10 tures. It is observed, as expected, that the magnetic resonance frequency of the structures, while it scales in- versely proportional to the structure length scale in the mm scale, it saturates to a constant value in the nano regime. This behavior depends on the design and it is independent of any ohmic losses in the structure. Among our designs, higher saturation value is observed for the fishnet design. Here we will demonstrate this quantitative power of our relations in the case of the wide-slab-pair system. For wide-slab-pair systems ( w = a$_{H}$ ) and examining the fields and currents at the magnetic resonance fre- quency, one can use for the total capacitance of the sys- tem the capacitance of two identical parallel plate ca- pacitors connected in-series, each of capacitance C = ϵ$_{0}$ϵ$_{b}$ ( w/t )( l/ 2 . 5), and for the electrons inductance the same relation as in Eq. (9), multiplied by 2 (to take into account both slabs of the pair). The calculated magnetic resonance frequency obtained by using these relations is shown with the dotted-dashed line in Fig. 6, and as can be seen there it is in excel- lent agreement with the magnetic resonance frequency obtained through realistic calculations. The permeability resonance becomes weaker and weaker as we go deeper into sub- µ m scale, and ultimately it does not reach negative values. The relative spectral width of the negative permeability regime which in larger scales is almost scale independent, in sub- µ m scales it be- comes smaller and smaller, approaching zero, and it has very slight dependence on the ohmic losses, while it shows strong dependence on the design, being quite narrow for the fishnet design. All the above results are explained through a simple RLC circuit model; in the inductance, L , the current- connected kinetic energy of the electrons is taken into account besides the magnetic field energy. This model is capable to determine optimization conditions for our structures, as to attain high magnetic resonance frequen- cies maintaining strong resonant response with a negative permeability region as wide as possible. The model ex- plains also the superior performance of the fishnet design regarding high magnetic resonance frequency and its re- duced performance regarding the width of the negative permeability region. Finally, we show that our simple RLC circuit model is capable not only to predict quali- tatively the behavior of our structures, but also to give quantitative results if it is accompanied by accurate for- mulas for the capacitance and inductance of the systems. To explain this discrepancy, we should point out that as the slabs become narrower Eqs. (9) for the capaci- tance and the magnetic field inductance become less and less accurate, and in the limit of w < t they should be replaced by the corresponding expressions for par- allel wire systems, i.e. L = µ$_{0}$l ln( t/w ) /π , and C = ϵ$_{b}$ϵ$_{0}$π ( l/ 2 . 5) / ln( t/w ). The last relations for L and C lead to lower magnetic resonance frequency saturation values compared to the ones predicted by the correspond- ing Eqs. (9), in agreement with the numerical results presented in Fig. 2. Using the same equations for the case of narrow slabs, one can see that they fail to describe accurately the scal- ing of the magnetic resonance frequency. In fact these equations predict no dependence of ω$_{m}$ on the width of the slabs, unlike the observed in Fig. 2 result, which shows lower magnetic resonance frequency for the nar- rower slabs. VII. ACKNOWLEDGMENTS VI. CONCLUSIONS Authors would like to acknowledge financial support by the European Union FP7 projects PHOME, EN- SEMBLE, ECONAM, NIMNIL, and the COST Actions MP0702, MP0803, by the European Office of Aerospace Research and Development (under project FENIM), and by the US Department of Energy (contract no. DE- AC02-07-CH11358). In this paper we examine the magnetic response of res- onant magnetic structures based on the slab-pair design, as the structures are scaled down from mm to nm scale. This response is examined using detailed numerical sim- ulations for obtaining the frequency dependence of the magnetic permeability (including its resonant behavior) through reflection and tranmission data of realistic struc- 7 N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay and C. M. Soukoulis, Phys. Rev. B 70 , 201101(R) (2004). 8 E. Ozbay, Zh. Li, and K. Aydin, J. Phys.: Cond. Matt. 20 , 304216 (2008). 9 K. Aydin, Zh. Li, L. Sahin, and E. Ozbay, Opt. Expr. 16 , 8835 (2008). E. 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