7.4.1 Attractive and Repulsive Pinning

We have studied the influence of the material parameters by varying the anisotropy constant $K_1$ of the precipitation between $0.4 \mathrm{MJ/m}^3$ (to mimic almost isolated cells or a close to paramagnetic - Cu rich - intercellular phase, $A$ and $J_\mathrm{s}$ have also been reduced) and the value for the cells. The demagnetization curves in Fig. 7.14 have been obtained for cells with $e=50 \mathrm{nm}$ and $\beta=60^\circ$, which gives $D \approx 125 \mathrm{nm}$, and $t=5 \mathrm{nm}$. For very low values of the anisotropy constant we find a very strong pinning effect (horizontal plateau in the demagnetization curve in Fig. 7.14). As $K_1$ approaches the value for the cells (2:17 phase) the pinning effect disappears.

Figure 7.14: Demagnetization curves for reduced magnetocrystalline anisotropy $K_1$ of the cell boundary phase (values in the legend in MJ/m$^3$) - attractive pinning.

If the magnetocrystalline anisotropy of the intercellular phase is larger than that of the cells, the second possible pinning mechanism is found: ``repulsive pinning''.

The demagnetization curves for repulsive pinning and different values of the anisotropy constant of the intercellular phase are shown in Fig. 7.15. For only slightly enhanced values of the anisotropy constant $K_1$ we find no pinning, but for $\Delta K_1 \ge 4.0 \mathrm{MJ/m}^3$ the pinning field reaches $1.5 \mathrm{kA/m}$. In this regime the pinning field is directly proportional to $\Delta K_1$. The results for attractive and repulsive pinning are summarized in Fig. 7.16. In addition it shows a comparison with the analytical model mentioned in Sec. 7.3.1. Obviously, the pinning fields are smaller than those expected from the analytical model. This effect has to be ascribed to the influence of thickness of the intercellular phase and the cell structure as described in Sec. 7.3.

Figure 7.15: Demagnetization curves for enhanced magnetocrystalline anisotropy $K_1$ of the cell boundary phase (values in the legend in MJ/m$^3$) - repulsive pinning.

Figure 7.16: Pinning field vs. difference in anisotropy constant between the cells and the cell boundary phase in a 3D model of the rhomboidal SmCo microstructure and comparison with the analytical 1D model of Kronmüller, Goll [91].