A hybrid model to calculate the magnetization of nanostructured permanent magnetic materials

We present our simulated initial magnetization curves for nanostructured permanent magnets based on a simple hybrid model. The model assumes that the reversible change in the magnetization curves obeys the Stoner–Wohlfarth (SW) model while the irreversible part can be attributed to the motion of the transition region (TR), which is a domain-wall-like magnetic moment distribution formed in the grain boundary due to exchange interaction between neighboring grains with different easy axis orientations. The calculated full hysteresis coercivity Hcm (=0.14HK) is in reasonable agreement with available experimental data, where HK is the anisotropy field. Both the calculated remanence Mr and coercivity Hc increase rapidly with the maximum applied field Hm at lower field (Hm<Hcm) but exhibit gradual saturation at higher field. These results are consistent with the so-called nucleation type material. We demonstrate that this simple model, although neglects the long range magnetostatic interaction, can provide a realistic description of the magnetization and demagnetization processes in nanostructured permanent magnets by comparing our calculations with the experimental data for various forms of rapidly solidified Nd–Fe–B permanent magnets. The calculated M–H, Mr–Hm and Hc–Hm curves show excellent agreement with the experimental data of hot pressed and die upset Nd–Fe–B magnets, where Mr and Hc are the remanence and coercivity, respectively.