Search for inelastic WIMP-iodine scattering with COSINE-100

We report the results of a search for inelastic scattering of weakly interacting massive particles (WIMPs) off ${}^{127}$I nuclei using NaI(Tl) crystals with a data exposure of 97.7 kg$\cdot$years from the COSINE-100 experiment. The signature of inelastic WIMP-${}^{127}$I scattering is a nuclear recoil accompanied by a 57.6 keV $\gamma$-ray from the prompt deexcitation, producing a more energetic signal compared to the typical WIMP nuclear recoil signal. We found no evidence for this inelastic scattering signature and set a 90 $\mathrm{\%}$ confidence level upper limit on the WIMP-proton spin-dependent, inelastic scattering cross section of $1.2\times {10}^{-37}\mathrm{c}{\mathrm{m}}^2$ at the WIMP mass 500 $\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}{\mathrm{c}}^2$.