We present the first constraints on the spin-dependent, inelastic scattering cross section of weakly interacting massive particles (WIMPs) on nucleons from XENON100 data with an exposure of 7.64 x 10(3) kg . days. XENON100 is a dual-phase xenon time projection chamber with 62 kg of active mass, operated at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy and designed to search for nuclear recoils from WIMP-nucleus interactions. Here we explore inelastic scattering, where a transition to a low-lying excited nuclear state of Xe-129 is induced. The experimental signature is a nuclear recoil observed together with the prompt deexcitation photon. We see no evidence for such inelastic WIMP-Xe-129 interactions. A profile likelihood analysis allows us to set a 90% C.L. upper limit on the inelastic, spin-dependent WIMP-nucleon cross section of 3.3 x 10(-38) cm(2) at 100 GeV/c(2). This is the most constraining result to date, and sets the pathway for an analysis of this interaction channel in upcoming, larger dual-phase xenon detectors.
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