7.3.2 Pinning on an Intercellular Phase

Then the influence of the thickness $t$ of an intercellular phase (a coherent precipitation) on coercivity has been investigated using a finite element micromagnetic model with static energy minimization. As compared to the simple planar interface, we now have three regions (cf. Fig. 7.6). The outer regions (indicated with ``I'') represent the cells, whereas the center region (indicated with ``II'') represents the intercellular phase. In Sm(Co,Fe,Cu,Zr)$_z$ precipitation hardened magnets, the SmCo 2:17 cells are separated by a thin SmCo 1:5 intercellular phase. Depending on the Cu content of this cell boundary phase, its domain wall energy might be lower (high Cu content) or higher (low Cu content) than that of the cells giving rise to ``attractive'' or ``repulsive pinning'', respectively.

Figure 7.6: Model geometry for domain wall pinning on an intercellular phase with parallel anisotropy axes. The chain of arrows indicates the magnetization distribution of a pinned domain wall.

In the former case, the domain wall prefers to stay in the intercellular phase, where it has a lower energy. However, its thickness has to be large enough so that the wall ``fits in'' [95]. Fig. 7.7 shows the dependence of the pinning field on the thickness of the intercellular phase in comparison with the ideal case of an intercellular phase of infinite thickness (where it reduces to ``pinning on a planar interface''). Analogously, the intercellular phase has to be thick enough to provide an energy barrier in the case of repulsive pinning. The results are also shown in Fig. 7.7, where the axes have been scaled to the exchange length of the intercellular phase and the field to the pinning field for infinite thickness of the precipitation (which is 2200 kA/m in Sm(Co,Fe,Cu,Zr)$_z$ [91]). As a result, the thickness of the intercellular phase has to be at least three times the exchange length. This corresponds to the domain wall width (which is usually defined as $\pi \cdot l_\mathrm{ex}$). For thinner precipitations the domain wall can either ``tunnel'' through the intercellular phase (repulsive pinning) or it does not fit into it (attractive pinning). Fig. 7.7 clearly emphasizes the similarity in behavior between attractive and repulsive pinning, which has not been covered in [95]. A misalignment of the anisotropy axes with respect to the interfaces up to $40^\circ$ has not shown any major influence on the pinning fields, provided the external field is applied parallel to the anisotropy axes. Such canted anisotropy axes give rise to magnetic charges at the interface, which generate a magnetostatic field. However, it is too small as compared to the anisotropy field to have any significant impact on the pinning field.

Figure 7.7: Pinning field for attractive and repulsive pinning as a function of the thickness $t$ of the intercellular phase. The thickness is given in units of the exchange length of the intercellular phase. The pinning field is given in units of the pinning field for infinite $t$.