  The emergence of ferromagnetism in two-dimensional van der Waals materials
has aroused broad interest. However, the ferromagnetic instability has been a
problem remained. In this work, by using the first-principles calculations, we
identified the critical ranges of strain and doping for the bilayer Cr2Ge2Te6
within which the ferromagnetic stability can be enhanced. Beyond the critical
range, the tensile strain can induce the phase transition from the
ferromagnetic to the antiferromagnetic, and the direction of magnetic easy axis
can be converted from out-of-plane to in-plane due to the increase of
compressive strain, or electrostatic doping. We also predicted an electron
doping range, within which the ferromagnetism can be enhanced, while the
ferromagnetic stability was maintained. Moreover, we found that the compressive
strain can reverse the spin polarization of electrons at the conduction band
minimum, so that two categories of half-metal can be induced by controlling
electrostatic doping in the bilayer Cr2Ge2Te6. These results should shed a
light on achieving ferromagnetic stability for low-dimensional materials.
