Frustrated three-dimensional quantum spin liquid in CuHpCl

Inelastic neutron scattering measurements are reported for the quantum antiferromagnetic material ${\mathrm{Cu}}_2({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2{)}_2{\mathrm{Cl}}_4$ (CuHpCl). The magnetic excitation spectrum forms a band extending from 0.9 meV to 1.4 meV. The spectrum contains two modes that disperse throughout the $\mathbf{a}-\mathbf{c}$ plane of the monoclinic unit cell with less dispersion along the unique $\mathbf{b}$-axis. Simple arguments based on the measured dispersion relations and the crystal structure show that a spin-ladder model is inappropriate for describing CuHpCl. Instead, it is proposed that hydrogen bond mediated exchange interactions between the bi-nuclear molecular units yield a three-dimensional interacting spin system with a recurrent triangular motif similar to the Shastry-Sutherland Model (SSM). Model-independent analysis based on the first moment sum rule shows that at least four distinct spin pairs are strongly correlated and that two of these, including the dimer bond of the corresponding SSM, are magnetically frustrated. These results show that CuHpCl should be classified as a frustration induced three-dimensional quantum spin liquid.