Fig. 4: Doping-dependent T_C increase.

a Calculated charge density (yellow surface), integrated over an energy range of 0.2 eV around the spin-minority conduction band minimum and superimposed onto the crystal structure of CrGeTe₃ and (b) corresponding top-down view of the surface layer. The lobes of the charge density around each Cr site point in between the Cr-Te bond axis, a signature of t_2g character, while the charge density around the Ge dimers is dramatically enhanced, pointing to a new conduction path involving the Ge sites. J₁, J₂, and J₃ paths are labeled with colour coded arrows. c Calculated values for J₁, J₂, and J₃, plotted as a function of doping concentration. The absolute value of J₃, in particular, shows a dramatic enhancement with doping. d T_C extracted from Monte Carlo simulations, considering different combinations of J_1,2,3, plotted alongside the experimental data. Here, J₃ is required (and has the equivalent impact of J₁ and J₂ combined) to match the shape of the experimental phase diagram. The dashed line through the experimental data points is the calculation for J₁ + J₂ + J₃ offset by 45 K, as a guide for the reader in showing the relative trends between experiment and simulation. e Schematic representation of the mechanism to enhance T_C enabled by the doped carriers in the minority-spin t_2g manifold. Hopping paths from Cr to Te include direct Cr-Te-Cr hopping (J₁), and higher-order paths (J₂) as well as effective Cr-Cr exchange pathways that are mediated via the Ge sites (i.e. J₃).