$^{23}$Na-NMR study on the one-dimensional superoxide spin-chain compound NaO$_2$

TL;DR

NaO2 is studied as a candidate one-dimensional spin-1/2 chain using $^{23}$Na-NMR across $T=0.3$–$250$ K and fields up to $16$ T. The measurements reveal a spin gap opening below $T_{\rm S3}=40$ K, with $\Delta(10.1\,\mathrm{T})\approx 38$ K and $\Delta(0\,\mathrm{T})\approx 51.2$ K inferred from susceptibility, and a dramatic drop in hyperfine coupling across the structural transition that marks a transition to a strongly one-dimensional phase. The spin-lattice relaxation rate shows thermally activated behavior below the transition and Tomonaga-Luttinger-liquid behavior with a Luttinger parameter $K\simeq 1/4$ above it, consistent with a quantum critical 1D spin chain. The results establish NaO2 as a rare π-orbital-based 1D spin chain with a spin-gapped ground state, highlighting the interplay of spin, lattice, and orbital degrees of freedom in a minimal 1D oxide.

Abstract

We report $^{23}$Na-NMR study on a candidate one-dimensional quantum spin system NaO$_2$. The Knight shift, linewidth, and spin-lattice relaxation rate $1/T_1$ were investigated down to 0.3 K under fields up to 16 T. The results reveal the opening of a spin gap of $Δ(10.1 {\rm T}) \simeq$ 38 K below $T_{\rm S3} =$ 40 K, consistent with a spin-Peierls-like instability. The hyperfine coupling constant was found to drop sharply across the structural phase transition at $T_{\rm S2} =$ 215 K, highlighting the pronounced one-dimensional character of the system. These findings establish NaO$_2$ as a rare example of a $π$-orbital-based one-dimensional spin chain that exhibits a spin-gapped ground state.

Figures (8)

• Figure 1: Typical $^{23}$Na-NMR spectra of powder sample measured at 90 K (Phase III). Dashed vertical line shows the zero-shift position $\nu_0/^{23}\gamma$, where $\nu_0$ is resonance frequency, and $^{23}\gamma = 11.262$ MHz/T the nuclear gyromagnetic ratio for $^{23}$Na. The enlarged spectrum (grey curve) highlights the singular points associated with the quadrupole splitting of the $I = 3/2$ nucleus, shown by dotted lines. From the spacing of these features, quadrupole frequency $^{23}\nu_{\rm Q} =$ 0.7 MHz and the asymmetry parameter $\eta =$0.31 were obtained.
• Figure 2: Representative recovery curves of the nuclear spin magnetization at several temperatures. The spin-lattice relaxation time $T_1$ is determined by fitting to the standard relaxation function for the central transition for $I = 3/2$ spins (solid curves)Narath.
• Figure 3: Powder $^{23}$Na-NMR spectra measured at several temperatures. The dashed vertical line marks the zero-shift position of the $^{23}$Na nucleus. Inset shows the spectra obtained at low temperatures down to 0.3 K, utilizing a $^3$He-cryostat.
• Figure 4: (Top) Temperature dependence of the magnetic susceptibility (after Ref. Miyajima_Kambe), with the low temperature Curie term subtracted. Arrows indicate the structural transition temperatures. (Bottom) Temperature dependence of the Knight shift and the linewidth (FWHM) of the $^{23}$Na-NMR spectrum at 10.1 T.
• Figure 5: Knight shift versus uniform susceptibility ($K$-$\chi$ plot) in Phases I-III. The data exhibit linear behavior, from which the isotropic hyperfine coupling constants $A$ were extracted: $A_I =$ 70(5), . $A_{\rm II} =$ 70(5), and $A_{\rm III} =$ 8(1) Oe$/\mu_{\rm B}$. Inset shows the schematic crystal structure in Phase III, where the O$_2$ molecules are aligned along $c$-axis (see text).