We present experimental constraints on the spin-dependent WIMP-nucleon elastic cross sections from the total 129.5 kg-year exposure acquired by the Large Underground Xenon experiment (LUX), operating at the Sanford Underground Research Facility in Lead, South Dakota (USA). A profile likelihood ratio analysis allows 90% CL upper limits to be set on the WIMP-neutron (WIMP-proton) cross section of $sigma_n$ = 1.6$times 10^{-41}$ cm$^{2}$ ($sigma_p$ = 5$times 10^{-40}$ cm$^{2}$) at 35 GeV$c^{-2}$, almost a sixfold improvement over the previous LUX spin-dependent results. The spin-dependent WIMP-neutron limit is the most sensitive constraint to date.
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