5.3.4 Domain Wall Model

Figure: Sequence of non-equilibrium magnetization configurations calculated in the domain wall model for the external field applied at $\theta =11.25^o$ corresponding to the first jump of the hysteresis loop.

Our second model, which will be referred as ``domain wall model'', consists of a $4 \mu m \times 4 \mu m$ system with a centered array of $4 \times 4$ antidots of diameters $D = 480 nm$, separated by $\lambda = 480 nm$. In order to implement a more realistic approach to the experimental situation, we artificially introduced a domain wall outside the antidots region allowing to analyze the influence on the antidots magnetization reversal of the lower field reversal of the perimetral region. To introduce the domain wall, the anisotropy constant was set to be zero in two regions of size $240 nm$ parallel and next to two of the simulated square sides (like a half frame). This domain wall exists already at the remanence and subsequent negative field values. This is a realistic assumption since the reversal field of the external region in experiment is several times inferior to that of the antidot-induced demagnetization processes. The remanence magnetization configuration in the interantidot region is similar to the obtained in the periodic model and the $\cos \theta$ dependence of the normalized remanence is also obtained. As experimentally, we observe two jumps except in the hard and easy axes configuration (see Fig. 5.20(a)). For a given field value the created domain wall triggers an additional domain wall that reverses all the sample as shown Fig. 5.19. As the domain wall passes by the different antidots, the magnetization changes to the intermediate easy axis direction and does not align in the field direction. The external zone has completely reversed but the antidot zone is aligned in the intermediate easy axis direction and that fact creates a domain wall in the outer region pinned at the antidot structure. After the first jump the magnetization rotates reversibly to the field direction. The process corresponding to the second jump is also an inhomogeneous process initiated in the outer line of antidots nearest to the external domain wall.

Figure 5.20: (a) Hysteresis loops and (b) angular dependence of the switching fields in the antidots arrays simulated in the domain wall model in comparison to the experimentally measured values.

(a)

(b)

Alternatively, the nucleation of the external domain wall was also implemented by assuming a triangular region, $320 nm$ wide, with null anisotropy located at one of the system corners. Only one jump in the magnetization was obtained for all the angles using that implementation. Regarding the angle dependence of the field values for the jumps appearing in the magnetization, the simulation with the ``half frame'' model and the experimental values are in very good agreement both in quality and in magnitude (see Fig. 5.20 (b)) indicating that the reversal in the antidot regions involves a domain wall created by the reversal of the external zone. The occurrence of only one jump when the domain wall is created at the corner is due to the fact that the event there is triggered for field values larger than the ones necessary to observe the second jump. In these simulations the nucleation in the antidot region, equivalent to that of the periodic model (see Fig. 5.18), is also absent, presumably because the simulation size in this case is different to the simulated in Section 5.3.3.

In the examined cases the antidot demagnetization process is not determined by the antidot itself but by the defects and nucleation sites in the non-lithographed area. The existing possibilities for a nucleation-propagation-pinning sequence are multiple and may be influenced by the presence of defects of different types whose nature is determined by the deposition or lithography techniques. This is a non desirable effect since we can not control the presence of the defects and the aim of the antidots was to externally control the coercivity of the film. On the other hand, we have seen that even in this case, due to the presence of the antidots, the coercivity of the film is enhanced.