We have studied the influence of the Mn content on the elastic properties of Fe-Mn random alloys (space group of Fm3m) using ab initio calculations. The magnetic effects in Fe-Mn alloys have a strong influence on the elastic properties, even above the Neel temperature. As the Mn content is increased from 5 to 40 at. %, the C_(44) elastic constant is unaffected, while C_(11) and C_(12) decrease. This behavior can be understood based on the magnetovolume effect which softens the lattice. Since the amplitude of local magnetic moments is less sensitive to volume conserving distortions, the softening is not present during shearing.
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