole and electron doping that limits the
control of the transition by doping. We here show, based on first-principles
calculations, that the asymmetry originates in the relativistic nature of the
valence-band-edge states of the pristine bilayer, which inhibits the magnetic
transition upon hole doping. Based on this finding, we propose an approach to
engineer this system so that it displays the AFM-FM transition for both hole
and electron doping by using moderate uniaxial strain along the soft direction
of the bilayer.
