Mn_5Ge_3C_x films with x>0.5 were experimentally shown to exhibit a strongly enhanced Curie temperature T_C compared to Mn_5Ge_3. In this letter we present the results of our first principles calculations within Greens function approach, focusing on the effect of carbon doping on the electronic and magnetic properties of the Mn_5Ge_3. The calculated exchange coupling constants revealed an enhancement of the ferromagnetic Mn-Mn interactions mediated by carbon. The essentially increased T_C in Mn_5Ge_3C is well reproduced in our Monte Carlo simulations and together with the decrease of the total magnetisation is found to be predominantly of an electronic nature.
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