  We report the first measurement of the atmospheric neutrino-oxygen
neutral-current quasielastic (NCQE) cross section in the gadolinium-loaded
Super-Kamiokande (SK) water Cherenkov detector. In June 2020, SK began a new
experimental phase, named SK-Gd, by loading 0.011% by mass of gadolinium into
the ultrapure water of the SK detector. The introduction of gadolinium to
ultrapure water has the effect of improving the neutron-tagging efficiency.
Using a 552.2 day data set from August 2020 to June 2022, we measure the NCQE
cross section to be 0.74 $\pm$ 0.22(stat.) $^{+0.85}_{-0.15}$ (syst.) $\times$
10$^{-38}$ cm$^{2}$/oxygen in the energy range from 160 MeV to 10 GeV, which is
consistent with the atmospheric neutrino-flux-averaged theoretical NCQE cross
section and the measurement in the SK pure-water phase within the
uncertainties. Furthermore, we compare the models of the nucleon-nucleus
interactions in water and find that the Binary Cascade model and the Liege
Intranuclear Cascade model provide a somewhat better fit to the observed data
than the Bertini Cascade model. Since the atmospheric neutrino-oxygen NCQE
reactions are one of the main backgrounds in the search for diffuse supernova
neutrino background (DSNB), these new results will contribute to future studies
- and the potential discovery - of the DSNB in SK.
