Magnetization reversal in nucleation controlled magnets. I. Theory

A statistical model, based upon earlier models of Brown [J. Appl. Phys. 33, 3022 (1962)] and McIntyre [J. Phys. D 3, 1430 (1970)] has been developed to examine the magnetization reversal of domain-wall nucleation controlled permanent magnets such as sintered Fe-Nd-B and SmCo5. Using a Poisson distribution of the defects on the surface of the grains, a "weakest link statistics" type model has been developed. The model has been used to calculate hysteresis loops for sintered Fe-Nd-B-type polycrystalline magnets. It is shown that the intrinsic coercivity measured for a bulk magnet should vary inversely as the logarithm of the surface area of the grain. The effect of demagnetizing field has been incorporated by a mean-field-type approximation, to calculate the overall nucleation field from the intrinsic coercivity. The hysteresis loops theoretically calculated are in excellent agreement with the overall form of those experimentally determined for similar nucleation controlled magnets. The model also predicts that for an inhomogeneous grain size distribution, such as a bimodal distribution, kinks will be observed in the second quadrant of the hysteresis loops.