5.2.2 Previous simulations

Figure: Calculated coercive force dependence on the interantidot distance $ \lambda $, for $ D = 80$ and $ 160 nm$ (easy, EA, and hard, HA, axis data) from the calculations in the Ph. D. thesis of J.M. Torres [Torres 05].

Trying to check the validity of the scaling law, in collaboration with J.M. Torres [Torres Bruna 05] we performed micromagnetic simulations, varying the geometrical parameters. It is this kind of problems where the utility of micromagnetic simulations is revealed, allowing to study the magnetic behavior where the experimental data are not available. Unfortunately, the sizes of the sample make impossible to reach, within the available resources, the real dimensions of the sample. A single periodicity cell was used but with periodic boundary conditions. The results obtained from that simulation showed two different types of behavior, each corresponding to a different concentration regime. For small values $ \lambda $, concentrated regime, there is a strong dependence on $ \lambda $ of the coercivity. The corresponding magnetic configuration is shown in Fig. 5.8(c), where clearly a domain structure is formed. For large values of $ \lambda $, diluted regime, the coercivity becomes independent of $ \lambda $. In this case the flux closure structures occupy a small portion of the film as in Fig. 5.8(a). A minimum of coercivity is obtained in the crossover between the two types of behavior. This corresponds to the case where the magnetic structures of closest antidots join each other (see Fig. 5.8(b)). In the simulations a similar behavior to the experimental one is observed if only small $ \lambda $ region is taken into account, but for simulated sizes much smaller than in real samples.

Figure: Magnetic moment configuration slightly before the array magnetization reversal for $ D=80 nm$ and the following parameter values: a) $ H=-0.036 T$ and $ \lambda = 280 nm$, b) $ H=-0.025 T$ and $ \lambda = 120 nm$, and c) $ H=-0.097 T$ and $ \lambda = 40 nm$ from the calculations in the Ph. D. thesis of J.M. Torres [Torres 05].

(a) (b) (c)

In real samples the demagnetization process can be determined by the nucleation of a domain wall in the exterior region, specially in the diluted regimen. In the simulations of periodic structure this domain wall was absent, but can be included using open boundary conditions in one of the in-plane directions. The influence of the external zone was analyzed using the same range sizes [Gonzalez 05]. The presence of the external domain wall reduced the coercivity but the qualitative behavior was preserved. The pinning of the domain wall by the outer antidots was also observed.