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Terahertz spintronics is an emerging field that bridges the boundary between magnetism and photonics, which make the magnetic material suitable for photonic applications. In this article, terahertz spin-wave resonances are used to investigate the effective permeability of left-handed behavior in an array of cobalt nanomagnetic vortices. The ultrafast magnetization and the toroidal moment of the cobalt nanomagnetic vortices play a major role in reducing losses in the left-handed metamaterial. The ultrafast magnetization dynamics of an array of cobalt nanomagnetic vortices are studied both analytically and numerically, and the results are used to study the variation of permeability as a function of frequency in the terahertz range. [ABSTRACT FROM AUTHOR]