We report the results of magnetic susceptibility $\chi$ and ${}^1\mathrm{H}$ nuclear magnetic resonance (NMR) measurements on a three-dimensional hyperhoneycomb lattice compound $\left[\right({\mathrm{C}}_2{\mathrm{H}}_5{)}_3\mathrm{NH}{]}_2{\mathrm{Cu}}_2{\left({\mathrm{C}}_2{\mathrm{O}}_4\right)}_3$ (CCCO). The average value of the antiferromagnetic (AFM) exchange coupling between the ${\mathrm{Cu}}^{2+}$ $(S=1/2)$ spins was determined to be $J\sim 50$ K from the $\chi$ measurements. No long-range magnetic ordering has been observed down to $T=50$ mK, although NMR lines become slightly broader at low temperatures below 1 K. The broadening of the NMR spectrum observed below 1 K reveals that the Cu spin moments remain at this temperature, suggesting a non-spin-singlet ground state. The temperature and magnetic field dependence of $1/T_1$ at temperatures above 20 K is well explained by paramagnetic thermal spin fluctuations where the fluctuation frequency of ${\mathrm{Cu}}^{2+}$ spins is higher than the NMR frequency of the order of megahertz. However, a clear signature of the slowing down of the ${\mathrm{Cu}}^{2+}$ spin fluctuations was observed at low temperatures where $1/T_1$ shows a thermally activated behavior. The magnetic field dependence of the magnitude of the spin excitation gap suggests that the magnetic behaviors of CCCO are characterized as an AFM chain at low temperatures.

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• Frustrated magnetism
• Quantum spin liquid
• Spin dynamics
• 1-dimensional systems
• 3-dimensional systems
• Nuclear magnetic resonance