Recently a big number of works devoted to search for new hydrides with record high-temperature superconductivity and at the same time the successful synthesis of potential high-TC superconducting FeH5 was reported. We present a systematic search for stable compounds in the Fe-H system using variable-composition version of the evolutionary algorithm USPEX. All known (FeH, FeH3, FeH5) and several new Fe3H5, Fe3H13 and FeH6 iron hydrides were found to be stable, resulting in a very complex phase diagram with rich structural relationships between phases. We calculate electronic properties of two potentially high-TC FeH5 and FeH6 phases in the pressure range from 150 to 300 GPa. Indeed, hydrogen-rich FeH5 and FeH6 phases were found to be superconducting within Bardeen-Cooper-Schrieffer theory, with TC values of up to 46 K.
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