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The basic idea proposed herein refers to the establishment of a negative refractive index by exploiting natural media with either a negative permeability or a negative permittivity. For this purpose magnetized ferrites or multiferroics are utilized in conjunction with periodic resonant electric dipoles. Likewise, magnetized cryogenic-solid state plasmas could be used with a periodic array of resonant magnetic dipoles such as split-rings. Intuitively it is expected that these natural media should be operating at their surface or leaky wave modes (possibly magnetostatic modes) and losses should be taken into account in order to preserve negative permeability (or permittivity) within a thin air sheet above their surface. These challenging questions will be addressed herein employing an eigenanalysis.