  To understand newly discovered superconductivity in Fe--based systems, we
investigate electronic structure and magnetic properties of Fe$_{1+x}$Te using
first--principles density functional calculations. While the undoped FeTe has
the same Fermi surface nested at ($\pi ,\pi $) as in Fe arsenides, doping by
$\sim 0.5$ electrons reveals a novel square--type Fermi surface showing a
strong ($\pi, 0$) nesting and leading to a different magnetic structure. Our
result strongly supports the same mechanism of superconductivity in
chalcogenides as in the arsenides, reconciling theory to existing experiments.
Calculated magnetic interactions are found to be critically dependent on doping
and notably different from the arsenides.
