Data taken by CRESST in 2000 with a cryogenic detector system based on 262 g sapphire crystals is used to place limits on WIMP dark matter in the Galactic Halo. The detector is especially sensitive for low-mass WIMPS with spin-dependent cross sections and improves on existing limits in this region. CRESST is now preparing for a second phase, which will use a 10 kg detector consisting of 300 g CaWO4 crystals with simultaneous detection of phonons and scintillation light to reduce background.
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