We have made systematic nuclear magnetic resonance measurements for ${}^3\mathrm{He}$ fluid formed in ${}^4\mathrm{He}$-coated nanochannels including the quantum-mechanically one-dimensional (1D) region, which is a possible candidate for a different type of Tomonaga-Luttinger (TL) liquid. Corresponding to the previous heat capacity measurements, a dimensional crossover into the 1D state at low temperatures was observed by the susceptibility. In the 1D region, increases of the spin-spin relaxation time inversely proportional to temperature were found, which is apparently similar to $T$-linear electron spin resonance linewidths for 1D spin chains. While the relevance for TL liquids is still controversial since the behavior is observed in both degenerate and nondegenerate fluids, increases of the spin-spin relaxation time were confirmed to be observed only when 1D conditions for ${}^3\mathrm{He}$ fluid are satisfied, indicating that it is a characteristic property of the 1D ${}^3\mathrm{He}$ fluid.

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• 1-dimensional systems
• Helium-3 superfluids
• Mixtures of 3He & 4He
• Nuclear magnetic resonance