The recent WMAP data have confirmed that exotic dark matter together with the vacuum energy (cosmological constant) dominate in the flat Universe. The nature of the dark matter constituents cannot be determined till they are directly detected. Recent developments in particle physics provide a number of candidates as constituents of dark matter, called Weakly Interacting Massive Particles (WIMPs). Since these interact weakly and are of low energy they cannot excite the target and can only be detected via measuring the recoiling nucleus. For all WIMPs, including the most popular candidate, the lightest supersymmetric particle (LSP), the relevant cross sections arise out of the following mechanisms: i) The coherent mode, due to the scalar interaction. ii) The charge coherent mode, with only proton contribution, as in the recent case of secluded dark matter scenario and iii) The spin contribution arising from the axial current. In this paper we will focus on the spin contribution, which maybe important, especially for light targets.
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