Charge doping into spin minority states mediates doubling of $T_\mathrm{C}$ in ferromagnetic CrGeTe$_3$

The recent discovery of the persistence of long-range magnetic order when van der Waals layered magnets are thinned towards the monolayer limit has provided a tunable platform for the engineering of novel magnetic structures and devices. Here, we study the evolution of the electronic structure of CrGeTe$_3$ as a function of electron doping in the surface layer. From angle-resolved photoemission spectroscopy, we observe spectroscopic fingerprints that this electron doping drives a marked increase in $T_\mathrm{C}$, reaching values more than double that of the undoped material, in agreement with recent studies using electrostatic gating. Together with density functional theory calculations and Monte Carlo simulations, we show that, surprisingly, the increased $T_\mathrm{C}$ is mediated by the population of spin-minority Cr $t_{2g}$ states, forming a half-metallic 2D electron gas at the surface. We show how this promotes a novel variant of double exchange, and unlocks a significant influence of the Ge -- which was previously thought to be electronically inert in this system -- in mediating Cr-Cr exchange.