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We have studied electronic and magnetic structures ofK$_{0.8+x}$Fe$_{1.6}$Se$_2$ by performing the first-principles electronicstructure calculations. The ground state of the Fe-vacancies orderedK$_{0.8}$Fe$_{1.6}$Se$_2$ is found to be a quasi-two-dimensional blockedcheckerboard antiferromagnetic (AFM) semiconductor with an energy gap of 594meV and a large ordering magnetic moment of 3.37 $\mu_B$ for each Fe atom, inexcellent agreement with the neutron scattering measurement. The underlyingmechanism is the chemical-bonding-driven tetramer lattice distortion.K$_{0.8+x}$Fe$_{1.6}$Se$_2$ with finite $x$ is a doped AFM semiconductor withlow conducting carrier concentration which is approximately proportional to theexcess potassium content, consistent qualitatively with the infraredobservation. Our study reveals the importance of the interplay betweenantiferromagnetism and superconductivity in these materials. This suggests thatK$_{0.8}$Fe$_{1.6}$Se$_2$, instead of KFe$_2$Se$_2$, should be regarded as aparent compound from which the superconductivity emerges upon electron or holedoping.

Ternary iron selenide K$_{0.8}$Fe$_{1.6}$Se$_2$ is an antiferromagnetic semiconductor