  Recent advances in electrostatic gating provide a novel way to modify the
carrier concentration in materials via electrostatic means instead of chemical
doping, thus minimizing the impurity scattering. Here, we use first-principles
Density Functional Theory combined with a tight-binding approach to compare and
contrast the effects of electrostatic gating and Co chemical doping on the
ferromagnetic transition of FeS$_2$, a transition metal disulfide with the
pyrite structure. Using tight-binding parameters obtained from
maximally-localized Wannier functions, we calculate the magnetic susceptibility
across a wide doping range. We find that electrostatic gating requires a higher
electron concentration than the equivalent in Co doping to induce
ferromagnetism via a Stoner-like mechanism. We attribute this behavior to the
formation of a narrow Co band near the bottom of the conduction band under
chemical doping, which is absent in the electrostatic gating case. Our results
reveal that the effects of electrostatic gating go beyond a simple rigid band
shift, and highlight the importance of the changes in the crystal structure
promoted by gating.
