We report a new peculiar effect of the interaction between a sublattice of frustrated quantum spin-1/2 chains and a sublattice of pseudospin-1/2 centers (quantum electric dipoles) uniquely co-existing in the complex oxide Li2ZrCuO4. 7Li nuclear magnetic-, Cu2+ electron spin resonance and a complex dielectric constant data reveal that the sublattice of Li+-derived electric dipoles orders glass like at Tg ~ 70 K yielding a spin site nonequivalency in the CuO2 chains. We suggest that such a remarkable interplay between electrical and spin degrees of freedom might strongly influence the properties of the spiral spin state in Li2ZrCuO4 that is close to a quantum ferromagnetic critical point. In particular that strong quantum fluctuations and/or the glassy behavior of electric dipoles might renormalize the exchange integrals affecting this way the pitch angle of the spiral as well as be responsible for the missing multiferroicity present in other helicoidal magnets.
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