Two coercivity models, a phenomenological model developed by Givord et al. and a micromagnetic model developed by Kronmüller et al., have been used to analyze the temperature dependence of the coercive field of sintered ${\mathrm{Pr}}_{17}$${\mathrm{Fe}}_{75}$${\mathrm{B}}_8$ and ${\mathrm{Pr}}_{17}$${\mathrm{Fe}}_{53}$${\mathrm{B}}_{30}$ permanent magnets. A general comparison of these two models is made. The micromagnetic model takes into account the misalignment of grains and the anisotropy imperfections at the grain surface. From the analysis based on this model it follows that the coercivity in sintered ${\mathrm{Pr}}_{17}$${\mathrm{Fe}}_{75}$${\mathrm{B}}_8$ and ${\mathrm{Pr}}_{17}$${\mathrm{Fe}}_{53}$${\mathrm{B}}_{30}$ permanent magnets is controlled by a nucleation mechanism occurring preferentially in the grain surface where the magnetic anisotropy is reduced and the local demagnetizing field is the highest. A simple proportional relationship between the micromagnetic parameters and ${\mathit{N}}_{\mathrm{eff}}$ is found. In addition, the effect of magnetic coupling among grains can be estimated with this model. The phenomenological model takes into account the geometrical effect of nucleated domains, the effect of the disturbance of domain-wall energy, and the thermal activation. From the analysis based on this model, it follows that the expansion of reversed domains takes place preferentially in regions where the domain-wall energy is reduced and where a spikelike reversed domain is energetically favorable. It is demonstrated in the present investigation that the phenomenological model corresponds approximately to the micromagnetic model when the nucleation process dominates the magnetization reversal process and the magnetic coupling between grains is weak.

• Received 3 November 1993

DOI:https://doi.org/10.1103/PhysRevB.50.3849