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A puzzle in the iron-based superconductor LaFeAsO_{1-x}F_x is that themagnetic moment obtained by first-principle electronic structure calculationsis unexpectedly much larger than the experimentally observed one. For example,the calculated value is ~ 2.0 \mu_B in the mother compound, while it is ~ 0.3\mu_B in experiments. We find that the puzzle is solved within the frameworkLDA + U by expanding the U value into a slightly negative range. We show Udependence of the obtained magnetic moment in both the undoped x=0.0 and dopedx = 0.125. These results reveal that the magnetic moment is drastically reducedwhen entering to the slightly negative range of U. Moreover, the negative Uwell explains other measurement data, e.g., lattice constants and electronicDOS at the Fermi level. We discuss possible origins of the negative U in thesecompounds.

LDA + Negative U Solves a Puzzle of too Large Calculated Magnetic Moment in Iron-based Superconductor LaFeAsO_{1-x}F_x