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To understand the magnetic properties of Fe$_3$GeTe$_2$, we performed thedetailed first-principles study. Contrary to the conventional wisdom, it isunambiguously shown that Fe$_3$GeTe$_2$ is not ferromagnetic butantiferromagnetic carrying zero net moment in its stoichiometric phase. Fedefect and hole doping are the keys to make this material ferromagnetic, whichare shown by the magnetic force response as well as the total energycalculation with the explicit Fe defects and the varied system charges.Further, we found that the electron doping also induces the antiferro- toferromagnetic transition. It is a crucial factor to understand the notablerecent experiment of gate-controlled ferromagnetism. Our results not onlyunveil the origin of ferromagnetism of this material but also show how it canbe manipulated with defect and doping.

On the origin and the manipulation of ferromagnetism in Fe$_3$GeTe$_2$: defects and dopings