Using the methods of Mössbauer spectroscopy and transmission electron microscopy, it was found that short-term (for 4 s) irradiation of cold-rolled foils of the Fe–6.35 at.% Mn composition with a thickness of 25 μm with Ar+ ions (E = 15 keV) with heating to 300–450 °C causes an α → γ phase transformation with the formation of the repeatedly enriched with manganese austenite (from 23.8 to 38.0 at.%). The estimates made do not allow us to explain these processes by the phenomena of thermal and radiation-enhanced diffusion. As an explanation, the role of nanoscale dynamic effects associated with shaking the medium by powerful post-cascade solitary waves is considered. Such waves, becoming undamped in metastable media and playing, in a certain sense, the role of temperature, cause a short-term giant increase in the mobility of atoms and the transition of these media to a state with minimum free energy. The concentrations of Mn c1 and c2 in the α-and γ-phases, calculated on the basis of decoding the Mössbauer spectra for irradiation temperatures 311, 378 and 449 °C, correspond quite well to the results of extrapolation of the lines of the equilibrium phase diagram to the low temperature region.