3.11 Figures of merit

In magnetic recording applications the energy barrier value has to be maximized in order to obtain large thermal stability, whereas the coercivity has to be minimized in order to be below the writing head maximum field. To compare the performance of different media R. Victora [Victora 05a] proposed a figure of merit, considering the ratio between both quantities defined by $2 E_B /[H_c\Sigma _i M_s^iV_i]$. According to the requirements, this figure of merit has to be maximized to obtain an optimum recording media. With this definition, the performance is compared with a bilayer in which both materials rotate coherently, which has the coercive field given by Eq. (3.1) and the energy barrier by Eq. (3.2). This bilayer has a figure of merit of $1$. The maximum value of this figure of merit is 4 [Lu 07]. In Fig. 3.41 we present for comparison the figure of merit for different media calculated in the previous sections in the case of an individual grain and a multigrain system (see Figs. 3.32, 3.33 and 3.38).

In the case of one-grain system, the best performance for $J_s/J_{\bot}>0.2$ corresponds to the media with high soft and hard layers magnetization mostly due to the additional shape anisotropy. The media with low magnetization hard layer and high magnetization soft layer is unfavorable for small and intermediate exchange but has the best performance for completely coupled system. As could be noticed here, the best performance in the case of multigrain systems corresponds clearly to the case of small magnetization soft and hard layers. However, this combination is benefited from the inclusion of the saturation magnetization in the denominator of the figure of merit. More than $20-40\%$ of the exchange is necessary in this case in order to maximize the figure of merit. The behavior in all the cases does not reach saturation. The difference in the best media for multigrain and one grain systems stresses the importance of performing realistic granular simulations to obtain the parameters that optimize the composite media.

Figure: Figure of merit $(E_B/K_{Hard}V) /(H_c/H_{k,Hard})$ 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)

We can also evaluate the media performance using a different figure of merit that normalize the quantity to the parameters of the hard layer: $(E_B/K_{Hard}V) /(H_c/H_{k,Hard})$ (see Fig. 3.42). Both figures of merit are equivalent for single media. This way, we compare the bilayer with a hard phase grain (with the same volume than the hard phase in the bilayer) that switches coherently. From this new point of view, the combination that obtains the largest figure of merit is $M_{Hard}=250 emu/cm^3$ and $M_{Soft}=1270 emu/cm^3$ in both multigrain and one-grain cases.

Finally, there is an intrinsic limitation in the optimization of two quantities only based on their ratio. The obtained set of parameter can optimize one of the magnitudes, while the other could have an unrealistic value. Additionally, the way the figure of merit is constructed could favor one or another material parameter combination and give different final conclusion. The two figures of merit of this section favor the combinations with small saturation magnetization in the hard layer, partially, because its presence in the denominator. Figs. 3.32, 3.33 and 3.38 represent a better picture of the media performance because they represent energy barriers and coercivity in real units. These values should be optimized to get in real units the switching fields below $1.7 T$ and energy barriers higher than $60 k_BT$.