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We report a detailed study of the specific heat and magnetic susceptibilityof single crystals of a spin liquid candidate: the hyper-honeycomb Cu oxalateframework compound [(C$_2$H$_5$)$_3$NH]$_2$Cu$_2$(C$_2$O$_4$)$_3$. The specificheat shows no anomaly associated with a magnetic transition at low temperaturesdown to $T\sim$ 180 mK in zero magnetic field. We observe a large linear-in-$T$contribution to the specific heat $\gamma T$, $\gamma = 98(1)$ mK/mol K$^{2}$,at low temperatures, indicative of the presence of fermionic excitationsdespite the Mott insulating state. The low-$T$ specific heat is stronglysuppressed by applied magnetic fields $H$, which induce an energy gap, $\Delta(H)$, in the spin-excitation spectrum. We use the four-component relativisticdensity-functional theory (DFT) to calculate the magnetic interactions,including the Dzyaloshinskii-Moriya antisymmetric exchange, which causes aneffective staggered field acting on one copper sublattice. The magnitude andfield dependence of the field-induced gap, $\Delta (H) \propto H^{2/3}$, areaccurately predicted by the soliton mass calculated from the sine-Gordon modelof weakly coupled antiferromagnetic Heisenberg chains with all parametersdetermined by our DFT calculations. Thus our experiment and calculations areentirely consistent with a model of[(C$_2$H$_5$)$_3$NH]$_2$Cu$_2$(C$_2$O$_4$)$_3$ in which anisotropic magneticexchange interactions due to Jahn-Teller distortion cause one copper sublatticeto dimerize, leaving a second sublattice of weakly coupled antiferromagneticchains. We also show that this model quantitatively accounts for the measuredtemperature-dependent magnetic susceptibility. Thus[(C$_2$H$_5$)$_3$NH]$_2$Cu$_2$(C$_2$O$_4$)$_3$ is a canonical example of aone-dimensional spin-1/2 Heisenberg antiferromagnet and not aresonating-valence-bond quantum spin liquid, as previously proposed.

Gapless spinons and a field-induced soliton gap in the hyper-honeycomb  Cu oxalate framework compound  [(C$_{2}$H$_{5}$)$_{3}$NH]$_{2}$Cu$_{2}$(C$_{2}$O$_{4}$)$_{3}$