Left-handed material are those that have a negative index of refraction. It means that both the permittivity and permeability of the material are both negative.
Till now, such material have been man-made, and they are called meta-material. This is because the material consists of structures made that is considerably smaller than the wavelength of interest. In this way, the EM wave does not see the material as consisting of discrete structures.
However, there is now a new report that showed for the first time that a natural material can have a negative refraction. Physicists in Germany has shown that metallic ferromagnet can exhibit such property up to the GHz range. This astounding result was published in PRL[1]. A summary of this discovery can be found at PhysicsWeb (requires free registration)
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[1] A. Pimenov et al. Phys. Rev. Lett. 98, 197401 (2007).
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