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It is generally difficult to experimentally distinguish magnetic multipolarorders in spin systems. Recently, it was proposed that the temperaturedependence of the nuclear magnetic resonance relaxation rate 1/T_1 can involvean indirect, but clear signature of the field-induced spin nematic ormultipolar Tomonaga-Luttinger (TL) liquid phase [Phys. Rev. B79, 060406(R)(2009)]. In this paper, we evaluate accurately the field and temperaturedependence of 1/T_1 in spin-1/2 frustrated J1-J2 chains combiningfield-theoretical techniques with numerical data. Our results demonstrate thatisotherms of 1/T_1 as a function of magnetic field also exhibit distinctivenon-monotonic behavior in spin nematic TL liquid, in contrast with the standardTL liquid in the spin-1/2 Heisenberg chain. The relevance of our results toquasi one-dimensional edge-sharing cuprate magnets, such as LiCuVO4, isdiscussed.

Field and temperature dependence of the NMR relaxation rate in the magnetic quadrupolar liquid phase of spin-1/2 frustrated ferromagnetic chains