Identifying the mechanism of hard magnet coercivity by its angular dependence

We completed the analytical framework of determining the angular dependence of coercivity for exchange-coupled phases connected with sharp interfaces in one-dimensional micromagnetics. For various thicknesses of soft phase in a hard matrix, the two types of angular dependence of coercivity, with or without a local minimum, were demarcated and illustrated as a phase diagram. The appearance or absence of a local minimum was confirmed as a sign of whether the switching was dominated by the spin rotation or by the depinning of the domain wall. The mechanism could transform from the former to the latter if the coupling ratio between soft and hard phases, epsilon(AM) = A(s)M(s)/A(h)M(h), was increased. The results explained the transformation of angular dependence curves reported in Nd-Fe-B-based permanent magnets.

Automated summary

We have completed the analytical framework for determining the angular dependence of coercivity in exchange-coupled phases with sharp interfaces. A phase diagram was used to illustrate the two types of angular dependence, with or without a local minimum, for different thicknesses of the soft phase in a hard matrix. The presence or absence of a local minimum was confirmed to indicate whether the switching was dominated by spin rotation or by domain wall depinning. The mechanism could transform from the former to the latter if the coupling ratio between the soft and hard phases increased. These findings explain the transformation of angular dependence curves in Nd-Fe-B-based permanent magnets.