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Magnetic states of iron-based superconducting compounds calculated by using GGA$+U$ method with negative \emph{U}

The magnetic moments per Fe atom in high-$T{_\textrm{c}}$ iron-based superconducting compounds, BaFe$_{2}$As$_{2}$ and LaFeAsO obtained from the first-principles calculation with local-spin-density approximation are much larger than those obtained from experiments. To resolve the contradictory results between theory and experiment we employed the so-called LDA$+ U$ (or more exactly GGA$+ U$) technique with negative \emph{U} in the first-principles calculation. The calculated values with negative \emph{U}, $- 0.09$ Ry and $- 0.10$ Ry for BaFe$_{2}$As$_{2}$ and LaFeAsO, respectively, are in excellent agreement with the experimental ones. By comparing the differences in \emph{d}-orbital occupation numbers and spin densities calculated by using a simple GGA and GGA$+ U$ with negative $U$, the magnetic moments of the two compounds are found to be similar to the case of low-spin state of metamagnetic Fe$_{3}$Al alloy.