On the origin of the above-room-temperature magnetism in the 2D van der Waals ferromagnet Fe$_3$GaTe$_2$

Recent advancements in 2D magnetic materials have attracted a growing interest driven by their unique properties and potential applications in spintronic devices. However, the scarcity of systems that exhibit magnetism at room-temperature has limited their practical implementation into functional devices. In this work we focus on the recently synthetised van der Waals (vdW) ferromagnet Fe$_3$GaTe$_2$, which exhibits above-room-temperature magnetism (T$_{\mathrm{c}}$ = 350-380 K) and strong perpendicular magnetic anisotropy. Through first-principles calculations, we examine the magnetic properties of Fe$_3$GaTe$_2$ and compare them with the widely known Fe$_3$GeTe$_2$ ferromagnet. Our calculations unveil the complex microscopic mechanisms governing their magnetic behaviour, emphasizing the pivotal role of the ferromagnetic in-plane exchange interactions in the stabilization of the elevated T$_{\mathrm{c}}$ in Fe$_3$GaTe$_2$. Additionally, we predict the stability, strong perpendicular anisotropy and high T$_{\mathrm{c}}$ of single-layer Fe$_3$GaTe$_2$. We also demonstrate the potential of strain engineering and electrostatic doping to modulate its magnetic exchange interactions and anisotropy. Our results incentivise the isolation of the monolayer and pave the way for the future optimization of Fe$_3$GaTe$_2$ in magnetic and spintronic nanodevices.