8.4 Multiple Easy Axes

Then we have studied the influence of a distribution of easy axes within the particle. As described above, we have varied the easy axis in the six parts of our model and calculated the coercivity. The results are summarized in Tab. 8.2. The left column indicates, how many of the six parts of our model have their easy axis parallel to the $z$-, $y$-, and $x$-axes, respectively. The results show, that the coercivity is decreased by a factor of three as compared to the nucleation field. However, the different distributions of easy axes show no significant influence on the coercivity. This behavior indicates, that the 90$^\circ$ domain wall at the interface between two misaligned parts of the particle determines the coercivity. Thus, already a single misaligned part is sufficient to reduce the coercivity by a factor of three.

Table 8.2: Coercivity as a function of the easy axis distribution: The first, second, and third number of a triplet in the first column indicates in how many of the six parts of the finite element model the easy axes are parallel to the $z$-, $x$-, and $y$-axis, respectively. Obviously, the coercivity is strongly reduced as compared to the nucleation field of a particle with a single anisotropy axis. However, the mixture of anisotropy axes does not have a significant influence for a particle with 30 nm edge length.

$\uparrow:\rightarrow:\nearrow$	$H_c$ (kA/m)
5:1:0	3330
4:2:0	3140
4:1:1	3310
3:3:0	3630
3:2:1	3420
2:2:2	3430

Finally, we have reduced the size of the particles and studied their coercivity. The shape and aspect ratio remained the same, the model has just been rescaled to the desired size. The exchange length of FePt is about 1 nm (cf. Tab. 8.1) and the resulting domain wall width about 3 nm. As a result, the properties of very small particles are modified due to the increasing importance of the exchange interactions. The results of our simulations are summarized in Tab. 8.2. The coercivity of (2:2:2) particles with the ``3 easy axes''-distribution (top left figure in Fig. 8.7) remains almost constant if we reduce the edge length of the particles from 30 nm (discussed above) to 15 nm and 7.5 nm. However, for an edge length of 3.75 nm (diameter of the particle: 7 nm) the coercivity is reduced to 2100 kA/m.

Figure 8.7: Coercivity as a function of the easy axis distribution and edge length of the nanoparticle. The easy axis distribution is shown in the top left figure for the ``3 easy axes'' (where two neighboring parts of the model have the same easy axis) and on the top right for the ``6 easy axes'' (where all neighboring pairs have perpendicular easy axes) distribution, respectively.

[``3 easy axes'' model]

[``6 easy axes'' model]

The ``6 easy axes''-distribution is characterized by the fact, that each pair of neighboring parts in our model has perpendicular easy axes. For this distribution we find a further reduced coercivity of 2000 kA/m, which drops to 600 kA/m if the particle size is reduced to 3.75 nm.