3.10 Multigrain simulations in generic soft/hard magnetic material

The single grain of the previous sections is, somehow, an unrealistic system but can represent isolated grains as those present in patterned media. In the case of conventional perpendicular recording thin film, the real sample will be a collection of magnetostatically and exchangely coupled grains. In previous works on composite media, the influence of other grains inside the film on a particular grain have been studied on the bases of an approach similar to the mean-field approximation [Suess 07]. In order to include the magnetostatic interaction between grains in a multigrain thin film we have modeled a system of $3 \times 3$ grains with periodic boundary conditions in X and Y. We have used the model II for the exchange interactions. The grains are supposed to be exchangely decoupled $J_{int}=0.0$. The energy barrier is calculated constraining only the hard layer of the central grain and relaxing the whole system.

Figure: (a) Coercive field, normalized to the anisotropy field ( $2 K_{Hard}/M_{Hard}$), and (b) energy barrier as a function of the interfacial exchange parameters for composite multigrain magnetic media.

(a)

(b)

Figure: Saddle point and remanence magnetization (minimum) profiles for a central grain in a multigrain film with $K_{Hard}=2\cdot 10^7 erg/m^3$, $M_{Hard}=1100 emu/cm^3$, $M_{Soft}=1270 emu/cm^3$ and $J_s/J_{\bot }=0.8$.

Fig. 3.38 shows the energy barrier and the coercivity as a function of the interfacial exchange in the film. The coercivity behavior is very similar to that of the single grain (see Fig. 3.32), but with an easy-plane anisotropy due to magnetostatics, which results in additional reduction of coercivity for small interfacial exchange. Compared with the isolated grain (see Fig. 3.33(b)), the energy barrier of the grain inside the film is drastically reduced. Furthermore, the energy barrier value decreases with increasing the interfacial exchange. The explanation to these facts can be found in the magnetization distribution shown in Figs. 3.39 and 3.40. The remanent state in the film is a wall centered at the interface and the saddle point is a wall centered in the hard grain. In the ideal case of a infinitely long wire P. Loxley [Loxley 01] derived an expression for the energy barrier:

$$E_B=4S\sqrt{AK_{Hard}}-4S\sqrt{AK_{Soft}}$$ (3.10)

where S is the area of the interface. To derive this expression the original minimum was considered to be a domain wall centered in the soft layer. If the minimum of the system corresponds to the situation when all the moments are aligned with the easy axis, the energy barrier is $E_B=4S\sqrt{AK_{Hard}}$, which coincides with the case of the domain wall mechanism of the previous section. The magnetic configurations that appear in our calculations are different from these two cases. In our case the domain wall does not fit into the soft magnetic material and, consequently, the domain wall in the minimum configuration is centered at the interface. However, Eq. (3.10) can give an insight into the physical origin of the reduced energy barrier: the shape anisotropy originated from the inclusion of the isolated grain in a film leads to the minimum different from that of the saturated state and reduces the energy barrier. Due to the dipolar origin of the anisotropy in the studied case, this reduction is less pronounced for small magnetization values as seen in Fig. 3.38. The reduction of the energy barrier with increasing exchange is due to the fact that the domain wall formation is more effective with more exchange coupling.

Figure: Effective energy plot (top left) and corresponding minima (a),(c) and saddle point (b) for a multigrain composite media with $M_{Hard}=1100 emu/cm^3$ and $M_{Soft}=1270 emu/cm^3$.

In the configurations represented in Fig. 3.40 we can see clearly how the moments configurations of other grains are affected by the central grain, due to the magnetostatic interaction. This effect is neglected in the mean-field approximation implemented in Ref. [Suess 07], which reduces the applicability of that approach. From Fig. 3.40 we can see that the final minimum, which is not equivalent to the initial one, is deeper because this form of flux closure allows more alignment with the easy axis with the cost of relatively low magnetostatic energy. The energy barrier reduction is an effect not desirable in magnetic recording. Possible solutions are a soft material with non-zero perpendicular anisotropy or a small saturation magnetization value. These solutions will affect the coercivity reduction of the bilayer.

Figure: Figure of merit $2 E_B /[H_c\Sigma _i M_s^iV_i]$ as a function of the interfacial exchange parameters for composite magnetic media in the case of: (a) individual magnetic grain and (b) multigrain magnetic media.

(a)

(b)