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The stacking fault energy plays a significant role in defining the type of plasticity mechanism which prevails in high-Mn steels. Therefore, a detailed understanding and control over the physical mechanisms that influence the stacking fault energies is crucial for effective design and optimization of such steels. We present results of a first principle study on the influence of the chemical and magnetic ordering on the composition dependence of stacking fault energies in austenitic Fe_1-xMn_x alloys, which are prototypes for high-Mn steels. Our calculations show that chemical ordering has a significant influence on the intrinsic stacking faults. We have further demonstrated that, although FeMn-alloys have zero net magnetization, the internal magnetic structure significantly changes the properties of the stacking faults. Specifically, we have shown for chemically disordered structures that the dependence of the equilibrium volume and of the SFE on their composition is strongly changed if they are under paramagnetic instead of non-magnetic exposure. These results prove the importance of atomistic simulations for the determination of the SFE and clearly indicate that the magnetic interactions and the chemical ordering in this system must be accurately captured by the theory.