  To understand the magnetic properties of Fe$_3$GeTe$_2$, we performed the
detailed first-principles study. Contrary to the conventional wisdom, it is
unambiguously shown that Fe$_3$GeTe$_2$ is not ferromagnetic but
antiferromagnetic carrying zero net moment in its stoichiometric phase. Fe
defect and hole doping are the keys to make this material ferromagnetic, which
are shown by the magnetic force response as well as the total energy
calculation with the explicit Fe defects and the varied system charges.
Further, we found that the electron doping also induces the antiferro- to
ferromagnetic transition. It is a crucial factor to understand the notable
recent experiment of gate-controlled ferromagnetism. Our results not only
unveil the origin of ferromagnetism of this material but also show how it can
be manipulated with defect and doping.
