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True magnetic-annealing effects, i. e., hysteresis loops with high remanence and rectangularity, with no increase in coercive force, can be induced in flat ring samples of bulk .015 cm thick polycrystalline Supermalloy at low temperatures by a new electron-radiomagnetic treatment. This treatment is possible because radiation produces vacancies in excess of the thermal equilibrium number, and this excess of vacancies accelerates diffusion of atoms, thereby permitting alignment of like-atom pairs by the applied magnetic field. This process is the only irradiation treatment for achieving true magnetic annealing effects in soft magnetic materials. Magnetic-field neutron irradiation induces rectangularity but at the expense of higher coercive force, due to the fact that in addition to excess vacancy production, neutrons produce additional and more complex defects. Other advantages of the magnetic-field electron-irradiation treatment over other processes for inducing rectangularity include shorter processing time and no induced radioactivity.