Spin-Dependent Weakly-Interacting-Massive-Particle--Nucleon Cross Section Limits from First Data of PandaX-II Experiment

New constraints are presented on the spin-dependent WIMP-nucleon interaction from the PandaX-II experiment, using a data set corresponding to a total exposure of 3.3$\times10^4$ kg-days. Assuming a standard axial-vector spin-dependent WIMP interaction with $^{129}$Xe and $^{131}$Xe nuclei, the most stringent upper limits on WIMP-neutron cross sections for WIMPs with masses above 10 GeV/c$^{2}$ are set in all dark matter direct detection experiments. The minimum upper limit of $4.1\times 10^{-41}$ cm$^2$ at 90\% confidence level is obtained for a WIMP mass of 40 GeV/c$^{2}$. This represents more than a factor of two improvement on the best available limits at this and higher masses. These improved cross-section limits provide more stringent constraints on the effective WIMP-proton and WIMP-neutron couplings.