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Geometrical frustration among interacting spins combined with strong quantumfluctuations destabilize long-range magnetic order in favour of more exoticstates such as spin liquids. By following this guiding principle, a number ofspin liquid candidate systems were identified in quasi-two-dimensional(quasi-2D) systems. For 3D, however, the situation is less favourable asquantum fluctuations are reduced and competing states become more relevant.Here we report a comprehensive study of thermodynamic, magnetic and dielectricproperties on single crystalline and pressed-powder samples of PbCuTe$_2$O$_6$,a candidate material for a 3D frustrated quantum spin liquid featuring ahyperkagome lattice. Whereas the low-temperature properties of the powdersamples are consistent with the recently proposed quantum spin liquid state, aneven more exotic behaviour is revealed for the single crystals. These crystalsshow ferroelectric order at $T_{\text{FE}} \approx 1\,\text{K}$, accompanied bystrong lattice distortions, and a modified magnetic response -- stillconsistent with a quantum spin liquid -- but with clear indications for quantumcritical behaviour.

Spin liquid and ferroelectricity close to a quantum critical point in PbCuTe$_2$O$_6$