The Cryogenic Dark Matter Search (CDMS) is an experiment to detect weakly interacting massive particles (WIMPs), which may constitute the universe's dark matter, based on their interactions with Ge and Si nuclei. We report the results of an analysis of data from the first two runs of CDMS at the Soudan Underground Laboratory in terms of spin-dependent WIMP-nucleon interactions on 73 Ge and 29 Si. These data exclude new regions of WIMP parameter space, including regions relevant to spin-dependent interpretations of the annual modulation signal reported by the DAMA/NaI experiment. DOI: 10.1103/PhysRevD.73.011102 PACS numbers: 95.35.+d, 14.80.Ly The nature of the dark matter which dominates structure formation in our universe is one of the most pressing questions of modern cosmology [1][2][3]. A promising class of candidates is weakly interacting massive particles (WIMPs) [4], particularly the lightest neutralino in supersymmetric (SUSY) extensions to the standard model [3]. Many groups have sought to detect WIMPs directly via their elastic scattering off atomic nuclei [5].The nucleon coupling of a slow-moving Majorana neutralino (or of any WIMP in the extreme nonrelativistic limit [6]) is characterized by two terms: spin-independent (e.g. scalar) and spin-dependent (e.g. axial vector). When coherence across the nucleus is taken into account [7], these two terms behave very differently. The neutralino has similar scalar couplings to the proton and neutron [3], and nucleon contributions interfere constructively to enhance the WIMP-nucleus elastic cross section. Thus, though neutralino-nucleon cross sections for such interactions are generally orders of magnitude smaller than in the axial case [8], scalar couplings dominate direct-detection event rates in most SUSY models for experiments using heavy target nuclides.In contrast, the axial couplings of nucleons with opposing spins interfere destructively, leaving WIMP scattering amplitudes determined roughly by the unpaired nucleons (if any) in the target nucleus. Spin-dependent WIMP couplings to nuclei thus do not benefit from a significant coherent enhancement, and sensitivity to such interactions requires the use of target nuclides with unpaired neutrons or protons. Spin-dependent interactions may nonetheless dominate direct-detection event rates in spin-sensitive experiments in regions of parameter space where the scalar coupling is strongly suppressed. This can provide a lower bound on the total WIMP-nucleus elastic cross section, since spin-dependent amplitudes are more robust against fine cancellations [9]. In general, consideration of such couplings when interpreting experimental results more fully constrains WIMP parameter space and allows exploration of alternative interpretations of possible signals [10,11]. In this work we explore the implications of recent results from the Cryogenic Dark Matter Search (CDMS) * Deceased PHYSICAL REVIEW D 73, 011102(R) (2006)