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The magnetic structures of iron nitrides are studied by Landau's theory of second-order phase transitions. It is found that the magnetization direction of ɛ-FeN must be parallel to the c-axis of the hexagonal structure, which may conclude the debates on the easy axes of ɛ-FeN in this field. The easy axes of α-FeN are turned out to be along [001], or [100], or [110] direction, with the former two cases already found by the experiments. The magnetization along [111] is forbidden, which solves rigorously the puzzle why the easy axes of the α-FeN on InGaAs and Fe are different from each other. Finally, the magnetic structure of γ′-FeN is also determined, and the result shows that there are three possibilities for the magnetization: parallel to the axial, or the body diagonal, or the face diagonal direction of the cubic structure, among which the first case has been found in experiments.


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