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We have investigated the low-temperature magnetism of sodium superoxide(NaO$_{2}$), in which spin, orbital, and lattice degrees of freedom are closelyentangled. The magnetic susceptibility shows anomalies at $T_{1}=220$ K and$T_{2}=190$ K, which correspond well to the structural phase transitiontemperatures, and a sudden decrease below $T_{3}=34$ K. At 4.2 K, themagnetization shows a clear stepwise anomaly around 30 T with a largehysteresis. In addition, the muon spin relaxation experiments indicate nomagnetic phase transition down to $T=0.3$ K. The inelastic neutron scatteringspectrum exhibits magnetic excitation with a finite energy gap. These resultsconfirm that the ground state of NaO$_{2}$ is a spin-singlet state. Tounderstand this ground state in NaO$_{2}$, we performed Raman scatteringexperiments. All the Raman-active libration modes expected for the marcasitephase below $T_{2}$ are observed. Furthermore, we find that several new peaksappear below $T_{3}$. This directly evidences the low crystal symmetry, namely,the presence of the phase transition at $T_{3}$. We conclude the singlet-groundstate of NaO$_{2}$ due to the spin-Peierls instability.

Spin-gap formation due to spin-Peierls instability in $\pi$-orbital-ordered NaO$_2$