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We report a systematic first-principles study on the recent discoveredsuperconducting Ba$_{1-x}$K$_x$Fe$_2$As$_2$ systems ($x$ = 0.00, 0.25, 0.50,0.75, and 1.00). Previous theoretical studies strongly overestimated themagnetic moment on Fe of the parent compound BaFe$_2$As$_2$. Using a negativeon-site energy $U$, we obtain a magnetic moment 0.83 $\mu_B$ per Fe, whichagrees well with the experimental value (0.87 $\mu_B$). K doping tends toincrease the density of states at fermi level. The magnetic instability isenhanced with light doping, and is then weaken by increasing the doping level.The energetics for the different K doping sites are also discussed.

A first principles study on the electronic and magnetic properties of Ba$_{1-x}$K$_x$Fe$_2$As$_2$